0.4.4 bounded implicit-contact sprint

Status: target and working evidence ledger, not a released capability or a claim of Abaqus/Standard parity. Baseline: merged PR #117, commit 683eb429. Scientific input, implementation revision, independent reference and acceptance tolerances must be recorded before a comparison is judged.

Claim boundary

Target the ordinary model.step(...) route for serial three-dimensional solids, prescribed rigid analytical or reviewed triangulated tools, finite sliding, quasistatic implicit increments, finite-strain J2, named multiple tool pairs and optional supported periodic MPC. Admit frictionless normal contact first; admit a Coulomb/geometry combination only after its own tangential-state and feature-switch tests. Comparison is on physical observables and accepted histories at equivalent stations, not bitwise equality with another solver or one cloud image.

Excluded from this claim: general self-contact, deformable--deformable implicit contact, arbitrary CAD/STEP surfaces, shell thickness/offset, distributed implicit contact, arbitrary history materials, impact and thermomechanical contact. They remain separate capability gates rather than being silently approximated by the bounded route.

Live gate status

Completed graded full-cycle path sensitivity (2026-10-26)

The graded 8-cell P2 cycle now completes with both controls. Initial increment 1/32 → 1/128 and accepted-plastic cap 0.00075 → 0.000375 change together here; the separate small-model experiment below isolates the initial increment. All recorded numerical source hashes match. The diagnostic tool/observer revisions differ and are recorded, so this is not called a frozen-tool run. Mesh, physical parameters, quadrature and solver tolerances are unchanged.

Factor	Coarse relative work/energy residual	Refined residual
0.25	0.819424%	0.019071%
0.50	0.575814%	0.014825%
0.75	0.337319%	0.008684%
1.00	0.204641%	0.006249%

Final contact force changes from 2.97514031 to 2.97852375 N (0.113724%); the largest common-station volume-mean PEEQ change is 0.015709%. Both runs retain open contact at factors 0.5/0.75 and active reference area 0.25 m² at 0.25/1.0. The refined run accepts 727 increments, rejects 15 trials, uses 2596 Newton corrections and respects its plastic cap (maximum 0.0003612952). Periodic equation mismatch stays below 3.5e-18 m at the common stations.

These are observed sensitivity results, not a retrospectively chosen accuracy certificate. They separate a large path-work error from the still-open spatial resolution question; they do not certify peak pressure or replace an external same-input reference. Setup/solve times are retained but are not speed evidence: refinement changes the numerical workload and short independent tests overlapped. Raw reports and their checked summary are evidence/contact/2026-10-26-graded-cycle-{coarse,refined}.json and evidence/contact/2026-10-26-graded-path-comparison.json.

Independent-reference handoff boundary

Use tools/diagnose_periodic_contact_order.py:make_step as the physical fixture source of truth. An external comparison must match the unit cube and interior reference patch, affine periodic equations, anchored translation, fixed plane, reference-area penalty measure and the piecewise-linear matrix path at factors 0, 0.25, 0.75 and 1. Interpolating one stretch and recomputing its lateral volume-preserving stretches between those knots would be a different path.

The finite-J2 material is multiplicative Hencky elasticity with a radial return in elastic logarithmic strain and a Kirchhoff-stress yield invariant. Its stored energy includes elastic and linear isotropic hardening energy; plastic loss is initial yield stress times accumulated plastic strain. A commercial solver's default finite-J2 model is not automatically the same constitutive law. Either match that law independently or label the comparison as a model comparison, not an implementation-error measurement. Keep reaction, contact area, smooth pressure moments, volume-weighted PEEQ and separate work/energy channels at common stations; mesh and path differences must be recorded.

Call-local observation work reduction (2026-10-26)

The design follows the separation of nonlinear residual and Jacobian callbacks in PETSc (SNESSetFunction, SNESSetJacobian). That separation is an architectural reference, not evidence of an AgentFEM speedup: the local callback must still preserve the same current force law, admission checks and ownership of trial/accepted State.

The affine Procedure distinguishes Newton assembly from residual-only norm/dual observations. Newton still receives current full Operator contributions and reuses its accepted trial assembly. Observations may call an optional add_current_residual hook; an unadapted provider keeps full evaluation. A failed hook propagates its error and destroys the temporary PETSc vector; it does not silently retry with different semantics.

The built-in smooth frictionless penalty Operator integrates the same current trace force without constructing an unused global contact tangent. Friction, faceted geometry and derived-law providers retain full evaluation and their admission checks. Initial regression exposed an inherited penalty shortcut in the augmented provider (16 failures); the corrected shortcut is restricted to the exact compatible implementation. The subsequent affected group passes 176 tests, with 16 already unsupported refined-triangle cases skipped. This scope deliberately does not assume every subclass has the same contact law.

An additional constraint-owned optimization shares incoming/outgoing dual evidence only inside one segment of the built-in piecewise-linear affine path. At each interior path knot the two work directions are evaluated separately. Derived or legacy constraints keep their two evaluations. This is call-local evidence reuse, not a force cache, changed work quadrature or residual lagging. The added tests cover both sides of exact/neighboring knots and preserve the legacy-provider behavior; the periodic/automatic-restart group passes 91 tests.

tools/benchmark_contact_residual_observation.py compares the combined change against the prior full/two-direction observation behavior on the same serial cyclic P2/J2/contact/MPC problem. It checks four-station fields, material states, stresses, tangents, contact observables, complete dual/energy histories and the accepted/Newton/line-search path. Whole-path timing must be obtained without a competing numerical job; reduced assembly counts alone are not a speed claim. Fresh no-competing-job ABBA runs now complete. The 32-increment screen reduces mean solve-and-observe time from 13.8168 to 13.0690 s (5.41%); the separate 64-increment confirmation reduces it from 25.6600 to 24.4457 s (4.73%). In the confirmation, full contact evaluations decrease from 412 to 282 and residual observations from 130 to 67, with the same 208 Newton corrections. All compared four-station fields/states/stresses/tangents, complete dual/energy histories and accepted/line-search paths agree exactly on this host. Raw evidence is in evidence/performance/2026-10-26-contact-observation-{screen,confirmation}.json. These isolate the observation change within the energy-enabled candidate; they are not a net revision comparison, a general speed guarantee, or a gain to add to earlier percentages. The explicit-composite path was not measured.

A separate cross-revision ABBA check measures the net cost, rather than hiding the new accepted-energy diagnostic overhead. Baseline 11accb3b has exactly the same src/agentfem tree as merged main 5e6cba5b; candidate b4401a86 adds the energy history and observation changes. Fresh serial children share one interpreter/numerical environment and one 64-increment physical fixture, warm a whole path before timing, and retain identical four-station physical array hashes, contact results, full dual histories and accepted/Newton paths. Mean solve/common-observe time is 25.6546 versus 24.7095 s (3.68% lower), while the candidate also records the new energy channels. This bounded result does not establish large-model or cross-machine speed, nor a multiplicative gain over the isolated optimization. Protocol and raw data: tools/benchmark_periodic_revision.py and evidence/performance/2026-10-26-periodic-net-revision.json.

The final follow-up also passes 27 focused equilibrium/augmentation lifecycle tests and two-phase material-only 1→2 / 2→1 MPI restart checks, including the complete accepted energy/dual history. Distributed contact remains unsupported.

A fresh native wheel at 63e3c23d passes 156 installed regressions from an isolated venv sharing the existing numerical dependencies, without development source-path injection. The standard init → check → run static-solid project also completes and publishes its result/fields. Scope, wheel digest, commands and limits are in evidence/contact/2026-10-26-installed-observation.json.

The installed exercise exposed an unrelated startup defect: CLI help eagerly initialized MPI, so a restricted network interface could prevent even usage instructions. A separate follow-up defers that import until the first actual communicator access, without guessing ranks or swallowing runtime errors. Seven startup tests deny numerical imports for help/version/invalid arguments; 45 ordinary CLI tests and two-rank single-rank-failure tests retain behavior. This does not make solver execution independent of MPI or certify a new host. After merging main 5e6cba5b, a second fresh-venv wheel at 0f2af133 passes all 163 installed tests, including startup, and the ordinary static-solid init → check → run workflow. Help also works in the restricted sandbox that previously prevented MPI initialization. Numerical tests still require their real runtime; this is not a clean Windows field trial or a runtime speed claim.

Initial-yield work diagnostic (2026-10-26)

The new accepted energy ledger localizes a path-error confounder before any further spatial sweep. In the 8-cell graded first-loading station, the first accepted increment (factor 1/32) already has plastic dissipation but zero contact potential. Its work-minus-internal-energy change is -0.0006944451 J; the total at factor 0.25 is -0.0006924962 J. Thus almost the entire difference is present before contact, not accumulated by later contact integration. This is accounting evidence for this fixture, not an error bound.

A frozen a36be758 4-cell/P2 full-cycle control varies only the initial increment from 1/32 to 1/128. All recorded runtime/tool hashes and other options match. The accepted plastic cap remains 0.00075, with bulk/contact quadrature 6/11 and unchanged physical parameters and tolerances.

Quantity	Initial 1/32	Initial 1/128
Relative mechanical residual at factor 0.25	0.788615%	0.058880%
Relative mechanical residual at factor 1	0.210555%	0.029839%
First-station contact force magnitude (N)	4.48342286	4.48353176
Final contact force magnitude (N)	3.70501173	3.70506365
Accepted increments / Newton iterations	232 / 806	237 / 812

The first-force change is about 0.00243%; the first residual is substantially reduced without relaxing its definition. Later errors remain, including on unloading/recontact. This is not a speedup measurement (another numerical diagnostic was active), a continuum certificate, or evidence for changing the global default. It explains why a plastic cap alone cannot guarantee path-work accuracy. The new diagnostic-only --initial-increment option isolates this control, and energy_increment_audit reports the largest signed contribution without replacing external work by stored/dissipated energy.

Evidence: evidence/contact/2026-10-26-initial-increment-{control,refined}.json. The 42 diagnostic tests pass, including inconsistent-coordinate refusal, outgoing/incoming force at path knots and ordinary Step energy consistency. Next compare a refined graded path at common physical stations; do not promote the small-model result into a full spatial or commercial-code validation.

Accepted affine material-energy ledger (2026-10-26)

Follow-up removes an unnecessary full contact tangent assembly from scalar energy observation. The contact Operator now integrates its current normal and friction energy channels directly from the same projection/constitutive response; it does not cache prior geometry or mutate accepted State. Certified-face Operators retain their existing evaluation fallback. Moving friction tests compare scalar versus full assembly before/after commitment through stick, slip, opening and recontact on analytical and triangulated surfaces. Curved P1/P2 trace tests also compare the potential. The affected group reports 131 passed and 16 explicitly unsupported refined-triangle combinations skipped. No end-to-end speedup percentage is inferred from eliminating this work.

The primal periodic J2 constructor now adds a scalar-only accepted observer. It integrates the material-owned stored energy and committed plastic loss, records the Operator-owned recoverable contact potential and friction losses, and reuses the existing affine/tool path work. Result balance uses final-minus- initial energy components, including initial penetration storage. The result's mechanical_energy_ledger reports evidence completeness, not verification. Mixed saddle-point and augmented normal-work combinations remain outside this ledger; a missing old checkpoint history is marked unavailable, never inferred.

Review found a real reporting omission: affine contact results previously summed only the normal assembly potential even when the Operator exposed recoverable tangential penalty energy. Results now use the Operator's total potential. The contact force/material update algorithms are unchanged.

The new scalar observer explicitly opts out of full-field snapshots. Existing observers retain their full copied fields by default. Small immutable history blocks provide constant-size rollback handles instead of copying the entire energy history each increment. A regression checks five accepted scalar stations with only two field snapshots. No runtime percentage is claimed.

Review extends this field-free declaration to the existing feature-path, certified-face and fixed-normal-work observers: they read the accepted station and their own Operator, never the copied displacement/field archive. New tests first reproduced four/five field captures despite sparse output; the corrected route makes only the two requested initial/final captures. Dense/sparse runs retain identical accepted diagnostic/checkpoint records and final fields. Thirteen focused parity, legacy-observer, corruption and rollback tests pass. This reduces unnecessary data movement; it is not a measured full-run speedup.

The focused 136-test group passes in the real fenicsx-env: independent virtual-work controls, diagnostic/restart tests, periodic J2/contact/friction, legacy field observers and scalar-history tests. Tests cover continuous versus restart histories, corrupted endpoint atomic refusal, old-checkpoint incomplete history, post-commit failure rollback, initial potential subtraction and moving tool/friction quantities.

The existing portable affine-J2 driver now explicitly compares the complete accepted stored-energy/plastic-loss history and affine path work, not only displacement/material fields. A two-phase material cell passes 1-rank write → 2-rank resume and 2-rank write → 1-rank resume in fenicsx-env using agentfem mpi-run --timeout 120. The restored half-path contains three scalar frames; the completed path contains five, equal across ranks and to an uninterrupted reference within rtol 2e-8 / atol 2e-10. The same assertions are included in the existing single/two-phase portable CI cases. These are material-only periodic-cell portability checks, not admission of distributed implicit contact or a four-increment energy-accuracy certificate.

Independent elastic virtual-work audit (2026-10-26)

The frozen 4c8bca1e diagnostic now checks the discrete elastic equilibrium without calling the production constitutive/contact assembly for the reference. It uses Basix basis tabulation, reference-cell geometry, an independent right-metric Hencky energy/stress calculation, explicit patch integration and coordinate-defined periodic virtual displacements. The production residual and potential are read only for comparison. This is an independent discrete elastic assembly audit, not a second nonlinear plastic solver or a continuum accuracy certificate. Plastic states are explicitly rejected by this oracle.

Uniform and combined-graded 8/12-cell P2 controls all pass. Relative full-force differences are at most 1.73e-13; relative energy differences at most 1.74e-14; independent reduced residual norms at most 2.37e-9 N (declared limit 1e-7 N). The graded reaction remains 18.64860612 / 18.53715898 N. The unchanged spatial trend is therefore not explained by the tested assembly/MPC algebra.

Evidence: evidence/contact/2026-10-26-independent-elastic-{uniform,edge_sine}.json. Reproduce with the directional-control command below plus --elastic-virtual-work-audit. Oracle source identity is included in each record. Nine focused oracle tests cover energy differentiation, rotation, independent periodic reduction, four mesh families, a perturbed non-equilibrium state and plastic-state rejection. No speedup is claimed.

The quadratic logarithmic strain energy is consistent with the elastic energy discussed by Neff, Eidel and Martin. Basis values/derivatives use the Basix finite-element interface. Remaining scientific gates are graded plastic increment sensitivity and the full loading/unloading path; the elastic audit does not close those gates.

Directional resolution discriminator (2026-10-26)

After Windows onboarding PR #123 merged at a862e123, the next experiment separates a confounder in the earlier combined grading: normal-to-boundary resolution and in-plane patch-edge resolution had changed together. normal_cosine changes only x coordinates; patch_edge_sine changes only y/z; edge_sine preserves the previously tested combined map. These are explicit diagnostic mesh choices, not runtime tuning or new public mesh defaults. All four families use the same cell count, P2 space, reference patch, material, penalty, bulk/contact quadrature 6/11 and first loading station 0.25. The elastic control uses yield stress 1e6 Pa and four fixed path increments.

Frozen driver 1481ec32 gives the following reference-area force magnitudes:

Cells per edge	Uniform (N)	Normal only (N)	Patch edge only (N)	Combined (N)
8	18.88425009	18.84128337	18.71742909	18.64860612
12	18.69374240	18.66504642	18.58301890	18.53715898

At both resolutions the isolated in-plane change affects the total reaction about 3.9 times as much as the isolated normal change. The combined response is not the sum of the two changes. Smooth edge/center pressure moments are retained in all eight compact evidence files. Every sampled active reference area remains 0.25 m², PEEQ stays zero and periodic mismatch is below 3.5e-18. Thus neither plastic history nor changing sampled contact area explains this particular sensitivity. This prioritizes in-plane edge resolution in the next bounded plastic/reference comparison; it does not prove which mesh is closest to the continuum solution, identify a constitutive defect, or establish full-cycle accuracy. No new runtime speedup is claimed.

Peak sampled pressure still increases between the two meshes, including 250.96 -> 255.86 Pa for combined grading. A scalar peak is not the pass/fail target for this experiment. Abaqus's adaptive-remeshing guidance warns that sharp contact edges can introduce singular fields and describes simplified provisional analyses for mesh studies. That motivates separating integrated observables and elastic controls here; it does not establish a singularity for this finite-penalty problem or justify changing its geometry.

Reproduce with tools/diagnose_periodic_contact_order.py, selecting each --mesh-family uniform|normal_cosine|patch_edge_sine|edge_sine separately, --cells 8 then --cells 12, --degrees 2 --increments 4 --contact-degree 11 --bulk-degree 6 --yield-stress 1000000 --until 0.25 --patch-partition, and a fresh --output. Each run was sequential, serial, one requested BLAS/OpenMP thread, with a 180-second subprocess bound. Evidence is evidence/contact/2026-10-26-directional-elastic*.json; it records driver and scientific source hashes and no field archives. The 37 focused tests pass, including coordinate factorization, all boundary P1/P2 periodic DOFs, volume/patch preservation and rejection of mismatched-mesh checkpoints. The constitutive and contact kernels are unchanged.

Task audit: call-local J2 spectral reuse is already implemented and measured in the 2026-10-19 entry below, not a pending optimization. The agent guide's obsolete single-pair/friction exclusions have been replaced with the current combination-specific admission matrix. Remaining gates are an independent same-input nonuniform reference, graded plastic-path refinement and bounded full-cycle verification, not another uncontrolled uniform mesh sweep.

Edge resolution and shared trace assembly follow-up (2026-10-25)

This follow-up starts from merged 6227b926; it does not reopen PR #118 or claim 0.4.4 release acceptance. The physical accuracy and equivalent-execution experiments remain separate.

Spatial discriminator. diagnose_periodic_contact_order.py --mesh-family edge_sine redistributes the existing unit-cube coordinates towards the fixed patch edges and contact boundary. It preserves the patch anchors, cell count, volume, periodic field equations and solver/material controls. The graded mesh is audited before fields and constraints are built. A changed mesh cannot load a uniform-mesh checkpoint. This remains diagnostic geometry, not a new public mesher or a case-specific solver in core.

At the elastic first station, graded 8/12-cell reactions are 18.64860612 and 18.53715898 N (0.598% coarse-relative difference), compared with 1.009% for the existing uniform pair. Both graded sampled active areas are 0.25 m² and PEEQ is zero. This is neither an independent reference nor a continuum-error bound. See evidence/contact/2026-10-25-edge-graded-elastic.json.

The bounded plastic probe reached its 1800-second deadline at accepted increment 326 (factor 0.24592998), with no requested station yet complete. Its record correctly says interrupted, not running or successful. The retained increment-300 checkpoint (factor 0.22938166) then loaded normally into the validated assembly candidate and completed the first station in a 154.78-second continuation. There was no checkpoint-identity override. The combined history has 333 accepted increments, eight rejected attempts and maximum accepted plastic increment 0.000321846, below the unchanged 0.000375 cap. Interrupted and resumed records retain separate source identities and checkpoint hashes. Their elapsed times include diagnostic pauses/concurrent correctness checks; neither is an isolated speed comparison or the time for a complete cycle.

First plastic station	Full displacement DOFs	Reaction magnitude (N)	Difference from uniform 12
Uniform 8	14,739	4.19262706	2.196%
Uniform 12	46,875	4.10251562	comparison only
Graded 8	14,739	4.08543432	0.416%

The graded sampled active area is 0.25 m² and MPC mismatch is 3.48e-18. Mean PEEQ is 0.02251850. Smooth edge/center forces are 2.96556176 / 1.11987256 N. Peak sampled pressure rises to 149.37 Pa (uniform 12: 139.99 Pa), so agreement in integrated force does not establish pointwise pressure convergence. The uniform 12 result is not independent truth, and grading changes resolution both along the contact boundary normal and near patch edges. This supports targeting resolution rather than another blind uniform sweep; it does not identify a unique error source or close continuum/full-cycle accuracy. Next science work needs an independent same-input reference and graded-path increment sensitivity. See evidence/contact/2026-10-25-edge-graded-plastic-interrupted.json and evidence/contact/2026-10-25-edge-graded-plastic.json.

Execution redesign. The normal-contact integration layer still evaluates every active point with its current normal, curvature, penalty and reference weight. It sums local matrices with equal ordered node stencils before COO expansion. Thus projection, friction history and point evidence are not cached or coarsened. Interleaved/distinct stencils remain valid; only adjacent equal stencils are combined. Floating-point association changes, not quadrature or the physical law. The PETSc adapter then coalesces repeated entries in stable lexicographic order and makes one subset-CSR insertion using setValuesIJV. Strong prescribed rows/columns are still filtered, and full contact terms still enter the existing MPC reduction. No new dependency or user option is introduced. This follows ordinary local integration before global assembly; the PETSc matrix interface provides the subset-CSR insertion rather than project-level sparse glue.

The isolated 32-increment ABBA screen retains all 113 Newton corrections, accepted factors and line-search/linear-reason histories. Submitted COO entries fall from 7,661,700 to 340,200; mean solve/observe time is 13.77687 -> 12.98744 s (5.73% less). The insertion timer is inclusive of validation/sorting/flush and is not added to whole-path time. Four-station displacement, material state, stress, force and tangent comparisons pass; maximum field/state/stress change is 1.318e-11. Record and reconstruction tool: evidence/performance/2026-10-25-contact-stencil-screen.json and tools/benchmark_contact_sparse_insertion.py. The reference uses pinned bf0033c4 row insertion and disables only local-stencil coalescing. This is serial implicit P2/J2/plane-penalty/MPC evidence, not an explicit-composite gain.

Fresh 64-increment confirmation, run after the other numerical process exited, retains 64 accepted increments and 208 Newton corrections. ABBA times are 25.88473 / 24.45214 / 24.48693 / 25.89431 s; means 25.88952 -> 24.46954 s, 5.48% less solve-and-observe time. All four stations also compare contact penalty potential; this is not a general energy-closure certificate. Maximum field/state/stress difference is 1.664e-11 and maximum relative tangent tensor error 1.765e-12. COO entries are 13,138,200 -> 583,200. Source identity, dependency versions, individual observations and gates are retained in evidence/performance/2026-10-25-contact-stencil-confirmation.json.

The preceding allocation-only full-tangent-reuse candidate is withdrawn. Its 8-increment screen differs by only 0.032% in mean time, which does not justify another runtime toggle/lifetime path. Preserve the unsuccessful finding in evidence/performance/2026-10-25-tangent-storage-withdrawn.json; it does not disprove reuse on other workloads.

Focused source acceptance after the combined assembly change:

• 215 tests across sparse insertion, analytical/facet contact, real DOLFINx traces, convex partitions, certified faces, frozen-equilibrium failure and periodic finite-J2 state/restart pass in 33.66 s.
• The expanded 2D/3D stencil tests and graded diagnostic tests pass 57 tests in 9.15 s (overlap with the preceding set; do not sum counts).
• Nonperiodic smooth/frictional contact and work/checkpoint transaction tests pass 82 tests in 8.56 s. Sixteen unsupported refined tetrahedral-face combinations are explicitly skipped, not claimed as covered.
• The shared adapter's augmented-contact caller passes five targeted open/recontact, restart and failed-outer-iteration checks in 17.13 s; the unrelated large-mesh reference is not repeated.
• Source lint and generated-documentation checks pass. Local REUSE tooling is absent; licensing CI remains required. The existing site/ changes are untouched and excluded from these commits.

Correctness tests overlap a bounded plastic diagnostic and their elapsed times are not performance evidence. The performance screen temporarily suspended that owned diagnostic and resumed it in a finally block. FI_PROVIDER=tcp and thread budgets are process-local; no machine-wide MPI policy is changed.

Integration boundary and focused diagnostic sprint (2026-10-25)

Sprint integration outcome. PR #118 merged on 2026-10-24 19:12 UTC at 897f1f744828ddb6680826d2b20ac4676cdb003b, after exact head d8392e9826e30e59a39e23b930b7928000a2fc1f passed all applicable checks in CI run 40121006505. The Linux serial suite reports 4988 passed, 428 skipped in 1681.91 s. Native installed-kernel, distributed lifecycle/restart, release smoke, Linux native distribution and macOS installed-wheel acceptance also pass as distinct gates. Do not add their overlapping counts or claim skipped native tests ran. No release tag or contact-maturity promotion is made. The historical attempts below remain part of the evidence, not outstanding copies of a resolved CI gate.

Release-scope audit finding. The material guide had placed finite-strain contact claims inside the small-strain J2/Chaboche description and retained outdated one-tool/affine-friction exclusions. Checking the actual dispatch revealed a separate defect: small-strain native J2/Chaboche and provider-neutral material capability predicates accepted registered contact or foundation Operators even though those builders did not assemble them. The native builder could omit them; the neutral builder already rejected them later. Six real model counterexamples failed the capability gate before the fix. Both built-in predicates now reject these unsupported compositions with one stable AFM-SMALL-STRAIN-BOUNDARY reason, consumed by capability and execution, before Step registration or field mutation. An external provider may still implement its own supported composition. No material conversion or new contact law is introduced. The combined constitutive/global-material subset passes 50 tests in 2.54 s, including all six counterexamples. The finite-strain numerical implementation used by the ongoing spatial diagnostic is unchanged.

An adjacent audit finds the same missing-assembly risk in power-law creep and quasistatic Maxwell. Four additional boundary counterexamples fail before their admission fix. All five families now share the same reason across capability, ordinary execution and compatibility builders. The initial expanded subset passes 95 tests in 13.76 s; 17 existing platform creep tests pass in 6.04 s. This rejects unsupported compositions; it does not implement new contact laws.

A fresh native wheel from 535e1eac repeats the ordinary installed partial, restart and continuous project after this safety fix. Its 99 selected tests pass in 4.75 s. Displacement, material vectors, contact force, accepted factors and contact work match both the same-wheel continuous run and the preceding 51c4a911 frozen candidate exactly on this fixture. An independent meshio reader finds one 384-tetrahedron block and finite fields at every exported station. Wheel identity, commands and the reused exact project source are recorded in evidence/contact/2026-10-25-installed-boundary-admission.json. The environment still shares numerical dependencies; this is not Windows or clean-machine proof.

The intermediate boundary-admission source bc7520cc additionally covers creep, Maxwell and compatibility entrypoints with one shared reason. Its independently installed native wheel passes 144 selected tests in 16.97 s, including ten contact/foundation counterexamples. The same ordinary continuous project again has zero measured difference in displacement, material, force, factors and work against 535e1eac; meshio reads all nine stations as one finite volume block. See evidence/contact/2026-10-25-installed-material-boundary-final.json. These concurrent acceptance runs are not performance measurements.

The adjacent harmonic Maxwell builder has the same omission (two additional pre-fix failing counterexamples). Its ordinary and direct-builder admission now uses that shared small-strain boundary reason as well. The final matrix covers five material families and six procedures, with twelve contact/foundation counterexamples; 107 selected source tests across the small-strain, Maxwell and harmonic modules pass in 15.30 s. No harmonic operator or numerical algorithm is changed.

The same 107 tests pass from a fresh native 38ab7e8c wheel in 17.69 s. An ordinary complete project again matches the previous installed candidate exactly in its five accepted arrays, and an independent reader opens all nine volume frames. The wheel hash, commands and evidence-reuse boundaries are in evidence/contact/2026-10-25-installed-six-procedure-admission.json.

Representative explicit acceptance against the installed bc7520cc wheel passes 81 tests in 55.53 s across test_strain_history_runtime, test_native_damped_body, test_finite_hex_explicit and test_builtin_q1_execution. They exercise native material transactions, body, damping and contact without confidential assets. The source changes since d5347eeb affect implicit J2/contact samples and small-strain admission, not the explicit Hashin-Puck execution kernel or accepted-series writer. This supports reusing the earlier complete 25-frame trajectory as historical evidence; it does not assign that trajectory's time to this newer package or claim a fresh full-model comparison. The test timing includes concurrent spatial work.

