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0.2.6 G07 B3 — Remaining gap resolution

Evidence ID: 026-G07-B3-GAP-RESOLUTION-001

G07_B3 = PARTIAL. This step analyzed the two remaining blockers without changing the solver, formulation, reference data, convergence thresholds, or G07 status.

TL HEX8 diagnosis

The unchanged production case is HEX8_m4_a10_compression_l0.2_d0.12 with four cells, aspect 10, distortion 0.12, compression load scale 0.2, and tolerance 1e-8. Fixed-step probes were run with the same physical history and 128, 256, and 512 increments.

increments failure increment load factor reason residual initial → final line-search reductions runtime fields
128 48 0.375 MAX_ITERATIONS 7.812500e-4 → 4.392803e-4 608 finite
256 96 0.375 MAX_ITERATIONS 3.906250e-4 → 2.819640e-4 667 finite
512 192 0.375 MAX_ITERATIONS 1.953128e-4 → 1.683841e-4 766 finite

The failure index scales exactly with the partition, so the physical failure factor remains 0.375; subdivision does not pass the limiting state. The residual drops sharply on the first Newton update and then decreases only slowly. The last recorded reduced-tangent diagonal ranges were finite and positive (2.5355..10.1477, 2.5504..10.1519, and 2.5449..10.1503 for the three partitions). The initial determinant minimum was 1.0; the last recorded determinant minima remained approximately 0.991. Mesh validation passed. No singular tangent, non-finite force/tangent, or invalid element was observed on these probes.

The primary classification is therefore SOLVER_ALGORITHM_LIMITATION, with step-size sensitivity as an observed contributing symptom. It is not classified as FORMULATION_BUG, MESH_PATHOLOGY, or REAL_BUG by this evidence.

The existing adaptive driver was also probed with a bounded minimum increment of 0.01, cutback factor 0.25, and maximum eight cutbacks:

partition accepted steps rejected attempts terminal result terminal factor terminal relative residual rollback
8 5 2 MIN_INCREMENT_REACHED 0.34375 1.536582e-4 TRUE
16 8 2 MIN_INCREMENT_REACHED 0.359375 5.484982e-4 TRUE
32 11 1 MIN_INCREMENT_REACHED 0.34375 1.536582e-4 TRUE

Cutback/retry preserves the committed state, but does not complete the history. Consequently TL_HEX8_COMPLETE_HISTORY = NO and no complete HEX8 external correlation is claimed. TL_HEX8_FINAL_RESULT = FAIL for the requested matched-path proof, bounded by this explicit algorithmic limitation. No functional fix was attempted.

ARC-002 refined-mesh window

The B1 coarse reference observed a turning point near load factor -0.03732654 and controlled displacement -0.89337693 for both radii. The same refined mesh was evaluated beyond the original B1 windows:

radius maximum steps runtime result turning point final load factor final displacement minimum det(F)
0.01 320 finite continuous path not observed -0.04006680 -1.11601411 0.53594888
0.02 160 finite continuous path not observed -0.04006683 -1.11601476 0.53594781

The refined path remains finite and continuous at both extended windows, but there is no turning-point observable to compare with the coarse mesh. Further extension does not justify inferring one: the refined path reaches an explicit invalid deformation before any detected turn at both tested settings:

  • radius 0.01, 640 steps: element 3, det(F) = -3.396911e-4;
  • radius 0.02, 320 steps: element 3, det(F) = -1.433152e-1.

ARC002_FINAL_RESULT = DEFERRED and ARC002_REFINED_TURNING_POINT = NO. This is a limitation of the declared refined-mesh turning-point evidence, not a fabricated pass or a formulation change. No turning point is extrapolated from the coarse mesh.

Scope, provenance, and closeability

  • B3 baseline: 921e026934fbdedce0d4b0537922d6d22ab10e0f.
  • Probe runner: scripts/run_g07_b3_gap_resolution.py.
  • Machine-readable evidence: qualification/0_2_6/g07_b3_gap_resolution/g07_b3_gap_resolution_evidence.json.
  • The JSON records the execution SHA, case definitions, policies, probe results, finite-field checks, mesh quality, residual histories, and Arc path digests.
  • REAL_BUG_FOUND = NO.
  • FUNCTIONAL_SOURCE_CHANGED = NO.
  • NUMERICAL_REGRESSION = NO for this source-unchanged diagnostic step.
  • Full regression is skipped by the declared B3 policy.

Remaining blocking gaps are G07-TL-008-HEX8-COMPLETE-HISTORY and G07-ARC-002-REFINED-MESH-TURNING-POINT-COMPARABILITY. G07 Owner closeout is not ready; no promotion is made.