Fresh remote confirmation of e4207c56 completes in CI run 40115587874: 4976 serial tests pass, 428 are skipped (including optional native modules absent in this job and tests requiring multiple ranks), and the subsequent distributed inelastic, finite-J2 invariants and installed release smokes pass. All applicable checks, including Linux native distribution and macOS installed-wheel acceptance, pass. This resolves the earlier Linux precision-test failure for that head; it does not certify later safety commits without their own CI, nor establish distributed implicit-contact support. Native distribution and the local installed explicit subset are separate evidence; the serial pytest count must not be presented as native-backend coverage.

At entry, PR #118 head d5347eeb passes all applicable remote checks, including Linux native distribution, FEniCSx and macOS installed-wheel acceptance. It remains draft. The candidate release contract now names bounded serial periodic J2/contact separately as experimental and explicitly excludes nonuniform mesh independence, Gaussian-diagnostic energy closure, portable combined-contact restart and transferring implicit performance gains to the explicit composite. This is a claim audit, not a tagged release or a substitute for final acceptance.

Equivalent material execution. With trial Fe = U diag(s) V^T, the same radial return gives Fe_new = U diag(exp(e_new)) V^T. Therefore Fp_new = V diag(exp(-e_new)) U^T F. The batched core now applies this identity using the existing SVD instead of reconstructing the left stretch and rotation and factoring their product again. The scalar implementation is deliberately unchanged as an independent arithmetic reference. No law, acceptance threshold, state schema, public option or tangent definition changes. Tests advance both histories independently through elastic/plastic loading, unloading, reversal, rotation and isochoric prehistory with condition numbers up to 10^4, including 1025 points. Existing numerical-tangent and chunk-boundary tests still apply.

An isolated 32-increment screen measures 2.87% less solve-and-observe time. A fresh 64-increment confirmation records ABBA 28.72407 / 27.53229 / 27.40486 / 28.00160 s: means 28.36284 -> 27.46857 s, 3.15% less. Every route retains 64 accepted increments, 208 Newton corrections and identical line-search/linear reason histories. Maximum U/state/stress difference is 5.042e-11; maximum per-point relative tangent error is 5.355e-12. This is a small bounded gain, not an order-of-magnitude improvement or an explicit-composite result. Timing excludes setup/publication and includes station observation. Both reports keep individual timings, gates, runtime hashes and fixed reference d5347eeb:

• evidence/performance/2026-10-25-j2-svd-return-screen.json
• evidence/performance/2026-10-25-j2-svd-return-confirmation.json

Cross-platform precision follow-up. Linux head 5d73ecf3 completed the unit/interface suite with 4961 passed, 428 skipped and one failure in the new zero-hardening, ill-conditioned cyclic-history check. One first-Piola component out of 9225 differed by 3.335e-8 (relative 2.400e-9), just beyond its componentwise rtol=atol=2e-9. Preserve the failure in evidence/performance/2026-10-25-j2-linux-component-gate-failure.json; later MPI and installed-demo gates did not run, so this CI attempt is not passed.

An optional 80-decimal-digit reconstruction probe advances its own history for selected condition-1/100/10^4 points. On the local numerical stack, both binary64 implementations have Cauchy errors below 6.03e-10. In the condition-10^4 cyclic case the new/old first-Piola errors reach 3.57e-8/1.63e-8: multiplication by F^-T magnifies small stress/history roundoff. Neither double-precision route is an exact reference. This is a local conditioning diagnosis, not reproduction of Linux's exact arithmetic, a performance test or new material physics evidence. Reconstruction tool and measured norms: tools/check_j2_return_precision.py and evidence/performance/2026-10-25-j2-high-precision-diagnosis.json.

The regression now compares first-Piola tensors per material point in the Frobenius norm, retaining the original 2e-9 relative and absolute budgets. Rotating a tensor no longer changes the comparison scale. Added tests reject a real error at a soft/zero point even beside a stiff point and reject nonfinite data. Both routes also satisfy P F^T = J sigma with a normwise matrix-product roundoff allowance. Cauchy, state, energy, det(Fp), monotonicity, independent finite differences and global timing-comparison gates are unchanged; no runtime code or tolerance changed. All 49 installed material/spectral/protocol checks pass locally. The final Linux-head confirmation recorded above satisfies this integration gate without changing production numerical tolerances.

Spatial discrimination. Accepted implicit-contact samples expose reference positions and the integration measure alongside current positions, weights and point IDs. Exports preserve this optional array when all providers supply it; older providers remain usable without fabricated reference coordinates. The square-patch diagnostic partitions pressure on the fixed reference geometry. A sharp edge-belt indicator has mesh-dependent sampled area, so a second smooth partition is mandatory for interpreting redistribution: center weight 256(y-.25)(.75-y)(z-.25)(.75-z), edge weight its complement. Their exact areas are 1/9 and 5/36; this is an observable, not a contact enforcement law or an error estimator.

At the first loading station, P2 elastic controls on 4/8/12 meshes give total reaction magnitudes 19.63306 / 18.88425 / 18.69374 N. Smooth edge contributions are 13.71058 / 12.75983 / 12.49675 N; center contributions are 5.92248 / 6.12442 / 6.19699 N. All have reference active area 0.25, zero PEEQ and periodic mismatch below 4e-18. Thus reaction differences persist without plastic history or a changing active area; edge-weighted redistribution exceeds the total change and is partly offset in the center. This narrows the diagnosis but proves neither a constitutive bug nor continuum accuracy. Evidence: evidence/contact/2026-10-25-periodic-elastic-pressure-moments.json. The diagnostic explicitly stops at 0.25 (complete_cycle=false); it does not claim reverse loading or recontact. Do not replace the nodal AL contract with Gaussian P2 silently.

Controlled plastic discrimination. The matching 4/8-cell P2 paths now both reach 0.25 within the 1200-second runner cap, using the same 0.000375 accepted-plastic limit, bulk degree 6 and contact degree 11. They accept 186/251 increments with 7/8 rejected attempts. Reactions are 4.48528146 / 4.19262706 N (6.52% relative to the coarse value). Smooth edge moments change 3.51572801 -> 3.13241176 N while center moments change 0.96955344 -> 1.06021530 N. Unlike the elastic control, the sampled active reference areas differ: 0.22584707 / 0.25. These are quadrature-sampled indicators, not exact areas of an independently reconstructed active-set boundary. The common plastic-increment cap is an accuracy control, not an identical accepted time grid: the two meshes take different adaptive paths. Consequently the measured force difference is a controlled spatial comparison with residual path error, not a pure spatial-error estimate. Tightening the cap is a separate check; a third mesh alone cannot establish path independence or continuum accuracy.

On the unchanged four-cell controlled path, contact degree 7 -> 11 changes reaction by only 0.00557%, with 186 accepted increments in both paths; the sampled active area still changes 0.22041742 -> 0.22584707 and the peak pressure 98.3622 -> 111.9195 Pa. This separates stable integrated-force evidence from quadrature-sensitive area/peak sampling. It does not support blaming the 6.52% spatial force gap on contact quadrature, nor treating sampled peak pressure as a mesh-independent engineering quantity. Degree 21 was first rejected by the existing 5/7/9/11 admission contract; no guard was bypassed or core option expanded. That rejection is retained, not presented as a nonlinear failure.

One independent path-control check on the four-cell mesh halves the accepted plastic limit to 0.0001875. At the same first station the force changes 4.48528146 -> 4.48618952 N (0.02025%), mean PEEQ changes by 0.01345%, and the sampled active area is unchanged. It accepts 369 increments instead of 186. This makes the coarse path error an unlikely explanation for the 6.52% spatial force difference, but does not bound path error on the finer meshes or later reversal. See evidence/contact/2026-10-25-periodic-plastic-half-limit.json.

A separate four-cell volume-integration check raises bulk degree 6 -> 8 with contact degree 11 and the original plastic cap. The first-station force changes 4.48528146 -> 4.48532134 N (0.0008892%), mean PEEQ changes by 0.0004557%, and sampled activity is unchanged. It accepts 189 rather than 186 increments. The adaptive paths therefore are not identical, but this joint sensitivity is far below the 6.52% spatial force gap. Alongside the contact-quadrature and halved-cap probes, it directs the next investigation toward approximation of pressure and activity, not another integration-order sweep. It does not prove finer-grid integration independence or finite-plastic continuum convergence. Evidence: evidence/contact/2026-10-25-periodic-plastic-bulk8.json.

Evidence files:

• evidence/contact/2026-10-25-periodic-plastic-pressure-moments.json
• evidence/contact/2026-10-25-periodic-plastic-quadrature7.json
• evidence/contact/2026-10-25-unsupported-contact-quadrature21.json

The first report began on d5347eeb with the working source subsequently committed as 51c4a911; its recorded tool/runtime hashes identify that snapshot. Later diagnostics explicitly hash the constitutive and contact implementations as well. Elapsed diagnostic times include concurrent correctness work and must not be used as acceleration measurements.

An independent polynomial trace oracle checks the alternative explanation of incorrect P2/Q2 contact interpolation: on the unit reference square, p=2(1+y^2+z^2) gives force 10/3, moment components +/-11/6, virtual work -1 for delta_u_x=yz, and quadratic tangent work 200/9. Tetrahedral P2 and hexahedral Q2, one/two cells per edge and contact degrees 5/11 pass all eight installed-core cases. This checks nonuniform trace force, moment, work and tangent independently, not full elastoplastic spatial convergence.

The bounded spatial comparison adds one 12-cell P2 first-station run, holding the physical model, plastic limit and integration rules fixed. Its purpose is to test whether the eight-cell active pattern and integrated moments persist; it is not another general mesh sweep. It uses the existing accepted checkpoint policy (every 50 increments, retain two) and a progress status file. No new solver or restart implementation is introduced by the diagnostic. A timeout must retain accepted checkpoints and remain a partial result. Full-cycle accuracy and independent same-input comparison remain open. The diagnostic's --restart option selects exactly one mesh/degree and calls the public Step checkpoint loader without changing identity checks. It skips already-passed reporting stations, preserves the source checkpoint and records its SHA-256; elapsed time denotes only the new segment. Installed tests check a resumed station against a continuous path and reject a changed penalty before advancement. This is diagnostic convenience around the existing State lifecycle, not a new core restart mechanism. The tool can evolve while a running segment continues from its already-recorded source revision; numerical runtime sources remain frozen.

Completed third spatial station. The 12-cell continuation reaches 0.25 with 305 accepted increments, eight rejected attempts and 956 Newton corrections including restored history. Maximum accepted plastic increment is 0.000321846, below the declared 0.000375 cap. The original segment was deliberately interrupted after increment 101; continuation starts from preserved checkpoint 100 (factor 0.11176629), repeating increment 101 rather than splicing trial state. Its nine recorded scientific runtime hashes exactly match the original segment. The original unfinalized report still says running; it is explicitly classified as interrupted, not counted as a success. The new segment completes within its 7200-second cap, saves a station checkpoint and records 5588.66 s for the continuation only. That is neither total elapsed from zero nor a performance comparison; bounded correctness work overlapped.

Cells per edge	Reaction magnitude (N)	Sampled active area	Smooth edge force (N)	Smooth center force (N)
4	4.48528146	0.22584707	3.51572801	0.96955344
8	4.19262706	0.25000000	3.13241176	1.06021530
12	4.10251562	0.25000000	3.00099137	1.10152425

Successive coarse-relative reaction changes decrease from 6.52477% to 2.14928%. The 8/12 sampled active areas agree and MPC mismatch is 3.47e-18 on the fine mesh. Edge-weighted redistribution remains larger than the total force change, partly offset by the center. Maximum sampled pressure still grows from 111.92 to 129.62 to 139.99 Pa. These observations support continued edge-resolution investigation; they do not certify a mesh-independent peak, an observed order, GCI, general energy closure or a complete loading/reversal cycle. The unequal mesh ratios and differing accepted grids must not be hidden by fitting an order. Raw continuation results, source/checkpoint hashes, interrupted-segment status and derived comparison are retained in evidence/contact/2026-10-25-periodic-plastic-pressure-moments12.json.

Stop/next decision. End the uniform-mesh sweep at this station. Engineering integration is already complete and should not wait on more open-ended science. The next bounded scientific study should isolate contact-edge spatial resolution on the unchanged patch, then compare to an independent same-input reference. Integrated reactions and smooth moments are primary; pressure maxima remain diagnostic. A successful local-resolution result still needs a separate fine-path sensitivity check before promotion. Do not open another penalty/integration-order sweep, new contact law or full-cycle expansion in this closeout.

Methodological sources: Simo's multiplicative return mapping and COMSOL's multiplicative-plasticity integration description support keeping the discrete flow and volume-preserving update explicit; neither provides our timing result. Contact stability and patch-test analysis motivates separating integral accuracy from approximation/stability. The publisher abstract was available, not the paywalled full text; the algebra and new pressure moments above are independently derived and tested here. The penalty convergence analysis by Chouly and Hild separates penalty regularization from FE discretization; its regularity assumptions and linear-contact analysis do not prove our finite-plastic convergence. COMSOL's contact guidelines also distinguish accurate pressure fields from global structural response. These support the diagnostic separation, not an automatic parameter recipe. Its contact-node discretization notes separately describe pressure interpolation, quadrature and the update solver; raising the displacement order does not justify reusing a lumped nodal pressure update without a compatibility argument. This supports keeping the current P1 nodal augmentation and P2 Gaussian diagnostic distinct. It is not evidence that AgentFEM's particular spatial discrepancy is pressure locking.

The deal.II step-42 tutorial is useful for separating active-set updates, plastic Newton linearization and local mesh refinement. Its small-strain formulation and refinement/state assumptions are not a drop-in replacement for the current finite-history Step. COMSOL's meshing guidance also explicitly distinguishes rigid from deformable source surfaces: the usual source/destination mesh ratio is not a remedy for this analytical flat rigid tool. The next spatial decision must follow the measured pressure distribution, not a copied commercial-software parameter recipe.

Installed candidate acceptance. Native wheel source 51c4a911 imports from its fresh venv, not the working checkout; all three optional native modules also resolve there. The environment shares the existing numerical dependency stack, so this does not claim a clean-machine installation. A project assembled from the existing public periodic-plane example uses ordinary agentfem run for a partial 0.25 path, a restart and a continuous eight-increment path. Displacement, committed material state, contact force, accepted coordinates and relative contact-work arrays have zero measured difference on this machine. Independent meshio reads show one 384-tetrahedron volume block per view and finite displacement arrays. The partial/resumed views intentionally share the restart station; the implicit example writes these views after its segment, not live during Newton iterations.

Separate installed suites pass 52 output/connectivity/live-publication tests, 66 execution/history/retention tests, and 18 physical-fixture/independent scalar plastic-contact tests. Two mixed-pair export checks additionally prove that an older provider lacking reference coordinates does not create a partial-looking global array. Live-view evidence comes from the live writer's independent reader and killed-next-frame tests, not from the post-solve implicit example. No tests were skipped. Timings here are not performance evidence because the bounded spatial diagnostic was also active. The wheel hash, exact project reconstruction driver, commands, tolerances and observed arrays are recorded in evidence/contact/2026-10-25-installed-periodic-contact.json.

Batched J2 tangent contractions (2026-10-24)

The existing logarithmic J2 derivative still evaluates the same nine dP/dF directions. Its chunk-local push-forward now forms the common U^T F^-T once and packs directions into 3x27/27x3 products instead of 27 separate 3x3 products per point. No material law, iteration tolerance, state owner, cache lifetime or public option changes. The 1024-point scratch bound remains unchanged.

The first global comparison failed a componentwise tangent gate: four of 746496 entries differed by at most 2.295e-9, while displacement, state, stress and the accepted Newton path had already passed. Keep that failure in evidence/performance/2026-10-24-j2-tangent-block-contractions.json, with its source reconstructable at a0c06894. The revised comparison uses each point's Frobenius stiffness scale, relative tolerance 2e-10, rather than assigning small off-diagonal entries their own scale. This matches the existing scalar/batch analytic relative gate and is five orders tighter than the independent numerical-derivative gate, 2e-5. The original displacement/state/ stress gates (rtol 2e-8, atol 2e-10), force checks and exact increment/Newton/ line-search/linear-reason comparisons are unchanged. Added tests reject real changes at individually soft points, zero-reference changes and nonfinite data.

Fresh isolated confirmation uses the public four-cell-edge cyclic P2/J2/plane penalty/MPC diagnostic, not the explicit composite model. After two full warmups, ABBA solve-and-observe times are 15.40445, 14.12869, 14.09898 and 15.38637 s: means 15.39541 -> 14.11383 s, 8.32% less elapsed time. All paths retain 32 accepted increments and 113 Newton corrections; maximum U/state/stress difference is 3.708e-11 and maximum per-point relative tangent error 4.543e-12. Four-station force, pressure, contact area, PEEQ and displacement comparisons pass. The same fresh report measures about 35.78% less analytic tangent time at 4096 material points; that kernel number is not a solver gain. Setup and file publication are excluded; station observations are included. Source hashes remain unchanged across the comparison. Evidence: evidence/performance/2026-10-24-j2-tangent-block-confirmation.json.

Seventy-five focused material/periodic-contact/reuse/protocol tests passed before the comparison-rule follow-up; forty material/protocol tests then passed, including independent finite-difference derivatives and a 1025-point chunk boundary with plastic history, repeated stretches and rigid rotation. Counts overlap. Final expanded targeted acceptance passes 177 tests, adding standard boundary and periodic global-J2 paths. This does not close spatial accuracy, independent external comparison, MPI admission or explicit-composite performance. A separate SVD-based plastic gradient reconstruction remains exploratory; it is not included in this core change or its timing claim.

Controlled P2 spatial-path diagnostic (2026-10-24)

The existing Gaussian-penalty diagnostic now accepts the existing automatic plastic-increment policy; it does not own a new solver. The eight-cell-edge P2 run at source 197ba2c8, bulk/contact quadrature 6/11 and plastic limit 0.000375 reached common stations 0.25 and 0.5 before its external 1800-second budget expired. Its process exited and the partial scalar evidence is retained as failed/TimeoutExpired, not completed or a numerical-convergence diagnosis: evidence/contact/2026-10-24-periodic-p2-controlled-path8.json.

At 0.25 its reaction is -4.192627056 N, compared with -4.181129794 N on the same mesh with 128 fixed increments (about 0.27% difference). The four-cell refined-prediction reaction is -4.485281459 N (about 6.52% spatial difference relative to that coarse value). The active reference areas also differ: 0.25 versus 0.225847069 square metres. At 0.5 the fine diagnostic opens contact, with zero force/pressure/penetration and MPC mismatch below 1e-18. These are two accepted stations only: reverse loading, final recontact, full-cycle path accuracy and spatial convergence remain unverified. The Gaussian route still has no normal-relative-work ledger; no general energy-closure claim follows. Do not launch a larger blind sweep from this partial result. Fixed-increment CLI validation again rejects non-positive/non-quarter-compatible partitions before starting a model; four regressions cover that diagnostic guard.

Accepted-plastic increment prediction (2026-10-23)

The two-hour solver sprint promotes the private work-reduction experiment into the existing automatic-increment policy, not a separate case solver. The optional inelastic_prediction_safety caps the Newton-based next proposal using the last accepted maximum plastic increment. Acceptance still enforces the same declared hard bound; failure cutback and mandatory load knots remain unchanged. This is a lagged workload predictor, not a local/global error estimator or an explicit stability bound. Defaults and old default checkpoint identities are unchanged. Enabled identity binds algorithm, safety and the expert affine acceptance-measure name.

Source-frozen commit b83a3936 was compared on a public four-cell-edge P2/J2 cyclic plane-penalty/MPC fixture with limit 0.00075. ABBA setup/solve/observe times are 186.897, 115.284, 114.090 and 185.903 s: 38.47% less mean elapsed time. Accepted increments are 250 -> 232; rejected attempts 140 -> 13; Newton corrections 1300 -> 806. This changes the discrete path and must not be presented as bitwise-equivalent execution or combined arithmetically with the separate 24.32% execution result. The maximum accepted plastic increment is 0.000748321, below the unchanged 0.00075 bound. A finite 512-increment reference primes compilation and supplies four common stations, not a continuum truth. Maximum candidate differences to it are 0.204% reaction, 0.0235% displacement vector and 0.00448% reference-volume mean PEEQ. Zero reaction uses absolute error, not a misleading relative error. Repeated U/state/stress/tangent pass rtol=2e-8, atol=2e-10. Runtime and driver hashes remain unchanged throughout the comparison; compact evidence is evidence/performance/2026-10-23-inelastic-increment-prediction.json.

Serial standard and affine global-J2 paths are admitted. Single-region dispatch was initially advertised by capability inspection although it lowered to a material map rejected by the backend. A failing regression established that mismatch; admission now follows the actual lowering. Regional, mixed and MPI prediction stay unsupported, without restricting their old increment policies. The real two-rank admission test passes on both ranks with a 120-second launcher limit. It checks early refusal, not distributed prediction success.

The expanded 48-test focused set passes (one MPI-only test skipped in serial). It includes ordinary/affine serial and portable-format restart, cyclic moving AL tool state/work rollback, invalid measure rejection, policy-identity mismatch, minimum-increment exhaustion and retained benchmark failure evidence. Portable combined-contact restart is still explicitly refused, not silently promoted. The independent scalar confined-J2 reference exercises loading, unloading, reverse plasticity and recontact with one/two-cell meshes and interrupted paths. Its original 3e-9 displacement gate first failed: the old 1e-8 complementarity product allowed a 4.678e-9 positive gap at pressure 1.895, product 8.866e-9. The reference fixture now uses stricter 1e-10 complementarity and 1e-11 penetration tolerances for both increment policies; original field/state/force error gates are unchanged and pass. No runtime default or timed fixture was changed to repair this test. Spatial convergence, general energy closure of the Gaussian diagnostic, and explicit-composite acceleration remain separate. The broader affected source regression passes 283 tests (one MPI-only test skipped in serial), followed by four benchmark-protocol tests. These counts overlap and are not summed. Generated API checks and a strict documentation build in a separate temporary directory pass; existing site/ edits are untouched. The benchmark also has a --refine-limit mode for a prospective fixed-reference/limit/half-limit comparison, which deliberately emits no ABBA speed claim.

That prospective refinement is now complete at frozen 33412d59, with no concurrent numerical run or build and unchanged source hashes. The 1024-step reference has final reaction -3.71250393, versus -3.69748392 for 512 steps (0.4046% change). Limits 0.00075 / 0.000375 give final reactions -3.70501173 / -3.71635888; the sign of their difference from a finite reference matters. Maximum four-station reaction differences are 0.20181% / 0.10384%, displacement vector differences 0.03834% / 0.01184%, volume-mean PEEQ differences 0.02909% / 0.001654%, and maximum PEEQ differences 0.08964% / 0.005264%. Open-contact station forces are zero in each path. The refined prediction takes 449 accepted increments, 18 rejected attempts and 1447 Newton corrections; its maximum accepted plastic increment is 0.000370597 < 0.000375. The coarse path reproduces the previous 232/13/806 counts. Observed individual times are 382.705 s reference, 114.241 s coarse prediction and 208.196 s refined prediction, not a new ABBA performance claim. Evidence: evidence/performance/2026-10-23-inelastic-increment-refinement.json. These results support controlled limit refinement, not an exact/global error bound. No third blind parameter/mesh sweep is started in this sprint. The next gate is compatible volume/contact/periodic approximation with loading-path error explicitly separated. No current experimental capability is promoted to commercial-code parity or released based on this timing result.

Combined implicit execution confirmation (2026-10-23)

After the individual mechanisms were selected, the combined serial J2/plane/periodic-MPC route was timed independently with twelve cells per edge and 48 increments. Reference A disables retained material responses and outer workspace reuse and uses direct MUMPS; candidate B enables the owners and the explicit managed GMRES policy. The ABBA times are 261.223, 196.909, 195.732 and 257.591 s, a 24.32% mean reduction, with no concurrent local numerical test or build. Setup is excluded and four-station observations are included.

All paths complete 48 accepted increments and 533 Newton corrections. Each candidate records 172 retained material responses, 435 preconditioner reuses, 98 builds and no fresh-PC retry. U, committed state, first Piola stress, tangent, pressure and normal relative work meet the predeclared rtol=1e-7, atol=1e-9 comparison. The report retains individual times, differences, policy and runtime/source identity in evidence/performance/2026-10-23-combined-affine-execution.json. The driver now preserves unsuccessful setup/solve/comparison evidence too. It captures code identity before the run, retains it on failure, and refuses to promote timing if the tool or selected runtime sources change during the comparison. Three targeted failure/provenance tests pass. The source used by the completed comparison remains reconstructable at commit d1e1a368. Follow-up dispatch review reproduced a missed invalidation when the actual preferred update_array_batch callback is replaced after a refresh. Its bound callback identity now participates in the one-shot guard alongside scalar and object-batch entries. The new regression fails before the correction; afterward 53 focused material-retention, adaptive-correction, workspace, automatic-restart and benchmark-failure checks pass. No constitutive formula or default solver policy changes. The recorded timing remains the earlier tested source result, not a new timing claim for this guard-only follow-up. This is a bounded implicit execution result, not continuum convergence, external-code parity, MPI admission or a full explicit-composite speedup.

Physical cell-recovery audit (2026-10-23)

Reference-rule averaging was correct for affine geometry but not a physical cell average on a variable-Jacobian map. For X(r,s)=(r*(1+s),s), the old recovery gave mean s=1/2 instead of 5/9, a 10% relative error. The corrected DG0 recovery normalizes w_q*abs(det(J_mesh,q)), keeps each owned cell separate, uses the backend DOF map for bulk assignment, and forward-scatters only after collective validation. It does not modify the constitutive state or infer a current-volume factor from displacement. Curved quadratic triangle recovery also matches the independent centroid 3/8.

Fifty-one serial recovery/constitutive checks pass, with three MPI-specific checks skipped; the latter then pass on each of two ranks. The first empty-rank test used a one-cell ParMETIS graph and failed during mesh construction, before recovery. Its MPI group timed out safely; a fail-fast diagnostic identified the external partitioner error. The corrected test explicitly assigns that cell to rank zero and verifies the deliberately empty rank. No partitioner or solver behavior was changed to make the fixture run. The wider affected source subset then passed 165 tests in 5.14 s, with the same three MPI-only cases skipped in serial. It includes result contracts, mixed-J2 energy diagnostics, contact traces and benchmark-failure persistence. Embedded-surface area weighting and changed mesh coordinates are covered too. The latter fixture evaluates physical coordinates through the backend rather than assuming a reference axis is aligned with physical y. The complete fourteen-test recovery file also passes on each of two MPI ranks (0.39 s per rank). It now participates in the existing distributed result CI group, whose launcher has a 180-second timeout.

Fixed-reduction linear ownership investigation (2026-10-23)

The serial affine outer Procedure can own the KSP and reduced product matrix for one augmentation attempt rather than recreate them for every frozen equilibrium. Current full tangents and PtAP values are still assembled at each Newton correction; there is no frozen Jacobian. Changed transformation identity, PETSc state or solver options reject, and attempt exit releases owned objects. The first source regressions pass 40 solver/material tests and 13 cyclic/contact lifecycle tests. Isolated twelve-cell/32-increment ABBA times are 151.933, 149.915, 150.727 and 152.032 s: a small 1.09% mean reduction. Every observed station array is identical, with 32 accepted increments and 355 Newton corrections in all four runs. This is allocation/lifetime consolidation, not a major acceleration. The evidence is evidence/performance/2026-10-23-affine-linear-workspace.json.

Do not assume consecutive tangents are identical just because the starting material response was retained. A four-cell cyclic probe finds zero exact consecutive matrices in 109 linear solves: the last factorization generally belongs to the preceding Newton iterate, not its accepted line-search endpoint. Consequently exact-matrix factor reuse is not implemented on this hypothesis.

A separate private algorithm probe keeps the current matrix and uses an earlier LU only as a right GMRES preconditioner. It checks the true unpreconditioned linear residual and rebuilds on failure; it must never be used with preonly. The first binding attempt failed because this petsc4py exposes reuse on PC, not KSP; that failure record is retained. Corrected four-cell/16-increment loading, unloading and recontact match the direct-solve fields within declared 1e-7 relative / 1e-9 absolute checks. All 109 corrections satisfy the configured true linear residual target; 87 reuse a preconditioner, without a failed-solve rebuild. This small model has no demonstrated elapsed-time advantage. Larger accuracy screening precedes timing and any public option design. The twelve-cell, 32-increment screen also matches all four accepted stations (32 increments, 355 Newton corrections). It reuses 287 preconditioners, needs no failed-solve rebuild, and uses at most 31 Krylov iterations. Its concurrent 156.23/137.19 s observations are not an isolated speedup claim.

If isolated screening selects this mechanism, the design is an explicit linear execution policy, not a contact/material tuning parameter. The owning linear sequence must keep the current operator, verify the true residual against the declared linear tolerance, rebuild once after a stale-preconditioner failure, and reject if the fresh correction still fails. Direct preonly must never reuse a changed factorization. Scope and cleanup follow the existing attempted increment; acceptance, rollback and restart do not retain the PETSc factor. Unsupported adapters (including an SNES translation that cannot enforce these rules) must reject the option rather than discard it. The default direct route and legacy checkpoint summaries stay unchanged. Required tests include current matrix changes, changed layout, a failed reused solve, a failed fresh solve, nonfinite true residual, exception cleanup, and continuous/restarted cyclic plastic-contact agreement. Do not ship a public option solely on the present two private accuracy probes.

The implemented opt-in public boundary is LinearSolverOptions(preconditioner_reuse= "adaptive"), initially lowered only by the serial affine Newton owner. The existing common Newton factory transports that linear policy; it does not add a contact-specific tuning knob. A raw KSP/SNES or unreviewed nonlinear adapter must reject it rather than silently enable PETSc lagging. The owner selects right-preconditioned GMRES, requires explicit linear tolerances/iteration limit, and rebuilds after an expensive correction (initial bounded threshold: eight Krylov iterations). Result diagnostics count reuses, rebuild retries and the maximum true residual-to-tolerance ratio. Default summaries omit the new policy key so existing direct-solver restart identities remain unchanged.

The isolated twelve-cell/32-increment ABBA screen subsequently measured 149.995, 129.921, 130.073 and 150.193 s (13.39% less mean solve-and-observe time), with all declared four-station comparisons passing. This selects the mechanism for integration, not for a full-run explicit performance claim. The integrated owner and option transport pass 131 focused serial tests; the separate two-rank admission test rejects unsupported distributed reuse before field mutation. Failed correction cleanup, true-residual false convergence, one-rebuild retry, restart and default-policy compatibility are exercised. Fresh 48-increment integrated ABBA confirmation finishes at 226.635, 195.011, 195.842 and 226.402 s: 13.73% less mean time. Each run accepts 48 increments and uses 533 Newton corrections. Candidate runs reuse 435 preconditioners and build 98, with no failed-solve retry. Their maximum true residual/threshold ratio is 0.998462. All four station comparisons pass; maximum displacement/state differences are about 1.33e-15/4.67e-14, and the largest tangent difference is 4.39e-9 under the declared relative/absolute criterion. See evidence/performance/2026-10-23-adaptive-preconditioner-confirmation.json. Do not add this percentage to retained-material or explicit-body measurements.

The distinction follows PETSc's preconditioner lagging and current-system KSP operators. These sources are algorithm guidance, not AgentFEM speed evidence.

Discretization investigation after graded-mesh failure

The next bounded diagnostic compares P1/P2 displacement with the already supported Gaussian penalty trace and explicit bulk/contact quadrature. tools/diagnose_periodic_contact_order.py builds periodic equations from all field DOF coordinates, not just mesh vertices, and keeps the same finite-area physical guides and interior patch. Tests apply arbitrary reduced fluctuations to check opposing-face jumps and the guides, including midsides. This avoids an apparently successful P2 solve with missing periodic equations.

This is not the existing nodal augmented-Lagrangian discretization, so no reaction difference can be attributed to polynomial order alone. First compare P1/P2 at common penalty/integration/path settings, then separately examine quadrature and penalty sensitivity. Failed solves remain in the scalar report; do not produce large field archives or tune a value to match the AL reaction. The physical-model and independent-reference gates remain open.

The first P2 diagnostic correctly failed existing initial-overlap admission: the old rule required both field and geometry degree one. The narrowed extension now separates these concepts for analytical planes: CG2 on linear tetrahedral or Q1 hexahedral reference geometry uses authoritative face vertices for the reference gap bound. High-order traces also carry off-face cell DOFs, so using all trace node IDs would falsely reject separated faces. Two real mesh tests exercise that distinction and exact touching/sub-picometre overlap; curved reference geometry stays rejected. This is an initial-reference proof, not a bound for deformed quadratic contact or permission for P2 nodal AL.

The corrected 4/8-cell, 32-increment P1/P2 Gaussian study completes all four loading/unloading/recontact paths. Final structure forces in x are respectively -4.05337/-3.68946 N for P1 and -3.29373/-2.73078 N for P2. These differences are not a convergence pass. Gaussian order seven and bulk order four are held fixed; integration sensitivity must be separated from spatial interpolation before interpreting the result. Maximum sampled penetration is about 0.00260 m in the final eight-cell P2 station; a converged nonlinear residual alone says nothing about adequate penalty accuracy. Evidence: evidence/contact/2026-10-23-periodic-contact-order.json.

The first reporting attempt failed after each first solve because it requested the AL-only normal-work recorder from a penalty Step. The observer now explicitly omits that quantity and marks work unavailable on this diagnostic route; it does not substitute zero or claim energy closure. The regression exercises the actual P2 solve and observer together. Source trace/initial-bound tests pass 163 checks, with eight two-rank-specific checks skipped in this serial run.

Ordinary quadratic tetrahedra can have zero equivalent pressure force at corner nodes; Abaqus's contact-control guidance distinguishes that node-to-surface issue from surface-integrated contact. It motivates this separate diagnostic, not automatic admission of P2 nodal AL.

The fixed eight-cell P2 sensitivity probes now separate integration from mesh order. Increasing only the contact rule 7 -> 11 changes final x-reaction from -2.7307783 to -2.7298206 N (0.0351%). Keeping rule 11 and increasing only bulk quadrature 4 -> 6 gives -2.7300627 N (0.00887%). Both complete all 32 increments and unloading/recontact. The two records are evidence/contact/2026-10-23-periodic-contact-p2-quadrature11.json and evidence/contact/2026-10-23-periodic-contact-p2-bulk6.json. These differences are far smaller than the current 4 -> 8-cell force gap; neither is a spatial-convergence certificate or a reason to increase every user's quadrature default. Sampled maximum penetration changes with the set of sample points and is not a continuous-face penetration bound.

Separate path and elastic spatial diagnostics (2026-10-23)

With the eight-cell P2 mesh, contact rule 11, bulk rule 6 and unchanged penalty, 32/64/128 accepted increments give final reactions -2.7300627/-2.9171279/ -3.0121821 N. Successive differences, relative to the finer result, are 6.4126% and 3.1557%. The maximum PEEQ changes from 0.1100375 to 0.1106489 to 0.1113156. The trend is consistent with a remaining loading-path discretization error; 128 accepted increments are not a path-independence certificate. These are diagnostics, not grounds to change every user's increment count. See evidence/contact/2026-10-23-periodic-contact-p2-time64.json and evidence/contact/2026-10-23-periodic-contact-p2-time128.json.

An elastic-limit control changes only yield stress to 1e12 Pa, holding the geometry, boundary path, penalty and integration rules fixed. All reported PEEQ values are zero; four increments capture the four loading stations. First and final loaded forces agree to roundoff, and unloaded forces are below 1.1e-10 N. Under the same Gaussian penalty formulation, the 8 -> 12-cell reaction change is 4.4570% for P1 and 1.0191% for P2. P2 forces on 4/8/12-cell meshes are -19.6330568/-18.8842501/-18.6937424 N. Records:

• evidence/contact/2026-10-23-periodic-contact-p1-elastic.json
• evidence/contact/2026-10-23-periodic-contact-p2-elastic.json
• evidence/contact/2026-10-23-periodic-contact-p2-elastic-coarse.json

This narrows the next decision: volume/trace approximation matters even without plasticity, and plasticity adds an appreciable path error. It does not prove locking, identify a unique error source, validate the finite penalty as an exact constraint, or compare P2 penalty directly to the P1 nodal-AL reaction. There is still no independent continuum reference. Do not launch another unstructured mesh/penalty sweep or admit P2 nodal AL without a compatible normal space. Next use a bounded common-path refinement at the selected P2 rules, then assess the penalty error separately. The supported nodal-AL capability remains P1.

The lifecycle audit confirms that the current path driver retains prescribed deformation-path knots, starts each constitutive trial from committed history, and already supports a maximum accepted plastic-strain increment. That bound is not an error estimator. Do not conflate local return-map convergence, global Newton convergence and path accuracy. A separate control audit found that fractional fixed counts could be truncated and several automatic controls admitted NaN, infinity or noninteger counts. Early typed/finite validation now rejects those inputs while preserving valid Python policy/checkpoint spelling. 107 focused controller, automatic-restart, material-substep and adaptive-contact tests pass (one MPI-only test skipped in serial). This changes admission, not the integration algorithm or default path.

For a later accuracy/cost experiment, MOOSE's radial-return documentation distinguishes global material-limited steps from local constitutive substeps. Local substeps may avoid some discarded global solves, but they cannot resolve an equilibrium/contact event skipped by the global path. They are not enabled here. A finite-strain implementation must specify its deformation interpolation, carry state sensitivities through the full sequence and differentiate that sequence, rather than returning the last substep's tangent; the general consistency issue is treated by Pérez-Foguet et al. (2001). First compare the existing global controller against common-path refinement; only pursue local substepping if material integration, rather than contact events or spatial approximation, is shown to limit useful step size. No new runtime dependency, automatic differentiation framework or hidden material path is introduced by this research note.

Worker-local nodal transport: coherent prototype withdrawn (2026-10-23)

A native prototype removed the complete Hex8 cell-displacement intermediate: kinematics and material/body workers gathered their 24 local values directly from the immutable nodal snapshot. It retained uncertain-geometry fallback, material repair, viscosity, current forces and accepted-state ownership. Thirty-nine arithmetic/lifecycle tests passed, and four 600-step late-state trajectories retained identical fields, material state and per-step histories. The ABBA times were 73.111, 73.065, 72.649 and 74.695 s. Mean reduction is 1.41%, while the two baseline runs differ by 2.17%. This does not select a useful whole-step speed gain; the option and implementation are withdrawn, with the prototype retained privately. Logical temporary removal is not a measured peak-memory reduction. See evidence/performance/2026-10-23-nodal-transport-screen.json. Reconsider with a measured memory limit or a combined dependency/critical-path change, not repeated short sampling until a preferred percentage appears.

Joined body/viscosity candidate (2026-10-22)

An opt-in native cell pass now gathers nodal velocity locally and evaluates the existing bulk-viscosity formula alongside body force. The public defaults are unchanged. It retains separate material work and viscous power, current damping stability bounds, exact material repair and the viscosity-conditioning fallback. All physical contributions validate before the ordinary trial is published.

The isolated native build and source path pass 133 focused native/body/material/ restart tests, followed by 16 restart tests including both cross-policy recovery directions and different worker/tile budgets. A later pure-native recheck passes all 13 damped-dispatch tests without requiring MPI initialization. These are source/candidate-build results, not a frozen installed release acceptance.

One real late-state pair advances increments 95,000 to 95,600 in 128.845 s and 118.889 s. Numerical U/V/A, material state/stress/gradient and the physical history snapshot match exactly. However the comparison harness incorrectly hashed dictionaries as NumPy object-array bytes (process-local pointers), which aborted the intended ABBA sequence after the first pair. The harness is fixed to fingerprint nested content and reject object-array pointer hashing; the original failed artifacts are retained, not relabelled as a completed test. The candidate's first-response comparison also agrees on ten body/material/ viscosity arrays, including work and damping bound.

The earlier permission blockage was resolved in the next authorized window. A fresh complete ABBA confirmation on 95,000–95,600 records separate-pass 82.892/79.564 s versus joined-pass 76.712/76.502 s: 5.69% less mean elapsed time for this late interval. All accepted U/V/A, material state/stress/gradient and physical residual history match exactly. Preparation, checkpoint loading and serialization are outside the timing. Evidence: evidence/performance/2026-10-22-joined-viscosity-confirmation.json. Do not extrapolate this interval into an achieved full-run improvement. Neither the reference case nor its completed 25-frame output was modified.

The next separate geometry experiment evaluates a current closest-point normal only at a strictly interior smooth Q1 point on a reviewed embedded, connected, outward closed surface. Edges, vertices, ambiguous numerical projections and unresolved orientation retain the existing two-ray classifier. This follows the smooth-surface sign argument described by Bærentzen and Aanæs, not an unverified transfer of triangular pseudonormals to warped Q1 patches. The private prototype passes eight geometry tests, including warped/concave surfaces, current refits, disconnected/nested shells, reversed orientation, near-zero fallback and unchanged rejection of distinct equally near faces. On the same 40 prescribed late geometries, ABBA contact times are 3.261/3.257 s versus 2.911/2.932 s. Ray queries fall from 307,140 to 5,094; all contact forces, gaps, weights and potential match exactly. This is not a dynamic trajectory or a complete-step performance claim.

The optional core sign_policy="interior_normal" now reconstructs its normal from current Q1 derivatives rather than trusting a callback's unit-normal transport. Connected-shell orientation is rechecked after geometry refits. 107 targeted geometry/explicit-contact tests pass, including a toroidal shell, both cross-policy checkpoint directions and rejection of changed provider identity. Checkpoint compatibility omits only the core sign arithmetic choice; actual execution provenance retains it. The default two-ray route is unchanged.

A whole-step combined ABBA on the same late interval records baseline 73.950/77.405 s versus combined 72.357/71.689 s, with identical accepted fields and physical history: 4.83% less mean time in this screen. Rays decrease 4,676,043 to 63,682 in the first pair (including setup), with identical 4,973,416 prepared points. This does not establish an additional gain over body fusion alone. Concurrent critical paths and changed CPU contention matter; do not add the geometry and body percentages. Next screen process-local worker budgets and confirm any selected combination on fresh runs.

Explicit Q1 classification reuse: tested, not promoted (2026-10-22)

A private prototype transported a certified inside/outside classification only while a conservative clearance exceeded query and surface motion. Every force and projection still used current geometry; expired certificates fell back to the existing two-ray classification. A second variant removed best-fit rigid rotation before bounding the residual motion. Neither cached old contact forces.

On 40 evolving prescribed geometries sampled between the last two accepted composite frames, the translated certificate reduced native classifications from 307,140 to 294,703, but ABBA elapsed sums were A=3.865/3.910 s versus B=4.135/4.129 s. Rotation compensation reduced them to 269,798, yet remained slower: A=4.190/4.320 s versus B=4.481/4.539 s. Forces, gap bounds, interpolation weights and potential matched exactly at every sample. This was geometry replay, not a dynamic trajectory or full-solver timing claim.

The active inside clearance had median 5.57e-6 mm, whereas the next global maximum surface motion was about 3.34e-5 mm. Nearly every inside point already had a positive certificate, so merely increasing clearance-query coverage is not the leading fix. Global motion bounds expire too quickly in this tested configuration. The prototype was removed from production code and retained as a recoverable private patch. Reconsider tighter spatially local certificates only with complete coverage proof and a whole-step benefit; do not retain extra cache/State complexity for a query-count improvement alone.

Edge-graded spatial diagnostic (2026-10-22)

An optional research mesh clusters coordinates near patch/support edges while preserving the physical patch, periodic face matching and default uniform fixture. The independent linear exact-constraint diagnostic gives forces 27.7036, 25.5705, 24.6039, 23.7530 and 23.3888 N for 8, 12, 16, 24 and 32 cells per edge. All patch reactions remain compressive; residual/gap bounds remain below 2.7e-13 / 1.1e-16. This is a separate discretization study, not an equivalent-execution speedup or proof of a converged continuum value.

The complete graded 12-cell, 256-increment finite-J2 cycle also meets the original penetration/complementarity bounds: maxima 4.711e-9 / 9.678e-8. Final reaction magnitude is 4.13932494 N and reference-volume-weighted PEEQ is 0.06307447. It takes 2634 Newton iterations and 962 augmentation updates. Unlike the uniform grid, graded elements require physical-volume weighting, not an arithmetic average of quadrature-point PEEQ. The tool now makes that distinction explicit. One graded mesh does not close spatial convergence; the uniform 12-cell force is 4.17988201 N and the uniform 16-cell force is 3.97145647 N, so agreement with one coarse result is not an accuracy criterion.

Evidence: 2026-10-22-independent-linear-graded.json and 2026-10-22-affine-j2-graded12.json under evidence/contact/. The fixture's graded option and periodic affine coordinate mapping pass 13 targeted tests together with the existing affine equilibrium reuse regressions.

The graded 16-cell/256-increment cycle finished on 2026-10-23. All 256 increments meet the original numerical contact gates (maximum penetration 4.689e-9 m, complementarity 9.866e-8). It takes 3148 Newton corrections and 1282 outer updates. Final reaction magnitude is 3.85809815 N, versus 4.13932494 N on graded 12: 7.2893% difference relative to the finer grid. The first loading peak differs by 3.7488%; final volume-weighted PEEQ differs by 0.4579%. Neither the smaller PEEQ difference nor successful nonlinear convergence substitutes for reaction convergence. Evidence: evidence/contact/2026-10-23-affine-j2-graded16.json.

This grading experiment does not close the spatial gate. Do not initiate another expensive graded cycle solely hoping to meet a percentage. The next discretization study must separate volume interpolation and boundary multiplier approximation. The current AL adapter explicitly owns a coalesced P1 nodal trace with disjoint reduced rows. Merely changing the volume to P2 leaves unconstrained midside contact/periodic degrees of freedom or violates that multiplier contract. A higher-order comparison therefore needs a compatible trace and periodic constraint construction, not a degree flag in this example. Adaptive plastic-contact examples such as deal.II step-42 inform the next study; their small-strain formulation and estimator are not an independent reference for this finite-J2 cyclic problem. External-code comparison and a converged spatial reference remain open release claims.

Retained material response, not a lagged Jacobian (2026-10-22)

The serial affine AL Procedure can request reuse of an unchanged built-in J2 response between outer equilibria. The transaction owns a one-shot, SHA-256 buffer guard scoped to that attempted equilibrium. It includes evaluated old/new gradients (so live expression inputs are checked), material identity and parameters, time, old/trial internal state, current stress, tangent, energy and diagnostic fields. Raw field storage avoids copying quadrature arrays merely to inspect them. No result array is cached or re-owned.

Every changed Newton displacement still receives its current constitutive update and tangent. A changed writable response buffer invalidates reuse too. Commit, rollback, restart, failure and leaving the scope discard retention; mixed pressure, regional/user material and MPI keep ordinary refresh. A failed optional guard falls back to that same refresh/error path. The guard is operational evidence, not a new scientific checkpoint identity or tolerance. Contact residuals and global tangent assembly are never reused by this change. This differs from PETSc Jacobian lagging, which deliberately changes how frequently the nonlinear Jacobian is rebuilt.

The first source checks pass 24 mutation/lifecycle/trajectory tests and the 18 existing AL/MPC exact-reference, restart and failure tests. These are scoped source results, not a new installed release or a continuum-accuracy certificate. tools/benchmark_retained_material_trial.py compares the actual implementation against normal recomputation, including the guard cost; it does not extrapolate the implicit-path speedup to the explicit composite run.

After adding callable and field-space identity guards, the fresh 12-cell, 32-increment ABBA confirmation records A=208.220/211.357 s and B=173.141/172.245 s: 17.68% less elapsed solve-and-observe time on this machine and implicit route. Both candidates reuse 116 unchanged material trials; all four runs take 355 Newton iterations and 32 accepted increments. U, committed internal variables, first Piola stress, algorithmic tangent, normal pressure and work histories are exactly equal at four common stations. Source hashes and thread settings are in evidence/performance/2026-10-22-retained-material-trial-confirmation.json. The smaller first screen measured 14.47%; these are different workloads, not additive speedups and not claims about explicit composite throughput. The final focused source group passes 37 tests covering retained response, affine assembly reuse and independent linear-reference amplitude scaling.

Independent spatial diagnostic (2026-10-22)

tools/diagnose_periodic_contact_spatial.py keeps the supported periodic mesh, patch and affine constraint elimination, but removes both plastic integration and normal augmentation. It independently assembles small-strain Hooke elasticity and exactly imposes the known active nodal patch. All contact reactions must be compressive; a tensile reaction rejects that assumed active set. It is a research diagnostic, not a replacement public contact solver.

Cells/edge	Contact force (N)	Edge-node share of contact force
8	27.73441371	81.38%
12	26.05503776	71.16%
16	25.21188874	63.84%
24	24.37327238	54.06%
32	23.95763141	47.70%

The free residual norm stays below 9e-14 and imposed-gap error below 2e-16 m. The reaction trend therefore persists without plasticity, penalty or an AL stopping criterion. This narrows the investigation to the spatial formulation and physical fixture; it does not by itself distinguish bulk approximation, boundary-patch discretization or edge regularity. The finite-Hencky material differs from this linear law, so numerical equality with the J2 fixture is neither claimed nor required. Keep the finite-J2 continuum-accuracy gate open. Evidence: evidence/contact/2026-10-22-independent-linear-spatial.json and evidence/contact/2026-10-22-independent-linear-spatial-fine.json.

2026-10-22 independent confined plastic-contact reference

tests/test_contact_plastic_coaxial_reference.py supplies a scalar reference independent of AgentFEM's material, contact and equilibrium implementations. For a homogeneous, transversely confined column, write F=diag(lambda,1,1) and Fp=diag(exp(p),exp(-p/2),exp(-p/2)). Quadratic Hencky elasticity and associative linear-hardening J2 then give q_trial=2*mu*log(lambda)-3*mu*p_old, delta_gamma=max(0,(abs(q_trial)-yield-H*alpha_old)/(3*mu+H)), p=p_old+sign(q_trial)*delta_gamma, and alpha=alpha_old+delta_gamma. The independent nominal stress is P11=(K*log(lambda)+2*mu*(2*log(lambda)/3-p))/lambda. A scalar bracketed root enforces P11 + penalty*max(0,u-gap) = applied_reference_traction.

The 32-increment cycle includes compression/tension reversal, contact opening and recontact, with genuine forward and reverse plastic flow. At every accepted station, two P1 mesh sizes and both analytical-plane and certified closed-face integration compare displacement, all nine Fp components, PEEQ, stored yield_stress*PEEQ dissipation and integrated contact force against that reference (2e-9 absolute / 2e-7 relative for fields/state/resultants). All four FE paths and the scalar path-coverage test pass. No material parameter or acceptance tolerance was fitted to the computed FE response.

This extends the earlier elastic-only spring reference to cyclic plastic history. It does not validate noncoaxial flow, curved feature transitions, MPC, a general energy closure or the inhomogeneous spatial convergence gate. The underlying multiplicative-plasticity framework is described by Simo (1992); the confined scalar fixture above is an explicitly derived test, not a claimed published benchmark.

2026-10-22 separated time/space refinement

The finite-area-supported periodic J2/plane fixture now has both 128- and 256-increment paths on 8- and 12-cell meshes, plus a complete 16-cell, 256-increment path. The refined study explicitly selects MUMPS after the same-model backend comparison below; its numerical and physical inputs otherwise match. All accepted stations meet penetration 1e-8 and complementarity 1e-7, including opening, unloading and recontact.

Cells per edge	Increments	Final force magnitude (N)	Displacement L2	Mean PEEQ	Signed relative-gap work (J)
8	128	4.38449911	0.0110007384	0.0635272994	-7.27418e-5
8	256	4.46981161	0.0110002343	0.0635578553	-1.86169e-5
12	128	4.09973201	0.0111094465	0.0631515272	-8.04070e-5
12	256	4.17988201	0.0111101705	0.0631811981	-1.89452e-5
16	256	3.97145647	0.0111379022	0.0629464910	-2.05871e-5

On the 12-cell mesh, 128→256 changes final reaction by 1.9175% and mean PEEQ by 0.0470%, relative to the finer path. At 256 increments, 8→12 changes reaction by 6.94% and mean PEEQ by about 0.60%, relative to the finer mesh. The next 12→16 comparison changes reaction by 5.2481%, mean PEEQ by 0.3729% and displacement L2 by 0.2490%. Reaction differences decrease, but this does not establish an asymptotic convergence rate or close the accuracy gate. Thus the spatial reaction gap is not explained away by the earlier coarse increment path. Time refinement reduces signed relative-gap work magnitudes on the 8/12-cell meshes; spatial refinement is not monotone in that quantity. It is not plastic dissipation or a general first-law certificate. Peak pressures/PEEQ are not substituted for these integral comparisons.

Evidence: 2026-10-22-supported-periodic-time-refinement.json and 2026-10-22-supported-periodic-refinement-12-mumps.json, plus 2026-10-22-supported-periodic-refinement-16-mumps.json. The 12-cell paths accepted 128/256 increments with 1271/2288 Newton iterations. The 16-cell path accepted all 256 increments with 2626 Newton iterations and 977 augmentation updates, in 3634.224 s. Maximum accepted penetration/complementarity are 8.813e-9 / 9.971e-8, within the original 1e-8 / 1e-7 bounds. Elapsed durations are scientific-study provenance, not an isolated speed comparison. Gate 8 remains open: next compare spatial discretization/contact enforcement at a fixed resolved path and retain the external same-input comparator gate. Do not lower accuracy requirements merely to promote this release target.

Elastic-limit diagnostic: the spatial gap is not plastic history alone

2026-10-22-supported-periodic-elastic-limit.json keeps the supported geometry, elastic constants, 40,000 penalty and original acceptance tolerances, but explicitly changes yield stress from 2 Pa to 1,000,000 Pa. This is a separate physical diagnostic, not a replacement material or an acceleration candidate. Both 8/12-cell, 32-increment cycles finish with exactly zero PEEQ and zero MPC mismatch. Final reactions are 27.18411331 / 25.52207474 N: a 6.5122% difference relative to the finer mesh despite no plastic flow. Displacement L2 changes only about 0.0295%. The elastic first/final loaded stations agree to numerical tolerance, unlike the history-dependent plastic cycle.

Therefore plastic integration alone cannot explain the spatial reaction gap. The same-mesh exact active-normal elimination now supplies that discriminating check. In test_affine_normal_augmentation_research.py, augmented/exact resultants are 27.1841132431 / 27.1841132697 N on 8 cells and 25.5220747284 / 25.5220747419 N on 12 cells. Displacement, state and nodal pressure comparisons also meet the pre-existing reference tolerances. Thus the elastic spatial reaction gap persists under exact enforcement of the same nodal constraints; incomplete augmentation is not its explanation. This does not prove continuum convergence, remove edge singularities, establish a general inf-sup condition or identify locking. The external comparison stays open.

The direct full-load diagnostic initially exhausted 60 outer updates on the 8-cell case (complementarity 3.462e-7, required 1e-7), while the 12-cell dense diagnostic exceeded its default 4096-DOF budget. The corrected diagnostic explicitly permits 120 outer updates and 8192 dense DOFs, without changing physical parameters or tolerances. A separate constructor misuse in the test harness was rejected and corrected. These are test-only budgets; the public 32-increment cycle above retains its 60-update policy. Five exact-elimination cases pass in 101.46 s, including the three earlier plastic discrete checks. Evidence and retained failure summaries are in 2026-10-22-exact-normal-elimination.json.

For the next discretization decision, compare a fixed physical patch and integrated reaction, not only nodal peak pressure. MOOSE distinguishes node/face enforcement from mortar surface discretization and documents the conditioning tradeoff of penalty parameters. These are useful design alternatives, not evidence that mortar is already needed here or that a larger penalty repairs a spatial error. First isolate the current discrete constraint from the continuum approximation; any later surface method must retain the same State/Result contracts and earn its own patch, force/moment, tangent and convergence evidence.

2026-10-22 linear backend and option-transport audit

The public Newton adapter silently dropped explicitly supplied inner linear rtol, atol and max_it on SNES; the affine adapter dropped atol. Both now preserve these controls. A real SNES regression inspects its actual KSP tolerances, not just a Python options dictionary. Explicit affected policies receive a versioned identity; a legacy-policy checkpoint is rejected before mutating accepted state, while a corrected checkpoint resumes equivalently. Unspecified default policies retain their old identity. The focused solver, affine lifecycle and standard/periodic finite-J2 suite passed 146 tests.

The sequential, same-input screen in tools/benchmark_affine_linear_policy.py uses the finite-area-supported periodic fixture, 16 increments, penalty 40,000 and unchanged nonlinear/contact tolerances. Four common stations compare displacement, committed material state, nodal contact force and relative-gap work. The default actual backend was PETSc's built-in serial LU, not MUMPS.

Cells per edge	PETSc LU	MUMPS LU	GMRES/ILU	Newton iterations for each
8	24.703 s	20.011 s	18.759 s	149
12	187.329 s	83.448 s	70.722 s	173

These are single sequential screens, not statistically established universal speedups. The 12-cell MUMPS screen used 55.45% less solve time, while GMRES/ILU used 62.25% less; all four stations satisfy the predeclared 1e-7 absolute/relative comparison and the observed maximum state difference is below 5e-13. The iterative route explicitly uses linear rtol 1e-12, atol 1e-14 and at most 1,000 iterations per correction; it performs 13,170 linear iterations on the 12-cell case. Results are in 2026-10-22-affine-linear-policy-screen*.json. This is an implicit solve finding, not an explicit-composite acceleration. No core default or scientific input is changed. MUMPS is selected explicitly for the subsequent refined scientific study, and its policy is stored in that study's report. Backend choice does not close the continuum/comparator gate.

The implementation reuses the existing PETSc-backed public policy, following PETSc's optional MUMPS backend and GMRES. Neither documentation promises these timings; they are local observations.

Next implicit cost hypothesis, not a selected optimization

A one-second read-only stack sample of the 16-cell refinement finds both MUMPS numeric factorization and small tensor algebra in the live execution. It does not establish whole-path percentages. Source inspection confirms that FiniteStrainJ2StateTransaction.refresh_trial requests the full material response, including its tangent, on trial refresh. Before extending another backend, count which residual/line-search evaluations actually need that tangent. A future stress/state-only request must be explicit in the material contract; never fill a missing tangent with zeros. A later Jacobian request must produce the derivative of that same trial from fixed committed history. Ordinary nonzero-BC lifting and mixed-pressure transformations currently use the tangent even outside a matrix assembly, so they cannot inherit a shortcut without their own dependency checks. Start with a bounded affine residual path only if a profile establishes redundant tangent work.

This is a candidate research direction, not implemented acceleration. The explicit composite response-only path already avoids algorithmic tangents; neither this idea nor a different KSP can be credited as an improvement to that explicit run. The separate elastic-limit fixture diagnostic varies only the declared yield stress to help distinguish spatial effects associated with plastic history; it must not replace the original plastic acceptance problem.

If factorization remains dominant on the larger mesh, collect the actual ordering, fill, numeric-factor time and memory before selecting another backend. MUMPS documents ordering and scaling, and PETSc exposes its controls. These are scoped solver-policy candidates, not permission to change global PETSc options, freeze an obsolete tangent, or assume symmetric positive definiteness in plastic/contact corrections. Compare total nonlinear work and the accepted trajectory, not only one successful factorization. The serial loop already calls PtAP(..., result=reduced_tangent) within each equilibrium solve; proposing that same reuse again is not a new optimization. Any longer-lived matrix-product cache must establish invariant sparsity and constraint reduction, and invalidate when either changes. PETSc's matrix-product reuse is distinct from retaining old numerical factors.

Gate	Current evidence	Still needed for promotion
1. Comparator	Internal/public-protocol tests; elastic and small-displacement published cases screened but not misidentified as finite-J2 comparators	Independent same-input finite-J2 contact run and frozen observables
2. Surface	Reviewed closed/open triangle geometry, bounded initial-overlap checks, and per-face same-plane proof with one bounded fallback subdivision	Rims, unsupported curved tools, ambiguous sharp features and target-path sliding coverage
3. Integration	Planar/convex partitions; certified zero-contact and smooth-branch faces; private wholly-interior and single-plane partially active reentrant edge/face local integral and tangent; bounded adaptive interior-ball cover; whole-face smooth numerical-touch admission	General active boundaries and feature sets; global signed-gap Step admission; other edge/point laws
4. Normal law	Penalty Step; opt-in ordinary serial P1 fixed/translating-plane AL Step, coalesced nodal multiplier, outer Newton lifecycle, joint restart and accepted tool/relative-gap work; bounded disjoint-normal-row MPC admission with exact active-constraint reference and cyclic restart; real-mesh/reduced-rank counterexamples retained	General multiplier space and transfer, overlapping-row MPC/curved/rotating admission, spatial stability and wider-path work accuracy
5. Friction	Locally planar Coulomb State; rigid-master spin transport tested; a separate smooth point tool can slide beside a frictionless certified-face tool	Admitted geometry-by-friction matrix; friction on sharp features remains rejected
6. Transaction	Total-system and restart tests for admitted penalty modes; opt-in serial standard-J2 certified-face research Step with work, plastic-history rollback/restart and two named tools; smooth-subset affine/MPC total-system path, now including a prescribed moving face; certified-face plus point pair in serial standard J2 and smooth MPC, including separate point-friction State	Sharp-feature MPC, MPI, changing feature topology and wider path tests
7. Result	Pair work/pressure samples; constant-normal plane AL signed relative work, prescribed tool work, discrete absolute-work bound and raw/contact-aware residuals; standard and affine/MPC research face-location extensive evidence and accepted-station coverage without point pressure	Cross-law first-law, between-station coverage and a defensible pressure interpretation
8. Science	Local/oracle/installed tests; independent elastic and cyclic confined plastic histories; separated inhomogeneous space/time refinement through 16 cells and 256 increments; moving-tool/restart screens; directional refinement through 128 slave faces	Full mesh x increment x law convergence and external observables
9. Release	Scoped solver screens; remote Linux and local macOS installed-wheel checks; unchanged explicit full trajectory with 25 verified frames; closing 0913ab9a installed regression	Final frozen release-candidate acceptance and bounded contact scientific gates; explicit runtime does not certify implicit contact

“Partial” here is not a release status. The test target, geometry and enforcement must all match before a gate can be marked closed. The new test_contact_face_science_research.py compares an opt-in certified closed-triangle face Step against the independently solved scalar equilibrium 1000 log(1+u)/(1+u) + k(u+0.05) = 30 for a homogeneous slender column with Poisson ratio zero and a strictly interior initial face. At k=500, the two tetrahedral meshes and one/three increments all give u=0.00334447328517 versus scalar root 0.00334447328519 (relative error about 5.7e-12); k=250/1000 also agree to better than 9e-12 relative. Contact potential matches the independently integrated k A (u+0.05)^2/2. Homogeneous deformation is represented exactly by both meshes, so this is a useful same-input spring-limit test, not a general mesh convergence study or an external finite-element code comparison. The companion Poisson-ratio-0.3 clamped column is deliberately inhomogeneous. At one/three increments and one/two/three cells across its cross-section, the whole-face closed tool and independently assembled analytical-plane backend agree in displacement and penalty energy to their declared tolerances. Its closed-tool center displacement changes from 0.00303999393425 (one cell) through 0.00319348675388 (two) to 0.00324430311741 (three); the penalty energy changes from 0.00703287986482 through 0.00707388762374 to 0.00708738984529. This is a directional refinement screen, not proof of the asymptotic limit. The same unchanged nonuniform setup was also run manually at four and eight cells per edge, the latter using exactly the declared 128 slave-face cap: center displacements 0.00326938245543 and 0.00330647510339, and penalty energies 0.00709406772191 and 0.00710395068898. The closed tool and analytical plane still agree at the eight-cell station. Differences along the 1/2/4/8 sequence decrease, but this one path has no independent continuum-limit solution and does not cover a changing active set or a plastic/damaged body; it does not close the release science gate. Nine focused inhomogeneous column comparisons now vary one, two or three cells per edge, one or three increments and penalties 250, 500 or 1000, according to the explicit test matrix. The independently lowered analytical plane and closed-triangle face agree in displacement and final penalty energy at each tested station. At two cells and three increments, the closed-tool center displacements for these penalties are respectively 0.01346611117, 0.00319348675 and -0.00958666389; penalty energies are respectively 0.00503498730, 0.00707388762 and 0.00816611425. This sensitivity is why a matched penalty must be frozen for any external comparison. Agreement between two representations of the same penalty law is not a zero-penetration limit or an independent finite-J2 validation. An added plastic clamped-column screen keeps six load increments, penalty 500, Poisson ratio 0.3 and J2 yield stress 1 across 1/2/3/4 cells per edge. The certified closed-face and separately lowered analytical-plane backends agree in displacement, committed material vectors and penalty energy at all four mesh sizes. Their closed-face maximum PEEQ values are about 0.04114/0.05617/0.06391/0.06384 and final contact potentials about 0.006190/0.005772/0.005874/0.005878. This is a useful plastic path and spatial sensitivity screen, not an external code or continuum-limit proof. The three-cell first increment required 34 Newton iterations; the previous 25-iteration cap rejects that input, so this screen explicitly declares a 100-iteration cap rather than concealing the extra solver work. A four-cell three-increment attempt also failed its line search. Contact integration agreement must not be mistaken for robust default solver convergence; yield-onset and increment-policy sensitivity remain open Gate 8 evidence. One additional two-cell/three-increment plastic path starts with a zero-gap closed triangular tool, translates it into the body and compares every accepted station against the separately lowered moving analytical plane. Displacement, committed J2 state, contact potential and cumulative tool work agree at the declared tolerances; tool work is nonzero. A checkpoint after the first accepted increment resumes to the same final displacement, plastic state, work and face-path evidence as the uninterrupted closed-tool run. This tests joint moving-tool/material lifecycle for a smooth face, not a changing edge/vertex feature or an external-code result. In a separate three-cell trial, automatic cutback from 1/6 with the 25-iteration cap exhausted eight cutbacks at a line-search failure; simply reducing the increment is therefore not a demonstrated remedy for this near-yield path. With the same declared automatic controls but a 50-iteration cap, it completed in seven accepted increments; the highest Newton count was 34. A fixed-old-State directional difference at the converged first-increment displacement, probed on both sides of the elastic/plastic return and restricted to free DOFs, matches the total J2-plus-certified-face tangent. The initial diagnostic appeared inconsistent only because it mistakenly perturbed strong Dirichlet DOFs while comparing a BC-eliminated matrix; the corrected check is now a regression. This case does not establish that the default 25-iteration globalization is robust. PETSc SNES offers several globalization rules rather than one backtracking policy; deal.II step-42 couples plastic-contact active sets with a safeguarded Newton path, while MOOSE's radial-return documentation distinguishes material-point substepping from discarding whole global increments. None is a drop-in fix for this observed case. The same three-cell/six-increment input now has a paired globalization regression: the existing basic Newton choice completes with the declared 25-iteration cap, whereas backtracking needs a declared 50-iteration cap. Their accepted displacement, committed plastic state, contact potential and external work agree to the test tolerance. A second two-cell/three-increment regression starts from exact zero gap and enters active contact; the same accepted-state comparisons pass under both globalization choices. On the first increment of the initially closed three-cell case, the observed Newton counts were 10 and 34 respectively; a separate four-cell, three-increment screen also completed its first increment in 11 iterations with basic where backtracking had failed its line search. This identifies strictly monotone backtracking as a candidate source of difficulty on this near-yield path, not as a generally inferior algorithm. basic can accept temporary residual growth, so the default and release claims remain unchanged. The next gate is a frozen matrix of load paths, active-set transitions, rollback/restart and negative controls before recommending any default globalization change. Raising a cap or changing one line-search option on a single case would conceal rather than resolve this gate. The same benchmark also starts from zero gap and advances into active contact. It permits a zero-force/open-side-tangent trial only when a whole-face coplanar coverage/competitor proof succeeds and the remaining vertex gap is within 8 epsilon * world_scale with the closed projector reporting zero. That numerical convention is recorded on the local certificate and refuses gaps of 1e-8 in either direction; it is not an exact-arithmetic theorem, and it rejects coordinates whose roundoff scale exceeds 1e-8 of the local face size. The initial contact tangent selects the zero/open-side generalized derivative at the penalty kink; every subsequent trial recertifies its branch. These statements are limited to the opt-in research route, and unproved rims or sharp transitions still fail closed. For a face that has a separate whole-face smooth-plane certificate, the two-feature research Operator now reuses the existing affine active-triangle clipper. Its P1 normal gap is affine and its penalty potential is quadratic, so the positive degree-two rule integrates the active reference area, residual and fixed-branch tangent without a conic two-feature partition. This is per-face dispatch from a fresh current-configuration proof, not a cached contact projection or an assumption that every tool is planar. A partly active face passes a re-partitioned potential-gradient and tangent finite difference; the reentrant two-feature regressions still take their original branch. A bounded immutable Gauss-rule cache also removes repeated Legendre-node generation without changing the rule. The reproducible tools/benchmark_certified_face_step.py alternates both certified routes on the same two-cell, three-increment J2 model, checks equal displacement and contact energy, and after two warmup pairs measured eight pairs on one Apple Silicon FEniCSx host: medians 0.7324 s (certified two-feature reference) versus 0.3043 s (smooth-face dispatch), about 2.41x for this small research Step. The ordinary analytical-plane Step on that model remains faster; this is neither a production speed claim nor an estimate for sharp-feature models, which correctly retain the more expensive rule. The certified-face provider now keeps only its last immutable trial and reuses it when the displacement, reference positions, rigid-motion factor, pair/tool identities and numerical settings match exactly. A changed Newton state or pose forces a new whole-face proof; the cache is neither checkpoint State nor a contact-neighbor approximation. The paired tools/benchmark_certified_face_trial_cache.py disables just this reuse in its reference run. On one Apple Silicon FEniCSx host, three-increment serial research Steps with 2/4/8 cells per edge had recompute/reuse median times 0.306/0.167, 1.215/0.674 and 5.740/3.582 seconds respectively, about 1.83x, 1.80x and 1.60x. The 8-cell case reaches the declared 128-slave-face cap. Geometry-proof calls dropped from 32/34/35 to 13/15/16; the paired script checks the same solution, committed material vectors, contact energy, face path and work history. These are small bounded research solves, not an Abaqus comparison or a production/full-geometry speed guarantee. Other models may spend little time in redundant face proofs. The reentrant-tool sample carries an engineering quality failure whenever a sampled slave face crosses nearest features without a certified transition integral. Release additionally requires a certified integral even if no switch or active point happened to be sampled. Exploratory inspection remains possible; an absence of sampled switches is not a whole-face certificate. For a reviewed closed solid, a current first-order slave face can now instead be certified strictly separated by an adaptive 1-Lipschitz signed-distance bound. A rigid-pose-aware complete AABB separation is checked first, so obviously distant faces require no nearest-feature/winding point query. That proves its normal contact integral is exactly zero at that accepted configuration. A manufactured counterexample with three apparently separated ordinary Gauss points and a penetrating face corner is correctly not certified. An unresolved budget, ambiguous projection, or any near/active contact leaves the integral uncertified. This is not a between-increment path-intersection proof and does not admit active nonconvex contact, friction, or lower-dimensional edge/point laws. Its reference geometric cost also is not a large-CAD performance guarantee. There is now a separate, deliberately stricter active subset: for a reviewed closed tool, each current affine slave triangle must project inside a completely covered coplanar master patch; its nearest-plane distance must beat every noncoplanar master facet by more than twice the slave-face radius (plus numerical margin). The difference of two distance-to-set functions is 2-Lipschitz, so this inequality certifies the closest feature over the whole face, not just at Gauss points. Distinct slave faces may select distinct certified master planes, but one face cannot cross a sharp feature. The patch check subtracts the union of coplanar master triangles from the projected slave polygon with a bounded halfspace clipper; an overlapping master-patch area sum is not accepted as coverage. It admits a flat triangulation seam but rejects a positive-area gap or proof-budget exhaustion. This is a bounded floating-point coverage certificate, not an exact-arithmetic CAD topology proof. It follows the classic reentrant polygon-clipping idea of Sutherland--Hodgman, adapted to subtract a triangle union rather than to integrate a second contact surface. The current Newton trial may then reuse the already proved analytical-plane active partition, with the closed solid's own signed-gap projection checked against each plane. Geometry proof is repeated on each trial and rigid pose. A real serial finite-J2 solve has matched the corresponding analytical plane in displacement, PEEQ and tool work, with a contact directional tangent, interrupted restart and explicit reentrant-edge rejection; the small runnable example exports one XDMF grid and unsmoothed contact samples. This does not solve a feature switch or physical edge/vertex contact: those remain rejected. The current per-face smooth-branch and 1024-slave-face/4096-master-facet bounds are intentionally narrow, and this is not an external commercial-solver comparator. The closed-solid projector now takes the reviewed facet normal directly on a smooth face, including a coplanar seam. Dividing a nearly zero point-to-foot vector by the gap previously amplified tangential roundoff and made strict projection/plane comparisons fail near closure. The geometric edge/vertex branch and the signed-gap classifier are unchanged. A near-gap two-sided normal regression and a serial finite-J2 seam-crossing Step exercise this numerical correction. The whole-face smooth-plane proof has now also been exercised on a reviewed open oriented triangle sheet through a distinct reviewed_planar_branch_partition mode. It uses the same complete coplanar coverage and noncoplanar competitor bound, but its gap is the sheet's one-sided oriented gap, not the closed solid's signed inside/outside distance. Serial finite-J2 tests compare displacement and tool work with an analytical plane through a coplanar seam, moving rotation, two simultaneously active named tools and interrupted restart. A face extending beyond the sheet's rim is rejected. A periodic-MPC J2 solve also checks the total reduced residual against the analytical plane. This advances the reviewed-surface slice of Gate 2; a true edge/rim law and general active nonconvex feature switch remain open Gate 3 work. The ordinary serial Step now also accepts an exact-name mapping from rigid contact pairs to their already admitted integration modes. A missing or unknown pair name is an early capability rejection, never a fallback to sampled Gauss integration. Each lowered pair retains its own mode in checkpoint identity; a two-tool mixed-mode finite-J2 path and interrupted restart exercise this composition. A separate two-active-tool regression now checks independently integrated pair forces, positive per-tool work, total work sum and joint restart while one tool uses the certified closed smooth branch and the other uses an analytical planar partition. A small rigid rotation of the closed tool also matches its equivalent analytical plane in a real finite-J2 Step. The serial periodic-MPC J2 route now admits this one named scalar mode on a wide reviewed smooth patch, with total-residual reduction, analytical-plane limit, interrupted restart and explicit reentrant-edge refusal tested. The affine route now also uses the same exact-name per-pair mode contract: one closed smooth branch and one analytical plane can enter a single total MPC system, survive interrupted restart and refuse a changed mode identity. This remains serial and does not admit a sharp-feature transition merely because the second tool is supported. The same-plane proof now uses the immutable triangle BVH to discover only facet boxes that can intersect the projected slave polygon or lie within abs(gap_at_center) + 2 * slave_radius + numerical_margin of its center. The 2-Lipschitz exclusion inequality and exact closest-triangle narrow phase are unchanged; a rejected box is a lower bound, never an assumed old contact state. A paired, alternating eight-repeat serial component screen on one Apple Silicon FEniCSx host, with 1024 small slave faces, measured median certificate times of 0.203/0.203 s (old/new, 1728 master facets) and 0.299/0.241 s (old/new, 3888 master facets). The latter is about 1.24x for this geometry-proof component near its declared 4096-facet cap. It does not measure full finite-J2 solve speed, improve the cap, or establish portability to another mesh or computer. The broad-phase candidate lists are also compared against exhaustive facet boxes in a deterministic test. For a nearby facet that fails the center/2r exclusion, the proof now has a second conservative route: the other facet's infinite plane is no farther than its finite triangle. The difference between its squared plane distance and the selected plane's squared distance is a quadratic over a P1 slave face. Six degree-two Bernstein coefficients bound that difference over the whole face. A strictly positive lower bound excludes the competitor without subdivision; an inconclusive bound retains the old subdivision or fail-closed result. One open-sheet and one closed L-wall fixture that previously needed refinement now pass with refinement depth zero, while a manufactured truly competing facet still rejects. A three-vertex-only distance test is separately shown to miss an interior competitor. This is still a single-smooth-branch certificate, not a conic feature-switch integral. For a finite competing triangle whose nearest-point KKT conditions place the whole slave face in one edge or vertex Voronoi region, the exact squared distance to that fixed feature is also quadratic. A second six-value bound may therefore exclude that finite competitor even when its infinite plane intersects the slave face. If the Voronoi region changes or the bound is within the numerical safety margin, the old subdivision/fail-closed route remains. This admits a formerly rejected near-reentrant face that is actually on one smooth plane; a face truly crossing the reentrant feature is still rejected. The near-edge numerical-budget fixture also still refuses an unproved branch. Edge/vertex competition here is not an active edge or vertex contact law. A six-increment serial finite-J2 model.step now also exercises a reviewed open sheet with this finite-vertex competitor: the whole-face certificate passes at refinement depth zero, disabling only the finite-feature bound restores the old coarse refusal, and the accepted displacement and tool work match an analytical plane. This checks the Model-to-Result route for this smooth subset, not a transition law or an external solver comparison.

The reproducible paired component screen tools/benchmark_planar_branch_certificate.py alternates the original subdivision route (both quadratic shortcuts disabled) and the new bounds at the same maximum refinement depth. On one Apple Silicon host, 200 measured pairs after 20 warmup pairs gave 0.911/0.290 ms medians for the infinite plane competitor and 1.649/0.309 ms for the finite-vertex competitor (reference/new). Both modes certify the same plane. The ratios, about 3.1x and 5.3x, apply only to these individual geometry proofs, not the full nonlinear solve. Other geometry can incur the six-value checks and show no gain; no full-solve speed improvement is claimed. An independent smooth-geometry branch is now under bounded evaluation. Even with an exact analytical sphere/cylinder projector and curvature tangent, three fixed Gauss points on a P1 slave face can all be open while a small positive-area circular contact patch is active. The opt-in radial_active_partition derives the active region from the radial distance-squared quadratic, splits the reference triangle at conic tangency and edge events, and uses positive 12/24-order quadrature. It screens the per-face potential, nine nodal residual components and 81 tangent entries against each other; inconclusive integration, an axis/center singularity, a bounded-cylinder rim or a point budget refuses the trial. The paired-order screen is not a rigorous error bound and cannot license general curved contact. A declared initial-penetration limit now uses exact affine-face radial extrema (closest point to the center/axis and maximum vertex radius), not sampled points; the 0.001/0.0009 sphere-overlap regression catches a patch that ordinary Gauss sampling missed. Independent circular-patch area, potential, force and tangent formulas at three heights and full-nodal finite differences check the local operator. A vertex-centered quarter-circle, a patch clipped by a slave edge, rigid-frame and length-scale changes, and a real-Step directional tangent exercise the less convenient geometries. Real serial finite-J2 Steps demonstrate both a sphere patch and a cylinder strip missed entirely by ordinary three-point Gauss; prescribed sphere motion and interrupted checkpoint/restart also pass. This is an analytical smooth P1/frictionless/scalar-penalty subset, not a sharp-feature solution, mesh-converged hard-contact result or external solver comparator. In the one-cell sphere regression the opt-in mode initially has 1152 positive-weight active points and finishes with maximum displacement 1.75747e-5 and contact potential 4.94207e-7; the otherwise identical three-point Gauss mode reports zero active points, displacement and contact potential. Those values expose a sampling failure in this manufactured geometry, not an accuracy/performance benchmark for a production model. The conic split now lives in a geometry-neutral contact_quadratic_region primitive. On the independent research oracle where a finite edge and a vertex exchange nearest-feature ownership along a parabola, its two positive branch integrals reproduce the oracle's potential, nodal residual and within-branch tangent at zero and nonzero in-plane nodal displacement. This validates the region integration building block only. A separate positive coarea rule on the quadratic equality boundary reproduces the oracle's moving-boundary tangent at those two states; its circular special case also matches the exact derivative of disk area. A vertical reference-coordinate boundary is handled by transposing the triangle coordinates, with an independent moving-area derivative test; a component singular in both orientations is still refused. The physical feature-specific residual jump and branch admissibility are still supplied by the oracle. The total tangent needs this term in addition to the two bulk tangents; no general sharp-feature Step is admitted by these geometric primitives. This division follows a useful but limited literature lesson: Farah--Popp-- Wall's segment/element mortar comparison treats contact zone boundaries and integration cost together, rather than assuming that more fixed Gauss points always resolve a moving interface. It does not validate our non-mortar P1 penalty rule. More importantly, Konyukhov--Schweizerhof's closest-point analysis shows why a general nonsmooth surface needs explicit edge/corner projection domains and uniqueness checks. Our conic integral handles a given feature division, not the proof that the two supplied physical branches exhaust a real tool's nearest features. A private, solver-neutral contact_feature_pair_research operator now combines that division with the complete bulk-plus-moving-boundary tangent for the squared distance to the union of two infinite affine features. At zero and perturbed nodal displacement it matches the independent parabolic edge/vertex oracle; all six nodal potential derivatives and force derivatives agree with re-partitioned finite differences, and a three- dimensional rigid-frame test checks covariance. The distinct-feature separator has no artificial boundary force, and an exact tie is rejected. All six triangle-connectivity permutations preserve the reordered residual and tangent. The integral's translational resultant and moment about the origin are checked against finite differences of a rigidly translated and rotated pair of features, giving a local virtual-work identity; this is not yet an accepted path-work ledger for a moving tool. This is deliberately not a unilateral contact law: finite edge/face projection domains, closest-feature exhaustiveness, inside/outside sign, initial overlap, physical pressure/work and accepted-state lifecycle are not conferred by an accurate squared-distance integral. Those are the next admission tests before any sharp-feature Step can use this operator. One of those checks now has a private, deliberately bounded implementation: contact_feature_pair_geometry_research takes a finite triangle union and certifies that each of two selected triangles keeps the same face, edge or vertex closest-point branch over the whole current P1 slave face. Its strict KKT inequalities are affine on that face, so checking all three vertices proves the branch region; distance to each fixed affine feature is convex, so its largest vertex distance bounds the selected pair from above. Every other finite master triangle is excluded over the whole slave face by its 1-Lipschitz center/radius lower bound, a common finite feature, a positive quadratic Bernstein bound, or an affine-feature dominance inequality over both convex hulls; otherwise the proof refuses. A separate brute-force nearest-triangle sample grid corroborates an edge/vertex fixture; an intervening third facet, a changing selected branch, degenerate face and unresolvable world-coordinate precision are rejected. This certifies the unsigned distance to a finite triangle union in a tiny selected-facet subset, not the sign of a closed tool or the contact traction. A reviewed surface can have many competing features; forcing its geometry into two selected facets would be unsound. This is a bounded floating-point margin check, not an interval-arithmetic or exact-CAD topology certificate. For a separately attested closed, outward-oriented tool, a winding-classified interior point and a boundary-distance ball now also certify that the whole slave face is inside at the current configuration. Composed with the two- feature certificate, the private local Operator has an actual frictionless reference-area penalty interpretation: on a wholly penetrated face, g=-distance and k*g*dg/dx is the derivative of k*distance²/2. A four-facet closed tetrahedron test exercises this face/face switching law against an independent exact linear-clip integral of min(x,y)², while a face reaching the boundary refuses the interior-ball proof. This is a narrow local physical subset, not a normal project Step or a finite-slip, restart or accepted-path-work validation. The conservative competitor check now also handles an additional facet whose fixed finite feature is exactly the same shared edge, or whose entire fixed-feature squared-distance difference has a positive quadratic Bernstein bound. A reviewed concave L-prism thereby admits one small, wholly interior slave face where its bottom face and true reentrant vertical edge exchange closest-feature ownership. Independent closest-point queries match the two-feature distance over a deterministic reference grid; all nine nodal potential derivatives and 81 tangent entries match re-certified, re-partitioned finite differences, including the nonzero moving-boundary term. The tool is attested embedded, with reference winding sign. This is local evidence for one nonconvex reentrant transition in a deliberately deep-penetration subset. A nearby face crosses the L-prism bottom boundary: its exterior portion is inactive, and the finite vertical reentrant edge ends at a bottom vertex there. The wholly-inside proof still refuses it. A second private path now clips the P1 reference face by one selected, transversely crossed tool-facet plane. It certifies constant opposite winding signs on the two resulting convex polygons by separating every other tool facet plane from their interiors. The finite feature pair is proved nearest only on the active polygon; a selected finite edge may end on the cut only when its endpoint lies on that same plane. The other facets are excluded by the bounds above, including affine-feature dominance for the adjacent wall. The private discovery helper proposes candidate facet identities from current nearest-point queries but returns an integral only after the complete polygon and competitor proof. It does not require a user-labelled special pair of triangle IDs; a missed proposal fails closed rather than falling back to ordinary sampled integration. A small facet budget and a second crossing tool boundary are explicit rejection tests. The first (activation-face) distance and force vanish on the cut, so its moving activity boundary has no distributional force/tangent contribution; the different moving nearest-feature boundary still has its coarea term. The partially active L-prism test checks the winding sign over a grid, re-clips and re-certifies at every finite-difference perturbation, and matches all nine nodal energy gradients and 81 tangent entries. Local tool force matches virtual work for all three small translations; the vertical-axis tool moment and both tilted-axis moments match small rigid rotations after fresh geometry proofs. Exact shared vertices that define a rotated master edge remain shared despite floating projector roundoff; unrelated near edges are not merged. This does not yet cover an arbitrary tool surface crossing, multiple activity planes or general large sliding. The local energy derivative is a structural residual: the force on the structure is its negative, while the reaction on the tool is its positive. The current global ContactTraceAssembly uses the former for prescribed tool-work evidence. This sign mapping is explicit in the private response and must be preserved before any Operator/Procedure admission; a local virtual-work test is not an accepted path-work ledger. contact_face_operator_research now aggregates separately certified partial and wholly active faces into shared global nodal rows and a COO tangent, without pretending that integrated face identities are quadrature-point samples. A two-face patch with shared nodes matches the gradient of its total potential and the derivative of its total force; an illustrative MPC matrix also satisfies Tᵀ K T = d(Tᵀ R)/dq. Distinct tool fingerprints, duplicate physical faces, noninteger identities and raw uncertified distance integrals are rejected. Each local certificate now carries immutable reference and current face vertices; the bridge refuses a stale Newton trial or a response swapped onto another mesh face. Face IDs, partial/whole status, finite feature kinds, reference-active areas and energies remain per-face evidence; none is renamed as a quadrature sample. This is an Operator bridge, not a global contact provider: it does not own Newton trials, accepted states, tool path work, restart, field export or a serial/MPI admission contract. The same bridge now accepts a third, exactly zero face outcome only after the existing strict whole-face separation proof. It records that face's positive gap lower bound; a failed or budget-exhausted proof is never treated as inactive. A batch mixing partial, whole and separated faces retains the complete face list while allocating tangent entries only for active faces; an all-separated batch has exactly zero residual, potential and tangent. Under a common arbitrary rigid change of spatial frame, the two-active-face patch's potential is invariant and residual, tangent action and moment about a transformed reference point rotate covariantly. These are fixed-trial operator tests, not a finite-strain material objectivity claim. The DOLFINx bridge recovers complete physical face IDs and node triples from the existing default positive CG1 tetrahedral contact trace, checking all three point IDs, shape weights and reference area before discarding the quadrature representation. A real unit-cube DOLFINx boundary lowered to two faces and a distant closed tool gave an exactly zero two-face Operator. It rejects a missing point, lumped rule or wrong area rather than making up face coverage. This is an input-identity test, not a loaded global contact solve. One bounded dispatcher now proposes the three proved face outcomes without user-selected master facet numbers. Its nearest-point samples only rank candidates; a complete geometry proof remains mandatory for every accepted face. A short reentrant translation path exposed a missed proposal, not a failed physical certificate: sparse points missed the second finite feature on three partly active states. The dispatcher now tries sampled candidates first and then the remaining pairs within its declared 64-master-facet cap; the full finite-feature/sign proof still gates every acceptance. That path now traverses separated, partially active and wholly active face states, and each accepted response agrees with the corresponding independently selected two-feature proof. This exhaustive fallback may be expensive on an unsupported mesh and is not a production search-complexity claim. Re-evaluating a mixed partial/whole/separated patch after a trial nodal perturbation succeeds with fresh certificates. A face crossing two tool activation planes is refused. This avoids case-owned facet-ID glue while keeping the present small-facet-budget and one-cut limitations visible. The pure complete-boundary trial function composes that dispatcher with verified face extraction and additive Operator assembly. If any face fails, it returns no partial Operator and reports its physical slave_face_id. A real DOLFINx tetrahedron with the two reviewed reentrant-tool boundary faces lowered through this path and reproduced the independently assembled local contact potential; the active faces were classified partial and whole. The companion distant-tool DOLFINx test classified both selected faces as separated. Neither test solves a global J2 equilibrium problem. For each finite-facet competitor, a vectorized slave/master AABB distance lower bound is now checked before the exact center-to-triangle projection. The minimum distance of the two boxes bounds every slave/master point pair from below, while the chosen affine feature's distance over a convex P1 face is bounded above by its maximum at face vertices. A strict gap between those bounds excludes that competitor without an exact query; inconclusive boxes retain the existing KKT/Bernstein proof or refusal. The far-competitor and near-true-competitor tests distinguish safe pruning from false acceptance. No full-solve speedup is inferred from this component change. Fixed-body prescribed-tool paths now re-certify the mixed two-face patch at each quadrature station. Translational, rotational and simultaneous translation-plus-rotation generalized work integrate to the change in contact potential; the simultaneous test takes the moment about the moving tool reference. This confirms the local force/moment sign and reference-point mapping. It is still not a path of accepted J2 equilibrium increments, so neither a total-system first-law claim nor checkpoint/work promotion follows. A real DOLFINx P1 tetrahedral elastic matrix and the certified two-face contact Operator now also enter the same manufactured Newton residual and tangent rows, with strongly fixed degrees of freedom. The converged free displacements match the manufactured solution. This checks FE row ordering and additive local linearization; it is not the finite-J2 Procedure, a line-search/rollback test or evidence that the face law is admitted in model.step(...). The existing point-sampled contact adapter and the private face-integrated Operator now share one narrow serial PETSc insertion routine for already computed nodal rows and COO tangent entries. It preserves the full tangent for prescribed-correction lifting while omitting constrained rows and columns from the inserted matrix; it rejects malformed/nonfinite inputs before mutation. A real PETSc matrix/vector test checks the constrained rows and free block against independent dense assembly, while 122 existing serial finite-J2/contact Procedure regressions passed after the refactor. This unifies the numerical insertion mechanism, not their evidence or accepted-State contracts: the face Operator retains physical face IDs, active reference areas and separate per-face extensive forces/moments, without fabricating contact-point IDs or a smoothed pressure field. For prescribed 3D tool motion, a separate private evaluator now maps the current slave trial into the unchanged tool's reference frame, repeats the complete face proof there and pushes nodal residuals, every 9-by-9 face tangent block, resultant and moment back into the spatial frame. The trial retains the actual motion factor and moving moment reference. Independent reconstruction of the moved triangulated tool agrees at three pose stations; finite differences, combined translation/rotation work and a large rigid frame change give separate checks. Reusing immutable tool topology avoids a per-trial mesh rebuild in principle, but no measured full-Step speedup or accepted-state motion ledger is claimed yet. A narrow private DOLFINx trial adapter now binds one named RigidContactPair, its complete P1 boundary trace and current displacement to that pure face Operator. It refuses friction, nonserial layouts and an initial-overlap limit whose signed-distance face bound cannot be proved within the declared refinement budget. It reuses the existing closed-solid 1-Lipschitz initial gap certificate, rather than interpreting three Gauss samples as the maximum initial penetration. A 0.1 limit is refused and a 0.5 limit is proved on the partially active reentrant fixture. The adapter checks exact pair, displacement and rigid-pose identities again before either PETSc insertion; changing the Newton displacement or tool factor after evaluation causes an addressable failure with no matrix/vector mutation. This creates a real Model-asset-to-Operator-to-PETSc path. The private adapter now also exposes a face-location diagnostics record and the ordinary constraint-dual sign/resultant, including the moving tool's moment about its declared reference point. A real DOLFINx trace checks the fixed and moved duals and pose rollback; these are trial observations, not an accepted-path work ledger or a point-pressure field. For the partially active reentrant fixture, a separate physical-distance quadrature splits the barycentric triangle at zero gap and closest-feature switches. Its potential and nine nodal force components agree with the certified local integral under independent 64/128-point convergence checks. This validates that bounded fixture, not every possible reentrant corner or Step result. The explicit certified_closed_two_feature_research mode now also lowers one named pair into the existing serial standard finite-J2 model.step(...) Procedure. A small real tetrahedral two-face calculation accepts two increments, emits face-location Result metadata (never invented point pressure), and produces a nonzero displacement. Interrupted serial checkpoint/restart reproduces the continuous solution and contact potential. A prescribed translating tool accumulates accepted work and reproduces it after restart; forced failure after energy recording atomically restores the prior displacement, committed material, tool factor and work history. The same checks have now been repeated with nonzero accumulated J2 plastic strain, so material history is not inferred from an elastic-limit test. At each accepted station the Procedure records whether every selected physical face was certified, maximum active reference area and active/mixed face counts. That accepted-station record survives serial restart and rolls back on a failed increment; a corrupted station count is rejected before checkpoint mutation. It does not prove collision-free motion between accepted stations or provide a physical point pressure at a sharp feature. The normal residual/tangent, material and strong-boundary rows share the ordinary Newton path; no second solver was introduced. Two named certified-face tool pairs now compose in that same Step, with separate face evidence, additive nodal force and potential, moving-tool work and interrupted restart. A stale pose on just one pair refuses the whole trial before PETSc mutation. One certified-face pair can now compose with one ordinary frictionless point pair in the same serial Step. The mixed wrapper first checks both displacement and tool poses, then adds separate certified-face and point contributions to the one Newton residual/tangent; a stale mixed trial is rejected before PETSc mutation. A directional difference checks the combined contact tangent. The result preserves distinct face and point diagnostics, two named duals and work records; moving-tool work and interrupted restart match the continuous run. A reviewed smooth point tool can additionally carry its own sliding Coulomb State beside a frictionless certified face. A fixture with active point contact has positive sliding dissipation; serial restart reproduces the displacement and dissipation, and a forced late acceptance failure restores plastic State, point-friction State, pose, work and both path ledgers. A damaged point-ID friction checkpoint is rejected without altering the receiving Step. Friction on the certified face and MPI explicitly refuse this research mode. These tests establish a bounded software lifecycle, not mesh/penalty convergence, an independent global reference, general finite sliding across sharp features, or product release. The accepted point-sample exporter rejects a mixed face/point Step before creating files: a point-only archive would silently omit the face-integrated part of the contact law. Face and point diagnostics remain separately available in the Step result until a face-location scientific archive is defined.

The affine/MPC Procedure now admits the same opt-in face mode for a serial, single-facet smooth closed-tool subset. A larger P1 face that no single interior ball covers can be proved by a bounded longest-edge subdivision: every accepted child lies in a winding-classified interior ball under the 1-Lipschitz distance bound; an unresolved or boundary-touching child refuses the entire face. Eight subdivision levels and a 512-child budget are explicit research limits, not a guarantee for all mesh sizes. On a wide triangular prism, the periodic finite-J2 Step reduces the complete contact/material residual, its reduced contact tangent matches independent directional differences, and its displacement agrees with the corresponding analytical plane. Interrupted restart preserves the accepted face-path ledger; a corrupted ledger is atomically refused. A front-face triangulation seam in a different otherwise smooth tool still fails the stricter two-feature certificate. A normalized prescribed translation of that same smooth face now uses the affine Procedure's ordinary load-coordinate method, rather than a test-owned motion loop. The fixture has nonzero committed J2 plastic strain; its reduced total residual closes, moving-tool work is nonzero, displacement agrees with a translated analytical plane, and serial interruption/restart preserves the solution and work. This does not admit finite-sliding sharp-feature MPC or an arbitrary rigid-motion schedule. Two independently named moving smooth faces also reproduce the single-tool solution when their penalties sum to the same value; per-tool accepted work adds to the single-tool work and survives restart. A second smooth-periodic test combines one certified closed face with one analytical-plane point pair, verifies the total MPC-reduced residual, agrees with the two-plane analytical representation and checks interrupted restart. A distinct periodic test holds the certified face fixed while a separate moving smooth plane slides with nonzero Coulomb dissipation; its restart matches the continuous result. Thus this is not admission of moving-sharp-tool MPC, general coplanar seam coverage or arbitrary industrial mesh contact.

For promotion beyond this research Step, the boundary adapter must keep its complete-face enumeration and current-Newton-trial proof for every selected face. Any unsupported feature set, second activation boundary, ambiguity or proof-budget exhaustion must still reject the trial atomically. The present ContactTraceAssembly requires quadrature point IDs and pointwise contributions; the new face-integral contribution therefore retains a separate face-level evidence record and the existing force/work sign convention. The standard Procedure now adds its total residual and tangent before strong-BC lifting and recomputes at line-search trials, then jointly commits or rolls back material, tool path and contact state. The DOLFINx nonlinear callback contract requires exactly this current-trial assembly DOLFINx nonlinear assembly. No face integral is disguised as three sampled trace points. Sharp-feature MPC, friction on research faces, MPI, between-station path certification, independent global comparison and mesh/penalty/increment convergence remain open. The opt-in research string must not be presented as a released general nonconvex solver; local virtual work is not by itself whole-path first-law closure. The same sphere fixture runs to completion on 1, 2 and 4 subdivisions per cube edge (6, 48 and 384 tetrahedra). The maximum displacement is 1.75747e-5, 2.49116e-5, 4.06294e-5; the final contact potential is 4.94207e-7, 4.84893e-7, 4.69293e-7, respectively. These are a mesh-sensitivity warning, not convergence or a recommended physical penalty: the pointwise maximum displacement changes materially. The exported accepted contact samples explicitly mark their IDs as snapshot-only and their pressure as force per reference area, not Cauchy stress. The initial-overlap bound and trial partition were also checked with the same face scaled from 1e-9 to 1e3 length units. A former absolute max(1, radius) roundoff allowance falsely rejected the small-unit initial limit; it now scales with the analytical radius and coordinate precision. Conversely, a unit-radius sphere translated to a 1e12 world-coordinate offset is refused because the geometry cannot be resolved to the declared integration tolerance in binary64. This is a precision gate, not an automatic rescaling or alteration of user geometry. The commercial analytical-rigid-surface guidance also notes that curved analytical geometry can reduce contact noise/search cost, while discontinuous master normals impair implicit finite sliding. That motivates an explicit model geometry choice, never hidden rounding of the user's specified sharp tool. The contact-boundary quadrature issue is also documented in Duong--De Lorenzis--Sauer's refined-boundary work; their isogeometric/mortar method motivates treating the active boundary, but does not validate this separate P1 radial rule or its paired-order screen. The runnable closed-tool example now has a separate one-axis-at-a-time mesh/increment/penalty sensitivity driver. Its eleven serial synthetic runs all completed with certified smooth branches, but their terminal tool work remains mesh- and penalty-sensitive, while the pointwise maximum PEEQ is not monotone under mesh refinement (details in evidence/contact/2026-10-19-closed-planar-branch-ladder.md). This is evidence against promoting the present tiny fixture as a converged hard-contact or external-solver benchmark. The driver is a reproducible diagnostic, not a release threshold or a performance promise. Both ordinary J2 and affine/MPC acceptance now validate the same typed polyhedral diagnostic contract: a missing mixed-feature count, a non-Boolean integration claim or inconsistent active face/edge/vertex totals rejects the accepted step and restores its previous State. A visually plausible but incomplete observation cannot silently enter the historical evidence.

Ownership for the next implementation is deliberately narrow: surface/search admission belongs under boundary_models/; feature integration and the fixed-multiplier law are Operators there, not new solvers; the outer AL loop, Newton/MPC ordering and atomic acceptance belong to the existing finite-J2 Procedure; accepted histories and checkpoint identity belong to State; force, work, field-location and trust claims belong to Result/Verification. The external comparator and convergence ladder are test/evidence assets, not hidden runtime heuristics. This keeps the public Model focused on declaring the contact pair and its physical/numerical policy.

Nine ordered gates and reading map

Each bibliography entry motivates a design question; none certifies AgentFEM. The gate stays open until its listed evidence exists at the proposed scope.

1. Frozen contract and external comparator. Freeze geometry, mesh family, units, initial clearance, rigid pose history, material parameters, solver controls and observables. Prefer a reproducible external Abaqus/Standard input/results pair supplied or reviewed independently; record contact formulation and enforcement differences. Predetermine observable-specific tolerances and a comparison station set. Current state: internal examples and local regression exist, but no same-input external benchmark for the nonconvex finite-J2 fixture. Reading: Abaqus' published finite-sliding rigid-surface verification/input list, its published C3D8 solid against analytical rigid cylinder input and finite-sliding C3D4/C3D8 surface-to-surface input list, its small-sliding stress/displacement verification cases, including augmented-Lagrangian examples, COMSOL's analytical/NAFEMS verification collection and NAFEMS advanced contact benchmark catalog. A published verification case is a comparator protocol, not an external result for our own geometry. In particular, that published three-dimensional meshed-rigid case deforms a shell around a cylinder, so its numerical output cannot be relabeled as a solid finite-J2 same-input comparator. The C3D8 rigid-cylinder deck is an elastic contact protocol: it specifies an analytical cylinder, a solid contact face, normal loading and later sliding, but changes friction and has distinct linear and geometrically nonlinear steps. It supplies an input, not numerical output for our finite-J2 same-input case. The C3D4/C3D8 surface-to-surface blocks use two deformable bodies rather than our prescribed rigid tool. Thus neither source closes the external J2 gate; the elastic rigid-cylinder portion can serve as an earlier interoperability checkpoint with matched material, constraints and observables. A more ambitious later comparator is NAFEMS Contact Benchmark 3, which includes elastoplastic contact and springback; its detailed material, geometry and published observables must be obtained and frozen before claiming a comparison. Keep this separate from the smaller same-input AgentFEM/Abaqus-Standard J2 plane/convex-tool pair needed for the bounded 0.4.4 claim. Additional comparator screening rejects two attractive but mismatched shortcuts: the public NAFEMS rounded-punch reproduction by SimScale uses linear elastic punch and foundation, although it provides useful geometry, mesh and contact observables; the open Frohne--Heister--Bangerth elastoplastic-contact study and deal.II step-42 provide an excellent semismooth/active-set algorithm reference but formulate the obstacle inequality for small displacements. Neither is the missing finite-strain J2 same-input result. NAFEMS also explicitly warns that mesh, element, contact and load-step choices must be matched before cross-code differences can be attributed to a solver. Until an independent deck and its accepted-station results are frozen, Gate 1 remains open rather than borrowing an unrelated published force curve.

2. Surface and search admission. Validate closed/open topology, outward orientation, self-intersection, initial clearance/overclosure and allowed free features; search and project in the current configuration on every trial. A local candidate cache may accelerate search only with a conservative coverage/invalidation proof, never by reusing old forces or normals. Test large sliding, seam crossing, geometry-scale changes and an intentionally missed-candidate trap. Current state: smooth projectors, triangulated BVH and reviewed closed-solid classifiers exist. Implicit rigid pairs now have an optional initial_penetration_limit in length units. On a first-order analytical-plane trace, the extremal nodal signed gap is an exact face-wise bound; this catches a corner penetration missed by quadrature. On a first-order triangular trace against a reviewed closed convex or nonconvex rigid solid, a bounded adaptive subdivision uses the true signed distance's 1-Lipschitz inequality to prove a conservative face-wise upper bound. It fails closed on ambiguous projections or if the declared depth/sample budget cannot prove the requested limit. For the convex subset, a support plane that dominates at every affine slave-face vertex dominates on the whole face; its nodal minimum directly bounds the initial penetration. Mixed-feature faces still use the adaptive certificate. A near-touching convex ordinary Step now passes a 1e-9 declared limit without refinement. This is only an initial-overlap result, not a later sliding/integration certificate. A reviewed open triangle sheet instead needs the explicitly selected reviewed_planar_branch_partition: complete coplanar coverage and nearest-branch dominance at the reference pose certify one oriented affine gap per slave face; its nodal minimum gives the initial limit. A rim/competing feature fails closed. The open sheet never inherits the closed-solid 1-Lipschitz signed-distance argument, and an arbitrary curved projector inherits neither proof. The current smooth-plane branch certificate has a separate conservative refinement: when the whole slave face fails only its coarse competitor radius test, it bisects the reference triangle once and admits the parent only if all four children independently certify the same oriented tool plane. This changes no quadrature or contact law. On the reviewed reentrant-tool fixture a wider face formerly rejected by the coarse 2r screen is now certified with positive child clearance. The same test succeeds on an open triangle sheet with a nearby noncoplanar competing patch; moving its slave face nearer the competitor still fails. The corresponding six-increment global finite-J2 open-sheet Step completes and matches the otherwise identical analytical-plane displacement and prescribed-tool work; the unrefined whole-face certificate rejects its initial trace. This tests the whole Model-to-Result path, not only a standalone geometric helper. Disabling refinement reproduces the old refusal, and a true closed-solid edge-transition face remains rejected. The depth and total subface budget are bounded; child planes that differ never become an approximate sharp-feature rule. The ordinary Step capability query reports unsupported geometry/order before Step construction. The explicit pair still rejects this policy. No branch silently moves slave nodes or the tool. Arbitrary large-CAD and ambiguous sharp features are not admitted. Reading: Abaqus finite-sliding/general-contact formulation, Abaqus meshed-rigid-surface verification and Abaqus initial-overclosure choices. The conservative subdivision follows the classical 1-Lipschitz signed-distance property, distinct from any particular neural approximation; see the distance-function discussion in Cavalletti--Mondino.

3. Contact-boundary/feature integration. Make the active integration partition a trial-geometry Operator input. A zero-gap boundary and a nearest-feature switch are different discontinuities: the latter can contribute a line term to the Newton tangent. Keep positive weights and one consistent residual/tangent partition; refresh a changed partition before accepting a Newton trial. Verify manufactured narrow-strip, two-plane and curved-transition oracles, then the nonconvex L-tool response matrix. Also distinguish a surface quadrature crossing a nearest-feature switch from actual edge--surface, edge--edge or point contact. A corrected surface integral alone does not establish the latter's nonpenetration constraints or pressure units. Either admit those lower-dimensional branches with independent force/moment and tangent evidence, or reject them explicitly at the current geometry; do not silently assign an arbitrary averaged surface normal. Abaqus/Standard itself distinguishes the bounded small-sliding surface formulation from finite-sliding general contact: its general-contact controls state that small-sliding assignments deactivate edge and vertex contact. This is evidence that a surface-only approximation needs an explicit scope, not evidence that our finite-sliding route may silently do the same. Farah--Wall--Popp use separate point, line and surface multiplier families for non-smooth finite-deformation contact point-line-surface, whereas Farah--Popp--Wall compare segment, element and hybrid mortar integration schemes mortar-integration. These are architecture comparisons, not drop-in algorithms or evidence that our one-sided P1 operator already has their coverage. Haikal--Hjelmstad's oriented-volume formulation is a third non-smooth contact direction oriented-volume, but is developed for quadrilateral/hexahedral body elements; it does not convert our tetrahedral slave and triangular rigid tool into a validated volume-contact operator by renaming the gap. Laursen--Govindjee's non-smooth-surface treatment makes the physical-corner issue an explicit unilateral constraint problem, analogous to a non-smooth yield surface. Separately, a 3D mortar derivation tracks not only clipped integration cells but also the derivatives of their moving vertices. These clarify the implementation split: first certify which positive-area slave regions belong to face, edge or vertex gap branches; then vary both each branch integral and its moving region boundary. A feature-aware quadrature sampler alone is neither the corner law nor a consistent Newton tangent. Current state: analytical planar clipper, research two-plane oracle and opt-in <=4-plane convex partition pass; the result now flags sampled mixed-feature slave faces for reviewed closed solids in both standard and periodic J2 Results, without claiming a complete transition integral or changing the Newton law. Nonconvex feature transitions remain open. Reading: Duong--De Lorenzis--Sauer refined-boundary quadrature and COMSOL contact quadrature guidance. The convex partition now admits only the actual default three-point P1 reference rule and its facet-ID grouping. Three arbitrary points whose shape values merely sum to one are rejected before their measure can be silently reinterpreted as that rule; this is an input-contract safeguard, not a new geometry or friction capability. An independent four-feature rectangular-window integral now matches the exact quadratic penalty energy, including the reference-area map; its perturbed directional derivatives and a real FEniCSx assembled tangent agree with the moving pairwise-line tangent. A small finite-J2 Step also completes and resumes from an interrupted checkpoint with the same displacement and tool work. A five-feature prism still fails closed. This only widens the reviewed convex slice; it does not establish nonconvex nearest-feature switching or physical edge/vertex contact. The cited isogeometric extended-mortar formulation is a comparison design, not a drop-in P1 facet implementation: its enriched pressure interpolation and two-half-pass force construction differ from our one-sided trace.

The next implementation must distinguish sampling from consistent differentiation. For a slave face partitioned into current nearest-feature regions A_i(u), write the scalar contact functional as Pi(u) = sum_i integral_{A_i(u)} phi_i(u,x) dA. At a feature-switch line, the adjacent phi_i agree because the selected distance is continuous, so the first shape-boundary term cancels. Their displacement derivatives need not agree when the selected normals differ; differentiating the assembled residual then has a moving-line contribution. This is a derivation for our piecewise-smooth penalty law, not a formula imported from another element. There is an additional geometry boundary: on an affine P1 slave triangle, squared distance to an admissible master face interior, edge interior or vertex is a quadratic in the slave coordinates. Equality of two such branches is generally a conic, not the straight line used by the existing convex support-plane partition. The latter is exact because its selected signed support gaps are affine; it must not be renamed as a generic nonconvex nearest-feature partition. The next candidate needs either verified conic/feature-region segmentation with its moving-boundary tangent or an explicitly approximate, error-controlled alternative with separate release criteria. This conclusion follows from our branch formulas and the cited 3D segmentation/linearization work; it is not a claim that the cited method already handles our closed-solid sign policy. There is a directly relevant mathematical construction in polynomial integration over a triangle clipped by a conic: it subdivides until conic/triangle intersections have tractable cases and integrates polynomial quantities over the selected region. It is not a contact algorithm: its own floating-point discussion warns of delicate classification and cancellation, and it supplies neither our signed rigid-solid geometry nor the moving-feature derivative. A realistic bounded route is therefore BVH candidate localization, admissible face/edge/vertex quadratic branches, verified conic-region integration, moving-boundary linearization, and a conservative unsupported fallback. Adding high-order Gauss points globally is neither a geometric proof nor a substitute for this partition. The local oracle now also checks a cheap preflight, not an integrator: six values of a known quadratic branch difference recover its degree-two Bernstein coefficients on a P1 triangle. Their extrema bound the whole face, catching a circle-like conic hidden inside a triangle whose three vertices all report the opposite branch. This can reject unsafe vertex-only admission or certify a single branch after subdivision; it does not decide the sign of a closed solid, prove which face/edge/vertex is geometrically admissible, or provide interval-certified floating-point bounds by itself. The candidate must reproduce both the integral and its directional derivative and pass the total Newton/MPC tangent check. A fixed quadrature rule, a frozen feature partition or a smaller Newton residual alone is insufficient. A new independent two-feature research oracle makes the conic problem explicit: squared distance to a horizontal edge and to a separate vertex has equality curve y=((x-3)^2+1)/2 on a P1 reference triangle. Its straight chord misses the curve by 0.027864 at the midpoint. Split positive Gauss integration gives the P1 residual; differentiating its moving parabola gives a negative semidefinite boundary term. The oracle now perturbs all six in-plane P1 nodal freedoms, including horizontal motion that changes the curve itself, at both zero and nonzero trial displacement. The full tangent's maximum error against independently re-partitioned central differences at the zero state is 4.0e-11 with that term, versus 0.1415 without it; the potential's independent first difference also matches the residual. At the nonzero trial the full tangent errors are 4.6e-11 versus 0.1412, and the potential-gradient difference is 7.3e-11 (tools/verify_quadratic_contact_feature_transition.py). This is a local candidate-feature calculation, not a signed-gap law for a complete closed tool, an exact-arithmetic proof or a public Step. tools/verify_contact_feature_transition.py is already an independent two-plane unit-triangle counterexample: its moving-line term exactly cancels a nonzero fixed-branch bulk tangent. It proves why the term is necessary in that manufactured setting, not that the closed nonconvex three-dimensional implementation has been supplied. A second independent oracle, tools/verify_reentrant_contact_integral.py, computes signed distances directly to the six segments of an extruded L boundary, without calling the AgentFEM projector. One affine slave triangle has all three ordinary face points outside the rigid solid, so its sampled penalty potential is zero, yet positive-area material near its corners penetrates: 128/256/512 positive-subtriangle refinements give potentials 0.000348765/0.000349677/0.000349913 at unit penalty. The last two differ by about 0.07%. This is a numerical refinement reference, not an exact-arithmetic certified integral, and supplies a concrete target for the nonconvex feature-partition work rather than an excuse to turn on a sampled full Step as though it were complete. The independent oracle now additionally subdivides only unresolved subfaces. The signed distance's 1-Lipschitz bound encloses their energy; fully inactive subfaces contribute exactly zero, while fully interior subfaces with one provably nearest straight segment use an exact quadratic three-point integral. At depth 10 it processes 24,777 subtriangles and brackets this potential in [0.000348447, 0.000351592] (unit penalty, per unit extrusion), containing the 512-grid reference while excluding the default rule's zero. This is a floating-point conservative-margin energy reference, not formally verified interval arithmetic. It also bounds each component of the total translation force in [-0.005760, -0.003644]; a separate 512-grid central-difference screen gives x-force -0.005333 inside that wide interval. Carrying the parent P1 shape functions through subdivision also gives componentwise bounds on the three reference-area nodal traction integrals; a separate 512-grid centroid estimate for the x components is approximately [-0.0038923, -0.0001697, -0.0012706], all inside their corresponding intervals. A separate P1 nodal-direction difference of the fixed-area potential also falls inside all six component intervals. These broad reference bounds are not a production residual, pressure field or Newton-tangent certificate. The unresolved cells still require feature-region geometry and moving-boundary differentiation for Step use. A new opt-in boundary_models.contact_energy_enclosure.bound_closed_contact_penalty_energy transfers the 1-Lipschitz signed-distance argument from that independent 2D oracle to any reviewed, closed 3D rigid tool and a current affine P1 slave face. It splits the largest uncertain reference-area cell first, retains a scalar distance at nonunique nearest-point queries without inventing a normal, and falls back to a finite tool-vertex upper bound if even the winding sign is unresolved. The ordinary implicit contact provider exposes the read-only diagnostic as closed_penalty_energy_enclosure(), with explicit depth, cell and face budgets; it is never part of the default Newton residual. On the same extruded L fixture, the default three-point rule reports zero while the new generic depth-6 interval is approximately [0.0001480, 0.0006654], containing the independent 512-subtriangle value 0.0003499. At depth 8 with 49,999 leaves, it narrows to [0.0002897, 0.0004174] in about six seconds on the development Mac. Those are floating-point conservative-margin bounds, not formally directed-rounded intervals; neither a positive lower bound nor a tight energy interval supplies a nodal force or consistent tangent. A trial combination with exact smooth-cell proofs only reduced the depth-8 width about 4% while increasing runtime from about six to ten seconds, so it was not retained. The subdivision-only experiment also remains negative: after depth 6, 254 child faces were still unsupported by the existing complete local Operator proofs. Gate 3 therefore remains open. Hiermeier--Wall--Popp's variationally consistent mortar study is a useful independent standard for varying all active contributions, but its symmetric two-body mortar formulation is not our algorithm.

A 2026-10-18 fixed-input screen used examples/finite_j2_closed_concave_contact.py with 12 increments, penalty 20, direct linear solve, backtracking, one MPI rank and one OpenBLAS/OpenMP thread. The table reports the accepted end state, not a timing comparison. q2 is the default positive face rule; q5/q7 are explicit quadrature-degree requests.

Cells/axis	Rule	Tool force x	Active reference area	Max PEEQ	Tool work
2	q2	-0.307580	0.416667	0.00671873	0.00806207
2	q5	-0.334865	0.447799	0.00670389	0.00895618
2	q7	-0.336957	0.441456	0.00726967	0.00876881
3	q5	-0.328318	0.445520	0.00812605	0.00888055
3	q7	-0.319265	0.446202	0.00820966	0.00869530
4	q5	-0.337238	0.428587	0.00841117	0.00874221
4	q7	-0.320473	0.452688	0.00852799	0.00867533

A further same-input q9/q11 check on the 2-cell mesh found tool-force x -0.336930/-0.321905 and active area 0.428296/0.440369; on the 3-cell mesh it found force -0.317957/-0.324226 and area 0.453882/0.450798. The higher positive Basix rules are now available as explicit study controls, not defaults. The q5/q7/q9/q11 force and active-area differences remain nonmonotone across this small mesh ladder. Completion, a small energy residual and a higher rule therefore do not establish a converged nonconvex result. Do not promote default q2 or q11 as a silent accuracy fix. The discriminating next experiment is a genuinely changing trial feature partition with verified residual/tangent, followed by a new mesh/increment/penalty matrix. This is a Gate 3 failure record, not a scientific benchmark result. An opt-in DolfinxImplicitRigidContact.quadrature_sensitivity() diagnostic now evaluates positive rules at the same current displacement and rigid pose, without another nonlinear solve or State mutation. On the accepted 2-cell q9 end configuration the q9/q11 structure-force x values were -0.336930/-0.320336 and active reference areas 0.428296/0.440369. This isolates a roughly 5% force difference due to the rule at one fixed configuration; q11 is not a reference truth. It is frictionless and scalar-penalty-only, and reports certifies_feature_transition_integral=false. The next algorithmic candidate is trial-geometry segmentation or a variationally consistent mortar/feature treatment, with line-tangent and coverage tests. Pinto Carvalho et al.'s rigid/deformable dual-mortar study motivates a distinct longer-term formulation, but its efficiency claims cannot be imported into this one-sided penalty implementation. A second opt-in fixed-configuration diagnostic now uniformly subdivides each affine P1 reference face into 4^level positive three-point subfaces. It preserves reference area and interpolation and is explicitly not a moving transition partition or line-tangent implementation. On that same 2-cell accepted q9 state, level 3 (1,536 samples) gave potential 0.008144 versus q9's 0.008140, but structure-force components (-0.334995, 0.010878, 0.020429) versus q9's (-0.336930, 0.016867, 0.012983). Close potential alone did not imply a reliable force vector. The level-0/1/2/3 active-area sequence was 0.416667/0.437500/0.416667/0.430990, also not a convergence certificate. Level 4 (6,144 samples) changed the area again to 0.436523 and the force to (-0.325105, 0.017034, 0.024163), while potential remained near 0.008136. Uniformly spending more points therefore did not close the feature-transition force question either. The production design now branches deliberately: a user-declared physical fillet/smooth tool can use the existing external SmoothRigidSurface extension and must pass the gap/Hessian checker and independent geometry comparison; the exact sharp nonconvex tool must wait for its own trial-geometry segmentation/line-tangent evidence. An implicit hidden normal average or silent fillet would change the model. This distinction follows Abaqus' explicit advice to smooth analytical rigid corners for finite-sliding Standard contact, not an assumption that AgentFEM's present mesh already has those fillets. Wolff--Bucher's assumed-gradient distance field is a different promising route for complex geometry, but its smooth interpolated gradient is a declared gap/geometry approximation. It cannot be advertised as the exact sharp-feature answer without an error study. A new algorithm may enter the Step only after both integral and differentiation checks, not merely a finer screenshot or work balance. The accepted closed-solid point diagnostic already distinguishes physical face, edge and vertex projections (not merely triangulation seams). Engineering verification now fails if a sampled active point belongs to a physical edge or vertex, even if no mixed-feature slave face was sampled; a corrected surface integral would not by itself define that separate lower-dimensional law. The diagnostic also rejects counts inconsistent with the active-point total. Exploratory results retain the observation without a trust upgrade; release still requires a certified integral. A real finite-J2 reentrant-edge Step now supplies the negative engineering test, not just synthetic metadata. Its Result exposes named face, edge and vertex active-point counts at the final accepted configuration beside the underlying per-pair metadata, so a user can inspect the reason without decoding a private trace. The runnable reentrant-tool example also prints the failed engineering feature claim beside status=completed; nonlinear completion is not silently presented as scientific acceptance. These final counts alone do not summarize earlier accepted increments. The ordinary serial finite-J2 Step now keeps a bounded per-pair path summary: maximum sampled mixed-feature faces and active physical edge and vertex points, plus whether every observed station used a certified transition integral. The initial and every accepted station contribute; failed increments roll back the summary and serial checkpoints restore it with count and pair-identity checks. Older checkpoints lacking it remain readable but mark the path incomplete. The summary is independent of output frames and the progress-event ring buffer, both of which may omit earlier states. It is still only sampled path evidence, not a whole-face coverage proof. The serial periodic/MPC path now records the same sampled maxima through its existing accepted-observer transaction: the initial and each accepted station are counted, late failures restore the prior record, and the identified recorder is checkpointed with the material and contact Operators. A damaged record is atomically refused. Older affine penalty checkpoints lacking the recorder load only through an explicit identity-compatible migration, marking historical coverage incomplete; subsequent observations cannot invent the missing past. An entirely observed flat convex path can now pass the narrow engineering claim of no observed uncertified feature transition, while its release integral-certificate claim still fails under plain Gauss quadrature. Thus a complete observation ledger is not a whole-face integration proof. For the separate convex route, accepted point diagnostics now say whether the reviewed changing-trial support-plane partition supplied its bounded feature integral. The default Gauss rule explicitly reports that no such certificate exists, even when no mixed-feature face happened to be sampled. Release-level verification now requires this certificate for every polyhedral pair; zero observed mixed-feature faces or active points no longer suffices. An empty or unattached accepted-path record cannot pass that claim vacuously; it must agree with current per-pair diagnostics. A future whole-face separation certificate may justify a separate no-contact release path, but point samples cannot. The narrow-strip tests in test_contact_active_partition.py and the missed-interior-overlap test in test_initial_gap_bound.py are concrete counterexamples to equating zero active quadrature points with separation. Engineering-level verification continues to report the narrower sampled diagnostic. This release guard does not itself supply a scientific reference or make the nonconvex operator accurate.

1. Normal enforcement as an explicit law. Retain penalty as one declared approximation. Prototype a separate opt-in augmented-Lagrangian law first on a fixed-quadrature analytical plane. With positive-outside gap g, fixed nonnegative multiplier lambda, and k>0, use p=max(0,lambda-k*g) during each Newton solve. Update the multiplier only after a converged solve; require separately specified global equilibrium, penetration and complementarity checks before the whole increment commits. Store stable point IDs, units, law and policy in State/checkpoint identity. Reject trial-changing contact quadrature until a conservative multiplier transfer is designed and tested. Current state: the ordinary Step remains penalty-only. A solver-neutral fixed-reference-trace AL candidate now has point-law, residual/tangent, spring-plane, independent scalar elastoplastic-bar indent/release and rollback tests. The scalar bar freezes old plastic history through each equilibrium solve, updates the normal multiplier only between converged solves, and commits both histories only at an accepted tool station; it is not an ordinary finite-element Step. A real serial DOLFINx tetrahedral trace also matches an independently UFL-differentiated plane/sphere functional, residual and tangent. There is still no global Step, MPI, or installed-package acceptance. A high-penalty L-tool trial failed Newton, so neither hard-contact convergence nor an AL benefit may be claimed. Reading: Abaqus contact enforcement controls, COMSOL penalty/augmentation trade-off, and Burman--Hansbo--Larson's augmented-Lagrangian FE analysis. The latter warns that a discontinuous multiplier approximation can need stabilization; Hansbo--Rashid--Salomonsson's stabilized obstacle formulation likewise explains that too many discrete multiplier constraints can make a system singular. Our independent point multipliers inherit neither proof and require a spatial-pressure/mesh check. A bounded opt-in fixed-trace rank diagnostic now builds the active weighted normal-constraint Jacobian and exposes duplicate point constraints: two active multipliers with the same nodal support and normal have row nullity one, whereas the three independent P1 triangle Gauss rows have full local row rank. This is a negative screen, not an inf-sup proof: it caps dense problem size and never certifies spatial stability. It can now also inspect J T when supplied the actual dense displacement reduction u = T q + u_bar; a three-point triangle that has full unreduced row rank drops to rank two when one normal DOF is fixed or tied by an MPC. This catches a different false positive than the duplicate-point screen, but the production Step still needs to pass its real reduction and a mesh ladder before using the result as an admission criterion. The global AL Step still needs a reduced-constraint rank/mesh-pressure study. The exact-penalty alternative computes a continuous displacement-dependent multiplier estimate and avoids the outer AL loop; its published examples also show conditioning sensitivity, even before contact activates, and parameter-dependent step refinements. It does not repair our unresolved nonconvex integration or silently replace the declared AL policy. If compared, count its local multiplier-recovery and tangent work and use the same mesh, J2 path and acceptance observables. Nitsche is a serious primal alternative: Chouly--Hild analyze small-strain unilateral contact without a separate multiplier or discrete inf-sup condition, and Mlika--Renard--Chouly extend an unbiased formulation to large-deformation elastic frictional contact. Neither result is a proof for our finite-J2 material, one-sided rigid tool or sharp nonconvex integration. A fair method comparison would use the same analytical-plane J2 path, penetration, reaction, Newton work and mesh ladder, while counting the additional boundary traction and its consistent tangent that Nitsche requires. Do not add a second public enforcement choice on the basis of a 1D penalty comparison alone. The ASiMoV DOLFINx contact implementation is useful concrete evidence that custom contact assembly and parallel surface workflows can be built on the same FE ecosystem. Its maintainers describe it as experimental and it uses Nitsche formulations; it is therefore an architecture/comparator lead, not a drop-in backend for AgentFEM's finite-J2 penalty State, rigid-tool work ledger or feature certificates.

A private global feasibility probe now substitutes the fixed-trace AL Operator into the existing serial J2 Newton assembly, leaving its material update provisional while manually iterating the multiplier. A moving planar tool compressed a plastic cube; with declared penalty 3000 and penetration/complementarity tolerances 1e-6 it required eight total Newton equilibria before one joint test-owned commit, with final PEEQ above 0.005. At penalty 300, another case still missed the tolerance after 30 equilibria. The repeatable regression locks only this bounded feasibility observation; it is not a public Step, a robust penalty policy, atomic checkpoint, or a general convergence proof. The slow outer convergence is consistent with the linear-rate cost identified in exact-penalty and motivates comparing a simultaneous mixed semismooth route such as Alart--Curnier, rather than automatically nesting dozens of solves in the product. PETSc's bound-constrained variational-inequality Newton options are another algorithmic reference, but a bound on displacement DOFs does not directly represent a nonmatching rigid-surface gap or cure multiplier-space instability. The next research comparison should hold the same fixed trace and J2 path while solving the Alart--Curnier-style semismooth mixed residual R_u(u,lambda)=R_bulk(u)-B(u)^T[lambda-k g(u)]_+ and R_lambda(u,lambda)=lambda-[lambda-k g(u)]_+. On an active point the latter has displacement derivative k B and zero multiplier diagonal; on an inactive point it has unit multiplier diagonal. This exposes why a rank-deficient reduced B T can make a simultaneous solve singular, even when a scalar example converges in one Newton step. It is a design candidate, not the implemented global law; a mesh-stable multiplier space or reviewed stabilization, consistent geometry derivatives, and joint accepted State remain mandatory before a public option exists. Two open implementations sharpen the comparison: GetFEM's contact bricks distinguish nodal rigid-obstacle and integral nonmatching-contact AL variants, while deal.II step-42 couples a primal-dual active set, plastic constitutive iteration and line search in a 3D obstacle example. The latter uses a small-strain law and nodal obstacle constraints, so it is an algorithmic lifecycle reference, not a same-input finite-strain J2/triangulated-tool validation. For our candidate, reduced-rank and active-set changes must be tested before comparing outer AL against a simultaneous mixed solve; neither package's documented convergence can be transferred to our multiplier space.

A real DOLFINx P1 planar-trace rank screen now makes the spatial issue concrete. With 1/2/3 tetrahedral cells along each side, the boundary has 4/9/16 normal displacement nodes but the three-point-per-triangle trace carries 6/24/54 independent point multipliers; its active Jacobian row nullity is 2/15/38. Reusing the existing positive vertex-lumped trace with coalesced shared nodes gives 4/9/16 multiplier points and zero row nullity in the same unreduced screens. Both discretizations can drive the private finite-J2 outer-loop feasibility probe to an accepted plastic state, but they give different PEEQ on that coarse mesh. Thus coalescing repairs this particular algebraic redundancy, not inf-sup stability, pressure accuracy, complementarity across faces or global product acceptance. The one-cell plastic feasibility fixture keeps the same rank result after its actual strong-boundary reduction; a mesh/pressure ladder remains a separate gate. This is consistent with the dual-mortar multiplier-space analysis and the reported boundary-contact inconsistency of unmodified dual bases; those papers motivate the space design rather than validating our nodal lumping as an equivalent mortar method. An actual periodic-J2 fixture is stricter still: its 24 Gaussian point constraints have unreduced row rank 22 and only rank 9 after the real 81-by-21 MPC transformation. The same surface's 9 coalesced nodal constraints have unreduced rank 9 but reduced rank only 5. Thus even the nodal candidate is not admitted under periodic MPC merely because its bare surface matrix is full row rank. The controlled all-active screen is an algebraic counterexample, not a physical pressure field: at the fixture's initial pose with zero accepted multiplier, just one point actually penetrates and its reduced active row has rank one. The all-active nullity therefore must not be reported as a failure of that particular physical increment. A multiplier basis compatible with the actual primal reduction and changing active inequalities remains research work. The bounded rank diagnostic now also reports active point IDs with a clearly negative gap but zero row in the current reduced linearization. In a deliberately shifted analytical-plane probe on that fixture, all nine nodal points are active, the reduced row rank is three, and four penetrated points have no first-order reduced displacement direction. This is useful preflight evidence for a proposed hard-contact law, not an automatic infeasibility claim: the probe does not establish that its current trial satisfies the affine MPC offset, and a curved gap could change at second order. No public AL Step is enabled by this diagnostic.

A second research-only screen used the same finite-J2 Newton owner with coalesced nodal multipliers against an independent homogeneous hard-plane J2 reference. For one and two tetrahedra per side, the outer law required four equilibrium solves, reached penetration below 3.4e-7 for a prescribed 0.002 indentation, and its tool force differed from the scalar reference by about 0.016%. This narrow positive result verifies a complete accepted increment on those meshes; it does not validate arbitrary pressure patterns, dual-space stability, changing contact sets, or a public AL Step.

The homogeneous hard-plane research probe now covers 1, 2, 3, 4 and 6 tetrahedral cells per axis. Each required four frozen-multiplier global equilibria; the accepted tool-force magnitudes stayed within 0.8147538507–0.8147538544 against the independent homogeneous target 0.8148807630, and PEEQ stayed near 0.001188541 on this prescribed uniaxial path. This is an unusually easy spatial case: the exact field is homogeneous, so nearly identical mesh results do not establish nonuniform contact-pressure stability, feature-switch convergence or a public AL Procedure. The trace and test-owned state remain research only.

A second, deliberately nonuniform oblique-plane J2 screen now runs the same test-owned nodal AL outer loop on 2/3/4/6 tetrahedra per axis. All four reach their declared penetration/complementarity tests, retain nonzero plastic history, have an independent active-row Jacobian after the actual strong-BC reduction, and show higher mean pressure where the prescribed tool compression is larger. This is a more discriminating path than homogeneous compression: the frozen 2/3/4/6-cell screen took 6/7/8/9 frozen-multiplier equilibria, and tool-force magnitudes were 2.712/2.711/2.719/2.725. Yet maximum PEEQ increased from 0.00956 to 0.01054, while the far-side nodal mean pressure fell from 0.246 to zero. These are not a monotone field-convergence or spatial-stability proof; there is no independent same-input contact benchmark. It therefore screens feasibility only; it does not promote the multiplier space or enable the public AL Step. In line with Burman--Hansbo--Larson and Hansbo--Rashid--Salomonsson, row rank at four finite meshes cannot replace a mesh-uniform inf-sup or reviewed stabilization argument. MOOSE's mortar contact design makes the missing contract more explicit: a multiplier couples to a weighted gap and its basis/normalization, not merely to a convenient list of Gauss-point pressures. Its documentation even distinguishes stored scaled multipliers from physical pressure and rejects incompatible restart settings. Its Petrov--Galerkin note reports that a dual multiplier basis may produce a negative weighted nodal gap; changing the test space is a deliberate method choice. These are reasons not to relabel our coalesced nodal feasibility probe as a stable mortar method. The next implementation should specify the primal/dual pair, coverage treatment, pressure recovery and restart identity together, then test a nonuniform contact-pressure field under mesh refinement and MPC reduction.

On the same 2-cell/axis, 12-increment, q7 L-prism diagnostic above, increasing the penalty from 20 to 200, 1,000, 10,000 and 100,000 completed the nonlinear solves but changed the final active reference area from 0.4415 to 0.4415, 0.4415, 0.1914 and 0.0967, respectively; maximum sampled penetration fell from 0.0470 to 0.0319, 0.0170, 0.00690 and 0.00174. Tool-force x changed from -0.337 to -1.927, -3.487, -5.099 and -5.705. This is not a hard-contact or penalty-independent limit: both the contact footprint and force change substantially. The older high-penalty Newton failure was a different trial and remains valid at its own inputs; neither failure nor completion generalizes to every setting. Adding an outer multiplier loop before fixing or bounding the nonconvex integral would hide, not resolve, that spatial uncertainty.

1. Friction and moving-feature State. Verify normal-pressure coupling, stick/slip return mapping, tangent, finite sliding, force/moment and dissipated work independently for each supported geometry. Reproject the tangential basis and carry accepted history across a facet seam without inventing a sharp-edge traction law. If an active noncoplanar edge or vertex is unsupported, reject and roll back. Current state: analytical and locally planar faceted Coulomb routes exist. Accepted tangential elastic slip now follows the rigid master's incremental rotation before the minimal old-normal-to-new-normal transport; exact co-rotation of a contacting plane has zero relative slip, unchanged recoverable energy and no spurious dissipation in both implicit and explicit FEniCSx checks. This fixes spin about an unchanged normal, which normal-only transport cannot detect. Sharp-edge friction is not admitted. Reading: Abaqus Coulomb law and finite-sliding term, Abaqus' local tangential slip/traction convention, COMSOL frictional-contact solver advice, and Duong--Sauer's surface-potential finite-sliding formulation. The last is a thermodynamic and tangent-design reference, not evidence for an unverified sharp-edge friction law.

2. One nonlinear Procedure and State transaction. Assemble the total material, contact and load residual/Jacobian before strong-boundary or periodic-MPC reduction. Newton, line search, cutback and convergence checks use that same total system. A rejected trial restores displacement, J2, normal multiplier, tangential State, projection, rigid pose and work; an accepted increment commits them atomically. Check interrupted versus continuous paths and corrupted-checkpoint rejection. Current state: these contracts pass for existing bounded penalty pairs; new enforcement and changing integration identities each need their own tests. Reading: PETSc nonlinear line-search/trust-region methods and COMSOL contact solver sequencing.

3. Results and mechanical evidence. Publish per-pair raw gap, pressure, normal/tangential force, moment, active area and slip with field location, interpolation and units. Keep rigid prescribed-motion work, frictional dissipation, material work/storage and numerical penalty or augmented functional distinct. An algorithmic Lagrangian is not physical stored energy. Current state: named force/moment/work and raw contact-point output exist on selected routes; the AL research candidate separately exposes physical tool reaction and generalized tool force/moment. Prescribed-plane translation/rotation finite differences confirm their work-conjugate signs. A general first-law closure and cross-method pressure convention are not established. Reading: Abaqus contact output semantics and COMSOL important contact variables.

4. Independent science gates. Run a small ladder: spring/plane exact solution; open/closed and unloading; smooth Hertz/contact footprint; planar sliding friction; convex corner; reviewed nonconvex transition; J2 loading/unloading; MPC and moving multi-tool composition. For each relevant rung check finite-difference total tangent, action/reaction and moment, mesh x increment x enforcement sensitivity, regional plasticity, failure rollback and restart. Distinguish integration-point fields from smoothed display fields and compare equivalent observables with the frozen external case. The first independent global scalar oracle now checks a nearly elastic finite-J2 unit bar and rigid-plane penalty against the series compliance limit F=delta/(1/E+1/k) at two mesh levels and two penalties; all four satisfy 5e-4 relative tolerance for delta=1e-4. This small-strain limit checks the total force path, not plastic flow, curved geometry or Abaqus equivalence. A second independent scalar oracle now constrains the plastic global path: a laterally fixed unit bar has F=diag(lambda,1,1), q_trial=-E log(lambda) in compression, dp=max(0,(q_trial-Y)/(3G+H)), and Pxx=E(log(lambda)+dp)/lambda for nu=0. Solving Pxx+k(lambda-x_tool)=0 predicts right displacement, contact force and PEEQ at two tetrahedral mesh levels; the tests compare all three without calling the AgentFEM material update as their reference. This checks a restricted homogeneous J2/contact state, not general forming. The same independent scalar return map also follows an eight-increment indent--release--reindent path. It checks displacement, contact force and PEEQ at loaded, detached and reloaded stations; the accepted mid-path checkpoint resumes to the same displacement, plastic history and tool work as the uninterrupted run. Under lateral constraint, release can reverse-yield before axial force vanishes, so a first-load PEEQ cannot be substituted for residual displacement. This is a bounded transaction and material-path reference, not nonconvex tool validation. The audit also found that automatic J2 incrementation could skip an interior tabular reversal, thereby changing the prescribed path while reporting Newton convergence. Interior table knots are now required accepted stations: fixed controls missing one fail before solving; automatic controls land on each knot without forcing an extra output frame. Tabular inputs are copied and their metadata identity frozen at creation, closing the caller-array mutation gap between runtime path and restart fingerprint. The denominator follows the MOOSE radial-return documentation. Requiring accepted stations at every interior tabular knot is AgentFEM's conservative stateful-path policy, not a claim about Abaqus' default increment scheduling. Abaqus documents explicit time points for evaluating a cyclic response at known load maxima/minima, and treats exact output times as a separate incrementation choice; these distinguish physical path resolution from output-frame frequency Abaqus direct-cyclic time points, Abaqus output timing. A separate diagnostic, not acceptance now runs examples/finite_j2_hertz_contact.py on a quarter finite block with a spherical tool. Holding --quarter --grading 2 --indentation 0.002 --radius 20 --increments 4 and the example's other defaults fixed gives:

cells/side	penalty	full tool force	active reference area	max penetration
7	100,000	0.712466	0.142459	0.00007267
9	100,000	0.696875	0.143011	0.00007231
11	100,000	0.692319	0.138502	0.00007205
7	300,000	0.726972	0.134057	0.00002812
9	300,000	0.710146	0.135631	0.00002568
11	300,000	0.706214	0.126903	0.00002499

Reproduce one row with python examples/finite_j2_hertz_contact.py --quarter --cells 11 --grading 2 --penalty 100000 --indentation 0.002 --radius 20 --increments 4 in the FEniCSx environment. At 11 cells, tripling penalty still changes force by about 2.0% and active area by about 8.4%; the area also changes nonmonotonically under refinement. Two versus four increments were nearly identical at the coarse elastic 2/3-cell levels, but that does not establish plastic-path or general time-step independence. On the 11-cell, 300,000-penalty row, increasing contact quadrature degree from 3 (4 points/face) to 5 (9) and 7 (16) gives tool forces 0.706214, 0.705531 and 0.705975 respectively, while active areas are 0.126903, 0.129983 and 0.127824. This makes force look much less sensitive than the active footprint; no quadrature degree is promoted on that observation alone. The half-space Hertz force printed by the example is only a scale reference: the solved problem is a finite, bottom-clamped block with finite penalty, finite-strain kinematics and sampled contact. Neither its Hertz mismatch nor completion alone certifies or refutes this formulation. The next gate needs a denser, independently checked finite-block reference and a declared pressure/area discretization tolerance, not a selectively chosen force match. An additional higher-order screen used the same quarter block, --displacement-degree 2 --bulk-quadrature-degree 4 --contact-quadrature-degree 7 --linear-policy gmres_gamg and four increments. At penalty 100,000, 5/7 cells per side gave full tool forces 0.685484/0.683987, active areas 0.149148/0.144965 and maximum penetrations 7.20347e-5/7.18637e-5. At 7 cells and penalty 300,000, these were 0.697151, 0.136021 and 2.4576e-5. The higher-order force varies less with this mesh change, but penalty and footprint sensitivity persist. This is a separate discretization screen, not a converged benchmark or a same-DOF performance comparison with P1. The nonconvex penalty sequence is not converged. Reading: NAFEMS benchmark catalog, Abaqus contact verification cases and COMSOL contact meshing advice.

1. Performance and installed release. Measure complete accepted-increment time, nonlinear iterations, search, assembly, linear solve, output and memory on frozen inputs. Keep robust direct solve as default; promote an optional iterative solve or cache only with same-path results and repeated platform-scoped evidence. Run ordinary installed model.step cases, early unsupported-combination checks, serial checkpoint/export, Linux/macOS CI and explicit platform availability report. Current state: opt-in GMRES/GAMG shows a same-host small-screen gain, not a universal speedup. A second, larger serial screen fixed the quarter finite-block sphere case at 15 Hex cells per side (3,375 cells), --grading 2 --penalty 100000 --indentation 0.002 --radius 20 --increments 4, with one OpenMP/BLAS thread. Only --linear-policy direct versus gmres_gamg changed. Reversed-order direct/GAMG/GAMG/direct runs took 28.071/11.675/11.326/ 28.084 seconds end to end (within-process case wall time), a 2.44x median ratio on this host and input only. All runs used 20 linear solves and returned tool force 0.68951518028 within 2e-12, active area 0.1453987193 and maximum penetration 7.18696e-5; GMRES counted 540 Krylov iterations. The direct/iterative linear phases were about 18.37/1.61 seconds, so the observed gain has an identified source. This case remained elastic, finite-block Hertz is not an exact scientific reference, and the screen does not establish the same speed or robustness for plastic loading, friction, sharp features, another mesh or another machine. A separate 4-cell/axis, 12-increment plastic J2 L-tool solve returned the same tool force, PEEQ, active area and failed engineering feature claim under direct and opt-in GAMG (differences below 1e-12 in reported scalar observables); this checks solver-policy consistency, not validation or a timed speedup on nonconvex contact. Keep the iterative method explicit opt-in pending those checks; distribution and independent scientific acceptance remain separate. Reading: PETSc GAMG near-nullspace requirement, PETSc profiling and Hoefler--Belli scientific benchmarking.

A separate plastic-contact runtime screen on the same host explains why changing KSP alone is not the dominant lever here. With an 8-cell/axis tetrahedral reentrant L-tool, 12 increments, penalty 20, degree-5 contact quadrature, direct solve and one OpenMP/BLAS thread, the pre-change accepted increment ledger attributed about 9.65 s to backtracking, 6.38 s to material updates, 4.90 s to residual assembly, 0.56 s to tangent assembly and only 0.80 s to 60 linear solves. Opt-in GMRES/GAMG reduced linear time to 0.42 s but the complete case remained about 28 s in both policies. Backtracking had already evaluated the accepted next-state material and total residual; the following Newton iteration was evaluating both again. The standard J2 Procedure now carries that accepted trial response and PETSc residual into the next iteration. Rejected trials still destroy their residual; basic/no-line-search keeps its former path. This is the same function-value handoff described in PETSc's nonlinear-solver iteration model, adapted to AgentFEM's material State transaction.

On the exact same source and machine, a temporary A/B harness restored the old discard-and-recompute behavior without changing tolerances or input. Bracketed direct runs took 28.59/28.51 s with discard versus 19.02/19.01 s with accepted-trial reuse (roughly 1.50x, or 33% less complete-case wall time on this input). The selected scientific JSON fields (quantities, histories, contact duals, mechanical ledger, feature path and verification) had identical SHA-256 in the old-behavior and new-behavior runs; both fields.h5 and fields.integration-points.h5 were byte-identical too. This includes the same failed engineering feature claim: the runtime gain does not validate the nonconvex contact law. It is not a cross-platform speed guarantee, and the finite-J2 affine/MPC Procedure needs its own ownership review before sharing this execution optimization.

Promotion rule

Gates 1--4 and 6--8 are mandatory for any claim involving nonconvex rigid features. Gate 5 determines the friction/geometry combinations allowed in the claim; a locally planar Coulomb test never licenses sharp-edge friction. Gate 9 is mandatory for a release. If the nonconvex gate remains open, publish only the actually verified smaller subset, still marked experimental where the independent physical evidence is absent. Full Abaqus general-contact parity is not a 0.4.4 claim.

First implementation evidence (bounded)

The opt-in research module boundary_models.normal_augmentation separates the signed algorithmic AL functional from physical contact energy. It binds accepted multipliers to a contact-pair identity, fixed reference trace (point IDs, node support, shape values, integration weights and reference query geometry), rigid-surface fingerprint, units and explicit acceptance/outer-iteration policy. It requires a converged total residual at each frozen-multiplier outer iterate, and atomically refuses mismatched restart State. Its spring/plane exact solution and smooth plane/sphere finite-difference tangent tests and the independent DOLFINx/UFL plane/sphere operator oracle are local mathematical evidence only. They do not establish the J2+contact+MPC product workflow. The next admission is a single supported analytical plane in the full nonlinear Procedure, with the same total-system and accepted-increment transaction as penalty contact; an adaptive integration partition must continue to reject AL until multiplier transfer is separately verified.

Whole-increment augmentation design, not a second solver

For that analytical-plane admission, keep FiniteStrainJ2StandardProblem as the only Newton/line-search/linear-solve owner. The contact Operator reads a fixed outer-iterate multiplier and contributes its total residual and tangent before the existing MPC reduction. The Procedure snapshots displacement, material State, tool pose/work and accepted multipliers once at the start of the increment, then repeats: solve total Newton with a frozen multiplier; test total equilibrium; test penetration and complementarity; if needed, update only the trial multiplier and solve the total system again. Only a converged final outer iterate permits one joint commit and one checkpoint. An exhausted outer loop or Newton/cutback failure restores the complete pre-increment snapshot. In particular, a converged inner Newton iterate is not a valid checkpoint, and its algorithmic AL functional is not physical stored contact energy. Result must reuse the ordinary constraint dual and accepted-path work evidence, but mark physical contact-energy closure unavailable until the finite-penetration enforcement residual is separately bounded; it must not insert the AL functional into contact_potential merely to make an energy equation appear closed. The current penalty ContactTraceAssembly explicitly requires a nonnegative physical potential, so reusing it as an AL wrapper would violate its contract. The new Operator needs a contribution type that exposes the same residual/tangent and force/moment protocol while keeping algorithmic and physical energy distinct. Admission requires the existing penalty Step to remain unchanged by default and the AL path to pass a fixed-trace restart identity, one plastic-history path and one MPC-reduced total-tangent comparison. A changing feature partition cannot use this State until a conservative, identified multiplier-transfer rule has its own tests.

2026-10-19: bounded fixed-plane AL enters the ordinary Step

steps.normal_augmentation(...) now explicitly selects a bounded experimental outer Procedure inside the existing standard finite-J2 Step. It is limited to one fixed frictionless analytical plane, serial P1 tetrahedra, a scalar penalty and ordinary strong constraints. Coalesced nodal reference weights remove the previously demonstrated duplicate Gaussian multiplier rows. An individual normal row with no free displacement after strong constraints is rejected. This algebraic check is not a mesh-uniform inf-sup theorem: no MPC, moving/curved tool, mixed space, changing trace or friction promotion follows.

The Operator keeps the multiplier fixed throughout every inner Newton and line-search trial. The Procedure reconfirms the total equilibrium residual before augmenting. The material always starts from the same pre-increment committed history. Only the final outer acceptance jointly commits material, displacement and multiplier; inner success cannot produce a checkpoint. Failed Newton, exhausted augmentation and an injected post-multiplier-commit failure all restore the preceding accepted boundary in targeted tests.

Complementarity now bounds both abs(lambda*g) and abs(p*g), where p=max(0,lambda-rho*g). Testing only the old multiplier could accept a large effective pressure with zero initial multiplier. The research multiplier checkpoint schema advances to v2, so old acceptance semantics are not silently restored. Pressure is force per reference area, and the algorithmic functional is not exported as physical contact energy. The mechanical-energy ledger is explicitly unavailable for this admission pending a bounded enforcement-work residual. Fixed-tool coordinate work remains zero, without a closure claim.

Evidence is in tests/test_finite_j2_normal_augmentation.py: actual plastic loading/unloading, independent homogeneous nominal-stress limits at two mesh sizes and two penalties, plastic displacement-controlled limit, joint restart, corrupted multiplier rejection, and public capability/execution scope checks. The independent prescribed-displacement comparison exposed a separate standard-J2 backtracking issue: provisional iterates must first satisfy the current nonzero strong boundary values. The repair is covered by a test that inspects every trial and compares with full Newton. The 202 existing standard/contact/periodic regression tests passed after this repair.

Additional independent discrete-limit tests now exercise nonuniform oblique-plane pressure (elastic and plastic) and mixed open/closed nodes. The partial-contact oracle repeatedly solves contact-free equality-constrained elastic-limit J2 problems, selecting active nodes from assembled reactions and gaps; it does not use the AL or penalty operator. At two and three cells per edge, displacement, active nodes and normal nodal forces agree with the AL Step within the declared test tolerances. This is a same-discretization enforcement check, not an independent continuum pressure-convergence result.

Two integration defects were found and repaired before promotion. First, accepted pressure export must use max(0,lambda-rho*g), not the inherited penalty-only response. Exported pressure times reference weights and normals now reproduces the assembled force; metadata states augmented enforcement and coalesced nodal reference location. Penalty-only sensitivity/enclosure methods reject AL rather than silently changing its law or multiplier trace. Second, automatic load adaptation must not treat the sum of all inner Newton counts as a single Newton difficulty. That earlier implementation exhausted 50 increments in an automatic-cutback test. The controller now uses the maximum inner Newton count; total iterations/timings and outer augmentation counts remain separately reported, and genuine outer failure still cuts back.

The new public examples/finite_j2_augmented_plane.py uses normal Model and Step APIs. On its two-cell-per-edge plastic block the half-path checkpoint continued through all four increments, final right displacement 0.00500004 m, with 198 augmentations in total. A 60-augmentation budget initially rejected the second increment (2.64e-7 m penetration versus the declared 1e-7 m limit); the example now explicitly permits 120 augmentations per increment without loosening the acceptance tolerance. This records actual cost and a bounded failure, not a speedup or universal convergence claim.

Next: retain the public fixed-plane slice as experimental; establish nonuniform pressure and active-set convergence evidence before selecting a general multiplier space. MPC needs a compatible reduced space, moving tools need accepted enforcement-work accounting, and changing feature partitions need explicit conservative transfer. The nonconvex geometry and independent same-input finite-J2 comparator gates remain open.

Fixed-plane follow-up: cost, reversed loading and integration checks

The runtime rollback token now uses immutable numerical arrays and owner/ policy identity. Disk checkpoint serialization remains a separate operation; a regression forbids checkpoint-list serialization during a normal solve. The global assembled fixed-multiplier tangent also passes a free-DOF directional difference, in addition to the local contact-law checks. Accepted events report outer augmentation count, maximum inner Newton count and actual line-search residual evaluations, rather than conflating them with load steps.

tools/benchmark_normal_augmentation.py records warmups, shuffled repeats, failed candidates, source hashes and every accepted field/material snapshot on the public four-increment example. An initial screen with the unchanged 1/128 line-search floor measured median solve/result times of 1.377/0.641/0.344 s for penalties 500/1500/5000 Pa/m at two cells per edge, and 3.319/1.494/0.752 s at three. This is roughly 75--77% less time on these small example problems by explicit numerical-policy selection, not a general software speedup or an explicit-composite-case claim. The example default remains unchanged. Geometry, material, load stations and acceptance tolerances were held fixed; all compared accepted fields met the script's declared screen.

Penalties 50000/500000 failed at the original line-search floor. A diagnostic with the explicitly smaller 1/8192 floor completed at two cells (median 0.261/0.425 s, versus 1.404 s at penalty 500 in that same run), but both still failed at three cells. Thus neither increasing penalty nor lowering the search floor is a general convergence remedy. A separate stricter componentwise comparison initially found off-diagonal stress differences of order 1e-4 Pa with the original contact acceptance. Tightening both runs' penetration/complementarity tolerances from 1e-7/1e-6 to 1e-9/1e-8 passes the unchanged componentwise comparison. Do not hide that accuracy/cost dependency behind endpoint displacement agreement. The numerical role and robustness tradeoff of AL penalty are consistent with COMSOL's contact settings.

An independent scalar reference now covers sixteen accepted stations of loading, separation, reverse plastic flow and recontact, at one and two cells per edge, with and without restart after reverse flow. For homogeneous F=diag(exp(e),1,1), zero Poisson ratio, signed plastic logarithmic strain a and PEEQ p, it uses q_trial=E*abs(e-1.5*a), dgamma=max(q_trial-Y-H*p,0)/(1.5*E+H) and P11=E*(e-a_new)/exp(e), followed by a scalar equilibrium root or the rigid stop stretch. No FE contact/material routine is used in that reference. Displacement, Fp, PEEQ, plastic dissipation and reaction match at every station. This is a homogeneous same-law verification, not spatial convergence or an independent commercial-code comparator, and does not close Gate 1 or 8.

That test exposed a real input-semantic bug: a signed loading amplitude was incorrectly rejected as a normalized progress coordinate. Constant/field strong values now accept finite signed scaling; fixed tools do not consume a motion coordinate. Independent boundary histories retain normalized input checks, and moving-tool schedules retain their admitted range. No moving-AL capability was added.

The first remote complete suite at 366824b0 reported 4301 passes, 359 skips and 13 failures. Eleven failures shared one builder defect: the default contact_integration='gauss' was being injected into mixed, no-contact J2 capability checks. That default is no longer misrepresented as an explicit contact option. A rejection test now uses the private line-search tuple contract, and an absolute-residual mesh test explicitly requests tighter Newton tolerances instead of relying on a mesh-dependent initial relative norm. Its original field and 1e-6 absolute residual assertions remain. The two affected files plus the new cyclic reference passed 52 local tests; the preceding runtime/policy/standard-J2 check passed 108. Remote integration must be rechecked at the final revision before promotion.

Call-local material linearization reuse

A whole-Step profile of the four-increment public augmented-plane example identified duplicate elastic-trial SVDs and matrix inverses in the batched J2 stress return and its consistent tangent. The material now retains those already-computed factors only within that update call. Nothing is cached on the material instance, committed State or checkpoint; scalar and independent derivative checks retain a recomputation path. No material equation, tangent, penalty, acceptance tolerance or load station changed. Three consecutive changed/retried batch updates use exactly three SVD calls, and reproduce the original accepted state and derivative.

The pinned comparison is bd9b3118's analytic tangent. The script tools/benchmark_j2_spectral_reuse.py measures complete columnar responses and the ordinary four-increment solve_result, excluding imports, JIT warmup, model construction and disk export. After a seven-pair screen, a fresh five-pair confirmation used three different mesh sizes. Every accepted displacement/field, final material state, reaction and iteration count was identical in this environment. On this Apple Silicon host:

Workload	Recompute median	Reuse median	Elapsed reduction
4096-point nonproportional material batch	0.02678 s	0.02162 s	19.2%
Whole Step, 3 cells per edge	0.7473 s	0.6612 s	11.5%
Whole Step, 5 cells per edge	2.4861 s	2.1581 s	13.2%
Whole Step, 8 cells per edge	10.6094 s	9.1895 s	13.4%

Raw timings, source hashes, ordering and declared thread environment are in evidence/contact/2026-10-19-j2-spectral-reuse-confirmation.json; the earlier screen is retained beside it. These are specific material and implicit-Step measurements, not a full explicit-composite speed claim or an independent physical-model validation. The environment variables request one BLAS thread; they are not a measured guarantee about every native runtime's worker count.

The related integration screen passed 402 tests, including material histories, analytic/numerical tangents, strong/mixed/periodic J2, AL, and finite-Hex energy. The preceding installed-wheel check at bd9b3118 reproduced full versus resumed displacement, plastic variables and contact checkpoint data exactly. A real two-rank negative test also rejects the unsupported AL combination before trace assembly; this is not distributed AL support. An output audit additionally requires the current accepted configuration before publishing an AL reaction dual, even when an earlier increment had already converged.

2026-10-19: nonuniform refinement and authoritative contact coordinates

tools/verify_normal_augmentation_spatial.py supplies an independent nonuniform manufactured elastic-limit solution, not another homogeneous patch: u_x = A*x*(1-x), A=0.02, E=1000, nu=0, with the analytical body force and nominal right-face reaction derived from P11=E*log(F11)/F11. The fixed plane constrains the right face; no plastic flow occurs. Three tetrahedral meshes use 2, 4 and 8 cells per edge and the same explicit AL policy. The retained report is evidence/contact/2026-10-19-normal-augmentation-spatial.json.

Cells per edge	Displacement L2 error	Gradient seminorm error	Contact-force absolute error	Maximum nodal pressure error
2	9.132e-4	5.775e-3	4.998e-2	5.067
4	2.289e-4	2.887e-3	1.250e-2	2.533
8	5.741e-5	1.443e-3	3.124e-3	1.281

Displacement orders are 1.996/1.996 and gradient orders 1.000/1.000. The exact contact-force magnitude is 20.6150; the finest nodal pressure error is still about 6.2%, so neither exact pressure nor general multiplier stability is claimed. Penetration is below 2.73e-10 for the declared 1e-9 tolerance. Elapsed times include measurement overhead and are not a performance comparison.

This refinement found that DOLFINx tabulated displacement coordinates can map an original mesh vertex at x=1 to 1+2.22e-16. A strict zero-gap audit then incorrectly reports overlap. After the existing adjacent-cell vertex/block identity match, linear traces now copy the authoritative mesh coordinates into their private reference buffer. There is no tool snapping, mesh mutation or tolerance relaxation. Real tetrahedral/hexahedral tests with Gauss/nodal rules retain rejection of a genuine 2**-45 overlap. Trace/high-order/implicit contact regression passed 168 tests (8 skipped); a bounded two-rank trace regression passed 36 tests per rank. Distributed trace evidence is not distributed AL admission.

Compatibility is explicit: loading a 7d2f4652 four-cell checkpoint under the corrected source rejects with Normal multiplier checkpoint trace basis differs. An affected pre-correction run must retain its original candidate; there is no inferred migration of multiplier history. The earlier successful bd9b3118 to 7d2f4652 restart comparison predates this geometry correction. The corrected source was then built with AGENTFEM_BUILD_NATIVE=0 and installed into an isolated target (no change to the user's installation). The public four-cell, penalty-5000 example passed continuous loading and half-load restart. Displacement, accepted displacement, plastic deformation gradient, equivalent plastic strain, plastic dissipation, contact State and checkpoint identity were exactly equal. Accepted increment numerics/counts also matched; timing and restart-event records are expected to differ. The wheel SHA-256 was 813bcbc66d640e0e5955ba359db493cf5a50d027638e1195f733a7e97f0ebafc. This is installed implicit-DOLFINx evidence, not optional native-accelerator validation. Two focused corrupted-multiplier/trace-identity tests confirm atomic restore refusal; the nonuniform two-mesh and independent cyclic reference follow-up passed five tests, with nine two-rank-only tests skipped in that serial invocation.

Fixed-plane accepted normal-work gate (2026-10-20)

This supersedes the earlier unavailable-energy statement only for the admitted serial fixed-plane AL path with complete accepted history. It does not close the broader Gate 4 or Gate 7 matrices above.

The existing contact-work module now integrates matched accepted pressure/gap endpoints. With positive gap on the admissible side and reference weights, Wn=sum(w*(p0+p1)/2*(g1-g0)) is positive work into the structure; Bn=sum(w*(p0+p1)/2*abs(g1-g0)) is its non-cancelling discrete bound. Positive-gap work is reported separately. Exact endpoint complementarity does not eliminate closure/opening quadrature work. The Abaqus contact-energy example explicitly distinguishes signed contact discontinuity work from physical stored energy; this is the reason for separate channels, not a claim of identical algorithms.

The Procedure uses the existing accepted energy frames and joint transaction; there is no new work State owner or solver. Augmentation/Newton iterations are not path stations. AL has no physical spring-energy history. The raw Wext-U residual is unchanged; the additional Wext+Wn-U diagnostic retains material/path integration error rather than being forced to zero. A bound on discrete work is not a bound on continuous-path error. No automatic energy verification is added. Legacy incomplete ledgers stay unavailable, and corrupt/missing/nonfinite/inconsistent new histories reject before restore.

Independent evidence uses the existing scalar finite-J2 stop reference, including load, unload, reverse plasticity and recontact. The reference uses no AgentFEM material or contact solver; stored Hencky/hardening energy, plastic dissipation and endpoint work are reconstructed independently.

Increments	Raw residual	Contact-aware residual	Discrete absolute normal-work bound
16	-7.80259e-5	-3.14497e-3	4.22724e-3
32	-1.25948e-4	-6.44190e-4	9.13273e-4
64	2.53142e-5	-6.84374e-5	1.06248e-4
128	9.08018e-6	-2.74590e-5	4.26926e-5

Units are joules for the unit-cube SI reference. The coarse raw residual is misleadingly small due to cancellation. The corrected residual and absolute work decline substantially under refinement, not identically to zero. This is a bounded cyclic numerical check, not industrial validation or a universal convergence rate. Reproduce with pytest tests/test_normal_contact_energy.py -q -s in fenicsx-env. The same suite compares contact work to an independent nodal-force dot displacement path and verifies reverse-plastic restart and post-recording failed-commit rollback. Test tolerances propagate the independently checked stretch accuracy into accumulated external work rather than borrowing a single-state energy tolerance.

Acceptance: 203 focused tests passed from an isolated installed wheel in 55.82 seconds, with the package import path asserted outside the checkout. This includes the new numerical-work checks and existing penalty, multiple-pair, mixed-J2 energy and contact-work transaction tests. The default public example also completed from that installation and exported fields, contact samples, checkpoint and result manifest. Its deliberately coarse four increments have contact-aware residual -0.00248248 J; completion is not energy verification. Correctness lint, generated-document consistency and strict documentation build passed. Native acceleration was disabled for this implicit-DOLFINx wheel; neither MPI AL nor accelerator performance is claimed. Wheel SHA-256: af0e97c59eb2f40bde7f8b25da565ae812a4e21017f9a485f8e8ec86d7dc45c1.

Prescribed-translation normal-augmentation gate (2026-10-20)

Decision: admit translation of the same analytical plane, not arbitrary moving geometry. The multiplier basis is attached to the fixed material-side reference nodes; rigid translation changes current gaps but not pressure identities or normals. Every trial projects current positions against the current tool pose. Rotations (including about a plane normal), curved tools, changing traces, friction, MPC and MPI augmentation still reject.

The established segregated AL method holds pressure fixed inside equilibrium iterations and updates it outside; see COMSOL normal contact. We retain that architecture and the existing ordinary finite-J2 Procedure. This is not a new coupled solver or a claim of mortar equivalence. Motion uses the same normalized rigid schedule and resolved Step amplitude as the existing penalty path; unloading/recontact does not erase plastic history.

For constant normal n, dg=n·(du-dq), so endpoint structural contact work splits into prescribed-tool work plus relative-gap work. The former already enters external_work; the latter uses the existing signed normal-work channel. Do not add total structural work to external work again. Tangential plane translation produces no work. AL still has no physical spring energy.

State: a converged endpoint is tied to both displacement and resolved tool factor. Changing either invalidates augmentation/commit evidence. Moving checkpoints use a v2 contact payload containing the JSON-native motion identity and accepted factor; restore validates it against the Step amplitude before joint publication. Fixed v1 contact payloads retain their format. In-memory rollback uses numerical snapshots, not per-increment JSON serialization. After-contact-commit failure restores displacement, plastic state, multipliers, tool pose and work together.

Independent checks:

• Scalar finite-J2 compression reference on two meshes: full accepted material state/pressure path, not just final force balance.
• Oblique translation: added tangential motion leaves displacement, plastic history and work unchanged.
• Global directional tangent with a tilted translating plane, fixed old material state and frozen multiplier.
• Load/unload/recontact with restart and atomic failed joint commit.
• Corrupt motion identity/factor refuses restoration; old optional None energy fields compare as unavailable, never coerced to numerical zeros.
• Current-point samples and ordinary Result retain the actual augmented pressure and separate tool/relative-gap histories.

The cyclic scalar reference is independent of the AgentFEM material update and contact solver. It solves the traction-free one-dimensional branch when open and imposes the translated stop when closed. The increment screen gives:

Increments	Tool work	Raw residual	Contact-aware residual	Discrete relative-work bound
16	0.0716047	-1.73303e-3	-2.85968e-3	3.08773e-3
32	0.0730628	-2.74924e-4	-7.57166e-4	1.06100e-3
64	0.0731485	-1.89257e-4	-2.56478e-4	1.47999e-4
128	0.0733219	-1.58346e-5	-4.29142e-5	5.96754e-5

All energies are J for this deliberately soft unit-cube reference. The corrected residual decreases by about 67 times; it is not forced to zero and the discrete-work bound is not a bound on total energy error. Reproduce with pytest tests/test_translating_normal_augmentation.py -q -s. The source-focused contact/J2/restart set passed 205 tests in 67.44 seconds. The public examples/finite_j2_translating_augmented_plane.py is the ordinary Model/Step entrypoint for the same compression/unloading/recontact workflow.

The same installed candidate passed 205 focused tests in 66.88 seconds. Public full/half/restarted 32-increment runs agree exactly in displacement, plastic deformation gradient, equivalent plastic strain, plastic dissipation, contact State, accepted energy history and checkpoint identity. Timing and restart events appropriately differ. A subsequent guard also reserves converged-but-uncommitted reaction duals for Procedure-owned work recording; a previous successful solve does not license public trial output.

tools/verify_normal_augmentation_spatial.py --tool-travel 0.01 independently checks the final nonuniform elastic-limit field u=(0.02*x*(1-x)-0.01*x,0,0), with manufactured reference body force. On 2/4/8 cells per edge, observed displacement orders are 1.996/1.995 and gradient orders 1.000/1.000. Contact force errors decrease from 0.0518575 to 0.0129639 to 0.00324105 N; maximum nodal pressure errors decrease from 5.22111 to 2.60956 to 1.31982 Pa. This is an elastic spatial benchmark, not a manufactured intermediate load path or plastic spatial-convergence proof. Reconstructable evidence is evidence/contact/2026-10-20-translating-normal-augmentation-spatial.json. Two-rank fixed and translating negative-admission tests both reject before distributed assembly; no MPI augmentation capability is promoted.

An additional nonuniform plastic gate uses a clamped block with Poisson ratio 0.3, free lateral motion and a translating plane at zero initial gap. The independent enforcement reference has no contact Operator: it prescribes the same normal displacement on the right face and obtains normal reactions from the full finite-J2 residual. Positive pressure is checked at every station, because a displacement constraint could otherwise pull a body that should separate. Eight accepted stations on 1/2/3-cell meshes are compared at penalties 1000 and 5000 Pa/m.

The exploratory 1e-8 m penetration / 1e-7 Pa m complementarity settings passed displacement/state checks but missed the unchanged point-pressure criterion on the three-cell mesh: maximum discrepancies at its first station were about 9.44e-5 and 5.50e-5 Pa. Tightening those contact tolerances by 100, without changing the mesh, material, pressure criterion or solver method, made all six comparisons pass. The final maximum pressure discrepancies over the full eight-station paths were:

Cells per edge	Penalty 1000	Penalty 5000
1	1.58e-7 Pa	9.88e-8 Pa
2	5.93e-7 Pa	3.27e-7 Pa
3	7.71e-7 Pa	6.72e-7 Pa

This demonstrates tolerance sensitivity of a point-pressure observable, not a reason to silently tighten every user's defaults or a proof of continuum pressure convergence. The reference shares the constitutive kernel, so it is independent enforcement, not independent material verification. Reproduce with tests/test_translating_augmentation_plastic_reference.py.

The candidate including that provisional-dual guard passed 251 focused tests from an isolated installed wheel in 76.74 seconds. Package imports were asserted outside the checkout. Native accelerators were disabled for this implicit-DOLFINx wheel; no native acceleration result follows. Wheel SHA-256: b4094ebfa5d67a87d09d2bdd54629b19ca9053e3661f69b0e015ddaa5b720dd8. Correctness lint, generated-document consistency and the external-directory strict documentation build passed.

Cyclic accepted-output follow-up

Installed CLI use exposed a common output defect, not a contact-law failure: at normalized Step coordinate 0.5 the cyclic tool amplitude is 1.0, and at coordinate 0.75 it is 0.0. The old exporter compared the accepted tool pose to the coordinate instead of the resolved amplitude. Both ordinary penalty contact and augmentation reproduced AFM-CONTACT-EXPORT-POSE after a valid solve. The shared Result exporter now checks the Procedure's resolved amplitude, records coordinate and amplitude separately, and continues to reject stale or nonfinite pose samples before creating output. This is not a bypass of pose validation and does not change the solver or loading.

The follow-up wheel passed 331 targeted tests in 94.13 seconds from an isolated installation, including ordinary friction and active/convex contact partitions. SHA-256: c93795ccb5c35c5a6d6c962d7db6e2b146abb97113fed7779af82b9caf4df544. The public example was then run from outside the checkout: one continuous 32-increment run versus save at 0.5, restart to 0.75, and restart to 1.0. Displacement, plastic/contact State, complete energy history and checkpoint identity are exactly equal. Increment diagnostics also agree excluding elapsed timings; execution logs correctly retain the two restart events. Both intermediate stations now export their accepted raw contact arrays and VTP view with the correct tool factor. This remains serial Mac evidence, not a cross-platform or performance claim.

Compatibility was also checked against an actual fixed-plane v1 checkpoint produced before this translation change (f226d34c candidate): the final state and four energy frames load without altering the numerical solution. That check is a completed-checkpoint restore, not a legacy partial-run continuation claim.

Next: finish remote CI acceptance, then address the broader mesh-by-penalty and changing-feature gates. Translation alone does not close the nonconvex L-tool, multiplier transfer or commercial local-parity matrix.

2026-10-20 design: optional multiplier-iteration acceleration

The next bounded experiment targets repeated converged Newton solves, not a new material algorithm or a relaxed acceptance criterion. A private weighted dynamic-Aitken probe reduced outer updates on the nonuniform plastic press and the unloading/recontact example while keeping the existing equilibrium, penetration and complementarity checks. This is screening evidence only.

Design before promotion:

• Procedure owns increment-local secant history. State still owns the frozen, trial and accepted multiplier; no accelerator can commit material or contact.
• Apply the projected map F(lambda) = max(0, lambda - penalty*gap). Use the fixed reference-trace area metric for the vector secant, then project the relaxed proposal onto nonnegative pressures. The penalty and Newton tangent are unchanged. The inner solve always sees a frozen multiplier.
• Reset history at each new increment/attempt and active-set change. Degenerate secants use the ordinary update; relaxation is bounded to [0.1, 10]. This safeguard is not a general convergence theorem or a promise that every problem is faster. Failed inner solves retain normal rollback/cutback.
• Add an explicit experimental acceleration="aitken" option; default "none" preserves the old path and checkpoint encoding. Accelerated checkpoints identify the numerical policy. No secant history crosses accepted boundaries.
• Validate scalar/degenerate maps, state witness and atomic failure, independent prescribed-displacement pressure, cyclic unloading/recontact, restart and work histories. Record actual outer/Newton work and alternate timing order.
• Do not extend AL admission to MPC, curved or changing traces in this change. The periodic reduced normal rows require a separately designed multiplier space and joint Procedure integration; deleting the guard is not a solution.

The research basis is the projected dual fixed-point formulation and dynamic Aitken/Crossed-Secant comparison in Koliesnikova and Ramière, arXiv:2603.12205, sections 2 and 4. Their constant linear stiffness and reported performance are not assumed for our finite-J2 Newton solves. We use a bounded, area-weighted variant with active-set resets, not their claim of parameter-unbounded performance.

Implementation and bounded acceptance:

• The option is now a core Procedure control, not a benchmark monkeypatch. Its State update remains witnessed by the current converged total residual. Fixed/moving default checkpoint v1/v2 encodings remain unchanged; opt-in accelerated provider checkpoints use v3 and refuse a changed policy.
• A 121-test focused pass covered the initial implementation, independent prescribed-displacement pressure on three meshes/two penalties, scalar cyclic reference/refinement, injected cutback, joint failure rollback and restart. Further closing checks are recorded in the task report, not added to this count when they overlap.
• The committed benchmark warms both policies and alternates three repetitions of the public 32-increment translating-plane example on a 3×3×3 cube mesh. Median solve times: default 2.058291 s; Aitken 1.403542 s, 31.81% less solve time. Outer updates: 106 → 45; Newton/linear solves: 209 → 140. All accepted displacement snapshots differ by at most 1.11e-10 m, final material state by 3.34e-10, final pressure by 5.02e-8 Pa and energy histories by 2.30e-8 J (the latter comparison also includes load coordinates). Setup was measured separately. This is a small same-machine implicit test, not a full composite run, universal speed guarantee or confidence interval.
• The first benchmark reader incorrectly treated the per-tool work dictionary as a float. It was corrected to flatten named tool channels and compare their availability; the solver and numerical tolerances were not changed.

No new MPC, rotation, curved trace, multiplier transfer or MPI admission was added. Those gates remain explicit future work.

Closing verification: 376 targeted source tests passed in 118.47 s, including the nearby finite-J2, penalty/friction, active/convex partition and pressure/work paths. Generated API consistency, correctness lint, diff checks and a strict documentation build outside site/ passed. A fresh isolated wheel ran the public 32-increment example with --acceleration aitken from outside the checkout, including accepted contact output, result manifest and checkpoint: 45 outer updates, final right-face displacement −0.015 m, tool work 0.0730628 J. Wheel SHA-256: 000f5fb3e096abe4cbff7eed2d00a16e07af01adcf7357c5c51334ddd3bee5de. This wheel smoke is not the same claim as running all 376 tests from that wheel.

Remote CI for the preceding 1e60e174 revision passed its unit/interface, installed/native and distributed checks, but the overall FEniCSx job was cancelled during the release-demo suite after about 30 minutes. It is not an all-green release gate. The subsequent a62cef23 revision passed Test run 39375343048 including Linux native distribution, FEniCSx and macOS installed-wheel foundation acceptance, and Documentation run 39375343074. The FEniCSx job took about 22 minutes 48 seconds; no CI timeout or scientific tolerance was changed to obtain this pass. PR #118 remains a draft, not a merged/released 0.4.4 or an independently validated commercial-contact match.

Partial-contact acceleration acceptance (2026-10-20)

The previous timing patch did not by itself establish accelerated behavior on a spatially partial contact region. The follow-up tests add:

• Both default and Aitken updates against a separate equality-constrained, elastic-limit primal-dual active-set reference on two meshes. The reference assembles no contact or augmented residual. It verifies the same discrete nodal obstacle, not an independent constitutive law or continuum limit.
• A 16-increment finite-J2 path against a tilted fixed plane, with plastic loading, unloading and recontact. Every accepted displacement, material state, pressure, active set and energy record is compared between policies. The test requires a genuinely mixed active/open patch and changing activity.
• A checkpoint at peak load, with all subsequent stations compared after restoration; an injected failure after contact commit must restore pressure, material, displacement and the accepted ledger exactly before a valid retry.

The tests are test_partial_contact_acceleration.py and the extended independent reference in test_finite_j2_normal_augmentation.py. This is correctness and lifecycle coverage, not another timing claim. No runtime default, pressure basis, numerical tolerance, geometry admission or MPI/MPC guard was changed. The focused source run passed 102 tests in 56.40 seconds, covering the partial patch, accelerator controls, ordinary and translating augmentation, independent plastic reference, rollback and restart. Correctness lint, generated-document consistency and diff checks passed. This follow-up does not substitute that source run for the preceding revision's installed CI.

Serial affine execution and actual-offset diagnostic (2026-10-20)

The serial affine Procedure now delegates its fixed-factor Newton equilibrium to _affine_equilibrium.py. The path owner still owns increment prediction, cutback, physical acceptance, material/contact commit, output and restart. The inner owner retains a full residual and its Operator contributions only at the identical current trial, avoiding the former norm-evaluation followed by a second residual/contact evaluation before tangent assembly. Changed displacement or material trial reassembles; no trial cache crosses an increment or checkpoint. PETSc resources are released on rejected trials and exceptions. The distributed affine implementation and unsupported contact combinations are unchanged.

tools/benchmark_affine_trial_reuse.py loads only the historical serial path function from frozen commit a5b5a8fc, retaining the same material and Operator implementations. It warms each path and alternates five measured repetitions, checking accepted iteration/line-search paths, displacement, material vectors, snapshot fields and contact nodal residual. The committed report is evidence/contact/2026-10-20-affine-trial-reuse.json:

Small serial path	Old median	Reuse median	Elapsed reduction
Fixed sphere	0.10193 s	0.09485 s	6.95%
Moving sphere	0.11023 s	0.10133 s	8.07%
Plane friction	0.09730 s	0.08907 s	8.46%
Automatic plastic cutback, no contact	0.07696 s	0.07700 s	no demonstrated gain

These tiny whole-path measurements identify avoided work, not a universal speedup, statistical confidence interval, or a composite-run forecast. The focused integrated source run passed 107 tests, with 10 MPI-only tests skipped. A subsequent single bounded two-rank run passed 28 tests on each rank, including those negative-admission checks and distributed affine tests. Installed and cross-rank restart acceptance must be recorded separately.

Closing checks found a missing transfer of the residual threshold into the fixed-increment failure report. It was repaired and a public-path regression now requires the diagnostic and exact accepted displacement/material rollback after an intentionally failed next increment. The expanded source run passed 218 tests in 63.60 seconds; correctness lint passed. An isolated native macOS wheel, imported outside the checkout with the source-path override disabled, passed 82 focused tests in 20.24 seconds. Its SHA-256 is 524b653c2030140f5f38aaf2bac2801bbb8ef7f29e04b08fca28c5fea9436473. The installed ordinary periodic-J2 checkpoint driver passed 1→2 and 2→1 rank restore. This checks preservation of the existing distributed no-contact route; it does not admit distributed implicit contact.

The new private contact_affine_gap_research.py constructs all supplied analytical-plane trace gaps as g(q) = A q + b, using actual reference coordinates, transformation and affine offset. Exactly zero rows with resolved negative offsets are algebraic incompatibility witnesses for this floating-point discrete system; merely small rows are not treated as zero. For a real periodic fixture at macro stretch 1.02, a plane limiting x to 1.01 conflicts at four immovable trace nodes, while x <= 1.03 has an explicit feasible witness. Direct projection at randomized reduced coordinates agrees with the affine gaps. This closes the earlier missing-offset diagnostic, not the AL/MPC solver or multiplier-space gate.

A bounded optional SciPy/HiGHS search uses free displacement variables and rechecks every gap of any returned candidate. Optimizer infeasibility alone is reported as unresolved, not a proof; the witness says nothing about material invertibility or points outside this trace. Tests include conflicting nonstationary inequalities, tiny nonzero rows and a false optimizer witness. The focused diagnostic/normal-law/CI-contract run passed 95 tests. The HiGHS API documents the variable bounds and numerical statuses used here. Multiplier identifiability and primal feasibility remain different questions; neither this screen nor removing duplicate rows proves spatial inf-sup stability.

CI operational repair: at a5b5a8fc, the FEniCSx job passed its unit/interface and installed/distributed checks, then hit its 30-minute job budget during the release demos. Its unit/interface stage alone took about 23 minutes 10 seconds. The job now has a 45-minute bound and process-local single-thread BLAS/OpenMP settings. No tests, scientific tolerances or solver policies were removed. This edit is not itself a successful release acceptance.

Bounded affine augmentation admission (implemented, 2026-10-21)

The actual-offset screen separates an incompatible imposed macro strain from an algorithm failure. A compatible interior face patch now has a separate hard-obstacle reference: eliminate the active reduced normal coordinates exactly, solve the same frozen-old-state J2 equilibrium without contact forces, then recover pressure from the body residual. Two penalties and two mesh sizes agree in displacement, plastic State and pressure; this is a discrete formulation comparison, not an independent constitutive model or an inf-sup proof.

The experimental public extension is deliberately narrower than general full-row-rank MPC: one fixed/translating analytical plane, serial P1 tetrahedra, one coalesced nodal pressure per contact node, and nonzero disjoint reduced normal row supports. Sparse row inspection can establish independence without a dense transformation or a machine-dependent rank tolerance. Overlapping or prescribed normal supports remain rejected, even when a more general method might handle them. This restriction is not a statement that those models are physically impossible.

The ordinary affine path now passes single material commit, failed-outer/callback rollback, translating-tool work, accepted normal work, restart and capability-negative tests. A pre-trial snapshot owns Operator rollback; the outer Procedure never commits material. Signed normal work uses accepted gap/pressure endpoints and remains distinct from recoverable penalty energy and physical dissipation. Output thinning must not thin this ledger. Ordinary serial and distributed paths retain their existing behavior. No curved, rotating, frictional, mixed or distributed augmentation is included.

The public cyclic example uses 16 increments, explicitly requests accepted displacement frames, and records loading, unloading and recontact. Separate tests resume from both loaded and unloaded boundaries and recover the same final material/pressure/work history. Automatic cutback discards a deliberately rejected converged outer trial; corrupt pressure, scalar work bounds and station counts are atomically rejected. Normal relative-gap work is stored at every accepted increment regardless of displacement-frame thinning.

Stage checks on the source tree: 168 targeted contact/affine/normal-work tests passed in 96.65 s; 180 workflow/result/solver and corruption checks passed in 45.24 s. Two MPI ranks each passed 30 tests in 1.97 s, including early rejection of both standard and affine distributed augmentation. This proves the negative capability boundary and preserves ordinary distributed MPC, not distributed contact support.

An isolated native macOS arm64 wheel (SHA-256 0abbe500410d56143b18db1c128db30f0db9f7390959ee851f5893a329be178d) passed 24 installed affine/rollback/restart tests in 45.66 s, plus the new frame-thinning/work-ledger test in 7.27 s. Its import location was explicitly outside the source tree. The public example completed 16 cyclic increments and 50 outer updates; final maximum penetration was 2.32004e-9 m. Independent meshio/HDF5 inspection read 17 complete U/UMAG frames, 384 tetrahedra and 125 points, with unwarped reference coordinates at every frame. The HDF5 file occupied 220169 bytes. The example now explicitly requests output_every=1; its first trial had retained only the ordinary default initial/final snapshots. These are small-example output facts, not a size estimate for the private 255041-cell composite model.

The first low-penalty research attempt (1000 Pa/m) did not meet the declared outer acceptance within 60 updates. Comparisons at 10000/40000 Pa/m on four cells per edge and 20000 Pa/m on eight cells passed the unchanged penetration and complementarity criteria against exact active-constraint elimination. Penalty-independent equilibrium is an observed discrete result in this matrix, not a universal convergence-rate promise or a continuum pressure certificate.

Remote CI for stage 8f0c52f8 reached 4436 passed, 361 skipped and one failed unit/interface test. That sole failure was the newly added workflow-policy test importing PyYAML in the deliberately minimal numerical environment; it was not a finite-element failure. The test now checks the fixed workflow text using the standard library. No numerical test, tolerance or stage was removed.

2026-10-21: explicit full-Newton policy is not an Armijo test

Audit of the common affine Newton loop found a real option-contract defect: line_search="basic" (and explicit None/"off") previously selected one trial of length one but still required Armijo residual decrease. On an assembled cubic residual, the mathematically valid first Newton step from u=0.1 to u=33.4 temporarily increases the residual before converging to u=1. The new regression first produced two failures (basic and None) and one pass (backtracking). A one-trial Armijo rejection is not basic Newton.

The corrected serial and distributed affine loops accept a finite, constitutively valid full trial in basic mode. An invalid full trial is rejected and restored; it is not silently backtracked or committed. Explicit no-search now also lowers to PETSc basic, rather than leaving SNES free to select its default. Default backtracking and its checkpoint identity remain unchanged. Corrected explicit basic/no-search identities reject legacy checkpoints whose algorithm would otherwise change on continuation. This follows PETSc's basic implementation, not a claim that full Newton is universally faster or more robust.

Evidence: 153 focused solver/workflow/material/restart/CI-scope tests passed with eight genuinely distributed tests skipped in the serial run. The final policy/reuse subset passed 17 tests, including an invalid full-trial restoration and moving augmented-contact restart comparisons against backtracking. Two MPI ranks each passed the periodic cubic total-reduction comparison (one test, five then-deselected tests per rank). This is ordinary distributed MPC evidence, not admission of distributed augmented contact.

2026-10-21: periodic plastic-patch sensitivity is measurable

tools/verify_affine_augmented_path.py uses the public example and reports displacement norm, reference-area pressure, resultant force, mean/max PEEQ, normal relative-gap work and constraint mismatch at the same four physical stations. It does not export full field archives or tune the physical problem to obtain a pass. The example's inexpensive 4-cell/16-increment defaults are a workflow demonstration, not a mesh/increment accuracy recommendation.

The 12-case matrix in evidence/contact/2026-10-21-affine-augmentation-sensitivity.json spans 4/8 cells per edge, 16/32/64 increments and penalties 10000/40000 Pa/m. Every case meets the unchanged penetration/complementarity tolerances. At fixed mesh and increment count, the two penalties give essentially the same discrete response. Increment and mesh sensitivity remain significant: for example the 8-cell final contact-force magnitude changes from about 0.69147 N at 16 increments to 0.75451 N at 32 increments.

The frozen cf1bfc36 installed wheel was then used for 128/256-increment refinement, recorded in evidence/contact/2026-10-21-affine-augmentation-time-refinement.json. All four cases pass numerical acceptance. At 8 cells, the final force changes from 0.8176322 N to 0.8273062 N (1.17% relative to the finer path); mean PEEQ changes from 0.05743225 to 0.05743618. At 4 cells, the corresponding force change remains 2.29%, and the 256-increment 4/8-cell forces differ by about 0.48252 N. Thus a successful solve and penalty insensitivity do not close the spatial accuracy gate. Point pressure/PEEQ maxima near the patch edge are not used as a universal convergence criterion.

The signed relative-gap work tends toward zero along the 8-cell time sequence (about -2.02e-4 J at 32 increments, -1.35e-5 J at 128 and -4.31e-6 J at 256). It is still an accepted-endpoint path quadrature, not elastic storage, irreversible dissipation or automatic first-law verification. These data do not establish an asymptotic order. Recorded costs include setup and scalar observation with lightweight development overlap; this study is not a paired performance benchmark.

The corrected-Newton wheel at 8da7b93b (SHA-256 a819e2515437cb0e8c81ba3f800bec782d261f464716b331eb45dee4554e001e) passed 33 installed policy/reuse/affine-augmentation tests in 76.15 s. The earlier cf1bfc36 default-backtracking checkpoint restored all 16 accepted increments with this candidate. A separate installed TCP-transport MPI check passed the periodic cubic comparison on both ranks; this process-local setting does not alter global MPI configuration or admit distributed contact. The complete remote cf1bfc36 workflow 39464864247 passed Linux numerical and macOS installed-wheel foundation acceptance; that does not automatically validate later commits or close the remaining scientific gates.

2026-10-21: distinguish a support-model defect from contact convergence

The original point-pinned periodic example was deliberately kept unchanged while inspecting its full-space accepted residual. With 4 cells per edge, 32 increments and penalty 40000 Pa/m, the resultant balancing the one-sided tool is about 1.18533 N in x. The eight nodes of the pinned periodic corner class carry that entire resultant; the sum on the other nodes is below 1e-11 N. Thus the point constraint is not merely removing a harmless rigid translation in a self-equilibrated cell: it supplies the net external reaction. This observation gives a concrete reason to question a continuum refinement claim for that fixture. It does not prove that all sensitivity comes from one cause or that any new fixture is automatically converged.

The 12-cell, 128-increment original-fixture run is retained in evidence/contact/2026-10-21-affine-augmentation-spatial-refinement.json. It completed all increments and numerical contact tolerances, with final contact-force magnitude 0.530237 N versus 0.817632 N on 8 cells. The subsequently started 16-cell run was intentionally stopped after the support diagnosis; it is explicitly marked incomplete, not a failed constitutive solve or a passed refinement point.

The example now accepts --affine-end-face-support, an explicit physical change: x-motion on the two z end faces follows the declared macroscopic affine motion. It reuses existing linear equations and the same contact law, material, Procedure and State. The contact patch remains free in its normal direction. This is a supported periodic structure, not a homogenization RVE or a numerical stabilization setting. The distinction matters: COMSOL's periodic-cell theory states the homogenization assumptions and its own rigid-motion handling; it does not justify adding arbitrary supports to an RVE. Our support conclusion comes from the measured force balance, not from borrowing a commercial capability claim.

Three installed-fixture regressions passed: the original corner-class resultant, the supported finite-area reaction and prescribed displacement, and rejection of a checkpoint belonging to the other fixture followed by supported restart/continuous agreement. They check the engineering problem being solved, not only whether Newton terminates. The sensitivity driver now records the fixture, installed runtime identity and transport setting, and atomically saves every common physical station so an interrupted experiment cannot lose all its intermediate evidence.

The supported-fixture matrix evidence/contact/2026-10-21-supported-periodic-contact-refinement.json completed all six 4/8/12-cell and 32/64-increment candidates at penalty 40000 Pa/m. Every accepted increment meets the unchanged 1e-8 m penetration and 1e-7 pressure-length complementarity bounds. At 64 increments the final force magnitudes are 4.588710, 4.229122 and 3.960610 N. The 8-to-12-cell force difference is still 6.78% relative to the finer mesh, while displacement L2 and mean PEEQ differ by about 0.96% and 0.59%. At 12 cells, doubling 32 to 64 increments changes final force by 5.89%. Consequently the new fixture has not passed a converged engineering-response claim either. The smaller sensitivity is not credited as a solver speed or accuracy gain: the physical support changed. Neither the sign nor the coarse-path relative error of the small signed gap-work quadrature is used as a dissipation test. The earlier two-case screen is retained separately. All costs here include setup/observations and brief lightweight test overlap, not paired timing.

The completed post-fixture checks were three source regressions, 82 focused project-execution/environment/CI-selection tests, lint, generated-document consistency and a strict documentation build. An adjacent read-only execution-environment improvement records allowlisted MPI transport/progress requests and Accelerate/NumExpr thread settings. It does not choose a transport, expose unrelated environment values or add restart restrictions. The private composite replay retains the earlier frozen 8da7b93b installation; this later diagnostic change is not injected into the running candidate.

Scoped linear-solver ownership (2026-10-22)

The frozen serial affine equilibrium now owns one KSP across its Newton iterations and releases it on success or failure. Every iteration still assembles and sets the current reduced tangent; neither numerical factors nor an old preconditioner are deliberately frozen. The scope ends before an outer augmentation, a new increment, or a changed constraint reduction. The general one-shot linear-solve helper also releases its owned KSP after configuration, operator, solve or diagnostic exceptions; borrowed KSPs remain caller-owned.

This follows PETSc's operator lifetime rules, not the distinct preconditioner-lagging option. The same-model 8-cell/16-increment supported-fixture screen has two warmups and alternating fresh/scoped/scoped/fresh measurements. Median solve costs were 25.2611 versus 24.8704 seconds (1.55% lower); this small single-host difference is not a substantial performance claim. KSP creations decreased from 149 to 59 over the path. All measured displacement/material/contact/work arrays had zero maximum difference and the accepted Newton paths agreed. Evidence and the reproducible driver are evidence/contact/2026-10-22-affine-linear-reuse-corrected.json and tools/benchmark_affine_linear_reuse.py. The first driver's post-solve result access error is retained separately; it was not a failed physical solve. The value retained here is bounded ownership and exception safety, with a small measured reduction in repeated setup, not a claim of 20% acceleration.

Supported-fixture time refinement (2026-10-22)

The eight-cell supported periodic fixture was continued with 128 and 256 increments at unchanged penalty 40000 Pa/m, penetration tolerance 1e-8 m, complementarity tolerance 1e-7, material and reversal stations. Evidence is evidence/contact/2026-10-22-supported-periodic-time-refinement.json. Both paths completed and every accepted increment met the numerical contact criteria; this is not an independent material or continuum verification.

Increments	Final force magnitude (N)	Displacement L2	Mean PEEQ	Newton iterations
128	4.384499107	0.01100073837	0.06352729940	1113
256	4.469811614	0.01100023434	0.06355785533	2075

The final force difference is 1.91% relative to the finer path, whereas mean PEEQ differs by about 0.048%. The signed relative-gap work approaches zero (-7.27418e-5 versus -1.86169e-5 J); it is not relabelled plastic dissipation. This narrows the temporal uncertainty without removing the separate spatial sensitivity or external-reference gate. In particular, the earlier 8-to-12 mesh comparison at only 64 increments is not a temporally converged spatial study. The next mesh comparison must use a sufficiently refined common path. Recorded costs include setup and observation, with brief independent test overlap; they are not a speed comparison. These runs loaded the pre-KSP-reuse implementation, and their runtime source identity is retained in the report.

Accepted-series output boundary audit (2026-10-21)

A secondary audit while the frozen private replay runs found two mutable descriptor aliases: caller-owned nested field selectors and a provider-owned state schema. Two tests failed before the fix; the series now owns independent small descriptors and freezes the schema only after its first successful frame. It does not add a whole-state copy or change the numerical trajectory.

Four additional failing counterexamples showed that the streaming adapter accepted a scalar under cauchy_stress, a different declared stress measure, a missing source location, or a location change between frames. It now requires its documented per-cell finite real 3×3 Cauchy stress and retains the source location/measure in metadata. A changed provider descriptor is rejected before writing the next frame. Existing valid frames can still be closed as an incomplete segment; no physical validation is inferred from correct labels or shapes.

The final combined output/project/cell-transport/journal/topology subset passed 85 tests in 3.73 s. This is a short source regression run, not a performance measurement. The ongoing private full run remains on its frozen 8da7b93b wheel: its provider already satisfies these contracts, and no runtime files were replaced during execution.

Interrupted output follow-up (2026-10-21)

A two-frame serial Hex8 counterexample exits the child process with os._exit after write_fields returns, skipping context cleanup and destructors. Before the fix, reopening the heavy-data file fails with bad object header version number. Complete-frame HDF5 flushes eliminate this reproduced failure. An atomically replaced *.partial.xdmf labels the last written view incomplete; an independent meshio reader verifies both frames, the volume topology and point/cell data after the child has stopped. Clean close atomically publishes the ordinary index and removes only its own partial index. Existing partial output is not overwritten. Flush, partial-index and final-index failures are tested explicitly.

The combined output/layout/project/response-material/history subset passed 158 tests in 6.74 s; lint and diff whitespace checks passed. These are correctness checks, not a performance experiment. The frozen private replay was not modified. This fix does not recover its previously damaged artifact, provide concurrent readers or guarantee mid-write/power-loss safety. The current per-frame-group format cannot merely toggle SWMR: that protocol requires predeclared appendable datasets and a separate compatibility design. The final result metadata and verified checkpoints still own completion and restart respectively; an incomplete visualization is neither.