026-G08 Linear Buckling Contract

Status

026-G08 is PASS_WITH_LIMITATIONS by explicit Owner closeout. This document defines the contract and summarizes the archived evidence; the active machine-readable decision is recorded in qualification/0_2_6/g08_owner_final_review.json. The earlier g08_owner_closeout.json remains retained historical evidence.

Audited route

The public route is linear_buckling, dispatched by src/solveur/core/router.py to LinearBucklingSolver in src/solveur/core/analyses/buckling.py. The current implementation:

• accepts one homogeneous family from TET4, TET10, HEX8 or HEX20;
• requires one homogeneous isotropic_3d material;
• accepts nodal dead loads and rejects distributed loads;
• solves a proportional preload through the existing Full Newton path;
• forms the initial-stress geometric contribution through the existing Total-Lagrangian assembly;
• uses SciPy sparse eigen routes (eigsh, with the controlled eigs shift-invert fallback for an indefinite bracket);
• returns the first critical tangent-instability factor and one normalized mode.

This is a linearized first-instability calculation. It is not a post-buckling, collapse, arc-length, physical-validation or general stability claim. Beam, shell and discrete elements are not supported by this solid route.

Historical evidence

The 0.2.5 record contains bounded TET4 Euler evidence, a bounded assembled-mesh trend, and a CalculiX adapter that can generate same-model solid decks. Those records remain historical and bounded. They are not silently promoted to a 0.2.6 gate result. The existing Code_Aster structural adapter explicitly records that it has no equivalent 3D solid eigen-buckling modelisation for this comparison; that row is NOT_APPLICABLE, not PASS.

Requirements and policies

The machine-readable contract is qualification/0_2_6/g08_requirements.json. The case-to-requirement mapping is qualification/0_2_6/g08_case_registry.json. The Owner bounded policy review is recorded in qualification/0_2_6/g08_owner_contract_review.json.

Requirement	Evidence required	Policy status
G08-001	input-scope and invalid-input matrix	existing implementation scope
G08-002	preload equilibrium and initial-stress tangent diagnostics	existing policy reference; no new numeric band
G08-003	analytical/reference critical factor	OWNER_APPROVED_BOUNDED; case-defined before execution, sign-consistent
G08-004	mode residual, norm and free-DOF mapping	OWNER_APPROVED_BOUNDED; normalized residual bands with near-zero rule
G08-005	compatible mesh sequence and successive factor changes	OWNER_APPROVED_BOUNDED; at least three levels and final adjacent change <=1% when eligible
G08-006	first-mode normalization and deterministic replay	OWNER_APPROVED_BOUNDED; first mode only
G08-007	fail-closed structured failure behavior	existing exact invariant policy
G08-008	formulation-compatible external comparison	OWNER_APPROVED_BOUNDED; CalculiX when comparable, Code_Aster non-comparable is skipped
G08-009	SHA, environment, command and artifact digest	existing V&V provenance contract

The bounded policy review is approved, but case-specific analytical and external tolerances must still be declared before execution and cannot be changed after observing results. No policy may be converted into a numerical PASS by a runner without its required evidence.

Execution evidence

The controlled execution record is archived in qualification/0_2_6/g08_execution_evidence.json, with the concise report in qualification/0_2_6/g08_execution_evidence.md. On source SHA 6589443e1404a2749ac6c0a9b911f00dd9cb8753, the campaign executed 23 cases: 21 PASS, 2 controlled expected failures and 0 FAIL. All four families were run on four mesh levels, and deterministic first-mode replay was checked for each family within the declared floating-point tolerance.

The TET4 Euler record passed its existing case-specific analytical screen. CalculiX completed comparable TET4, TET10 and HEX8 rows; the HEX20 deck failed in the external tool and is retained as an explicit blocked row. This is partial external evidence, not a universal correlation claim. The mesh final-adjacent <=1% eligibility is reached by TET4 only in this campaign; TET10, HEX8 and HEX20 remain bounded trend evidence.

Supplemental mesh extension

The supplemental extension is archived in qualification/0_2_6/g08_mesh_extension_evidence.json and qualification/0_2_6/g08_mesh_extension_evidence.md. It reuses the historical levels 1/2/4/8 and executes levels 16 and 32 for TET10, HEX8 and HEX20 on source SHA 151662ac4781718a7fbe3d1e527675ec9e513ad4, with dirty=false. All 12 extension observations, including deterministic replays, passed. The direct level-16-to-level-32 changes are TET10 0.081448%, HEX8 0.167113% and HEX20 0.912621%, classified CONVERGED_BOUNDED under the unchanged Owner policy. This supplemental evidence does not alter the historical Owner closeout or promote any family retrospectively. HEX20 remains bounded evidence with strong coarse-history sensitivity, no comparable high-order analytical oracle, and a BLOCKED_EXTERNAL_TOOL CalculiX retry.

Targeted HEX20 CalculiX rescue

The blocked HEX20 buckling retry was reproduced as a verification-deck defect: the C3D20 continuation line began with an empty field. The correction is limited to src/solveur/verification/calculix_buckling_025.py; no FEM formulation, eigensolver or solver behavior changed. The regression test is tests/unit/test_calculix_buckling_025.py.

The controlled rescue evidence is archived in qualification/0_2_6/g08_hex20_calculix_rescue_evidence.json and qualification/0_2_6/g08_hex20_calculix_rescue_evidence.md. It runs the same HEX20/C3D20 model at one, two and four cells, with deterministic replays. The QF / CalculiX factor differences are 1.696%, 2.094% and 0.738%, respectively, inside the pre-existing 10% bounded correlation screen. First-mode comparisons are reported after arbitrary eigenvector sign alignment without inventing an external MAC threshold.

This rescue resolves the malformed-deck blocker for the tested cases, but it does not rewrite the historical closeout, promote HEX20 automatically, or change the G08 status from PASS_WITH_LIMITATIONS. Mesh-sensitivity limits, the failed high-order analytical screen and the lack of a Code_Aster equivalent remain explicit.

Independent high-order analytical screen

The supplemental analytical evidence is archived in qualification/0_2_6/g08_high_order_analytical_evidence.json and qualification/0_2_6/g08_high_order_analytical_evidence.md. It declares a fixed-free homogeneous isotropic solid column, Pcr = pi^2 E I / (4 L^2), E=1e6, L=4, b=h=0.5, and a uniformly distributed compressive nodal dead load before execution. The signed reference total is F_REFERENCE_TOTAL = -1.0; the physical comparison is Pcr_QF = abs(lambda * F_REFERENCE_TOTAL). TET10, HEX8 and HEX20 are each tested at lengthwise levels 1, 2 and 3, with a replay of the final level. A separate diagnostic uses two axial cells and one, two and three layers in each transverse direction.

The superseded screen used a positive total UX load (tension) and compared its factor directly with positive Euler Pcr; that comparison is therefore marked invalid and is not used as evidence. In the corrected compression screen, TET10 reaches 3.269% Euler error at axial level 3 and HEX20 reaches 3.622%, while HEX8 remains at 298.413% at that level. All reported modes are global-bending candidates, residuals are finite, and final-level replays are deterministic. The transverse diagnostic leaves TET10 and HEX20 between 5.162% and 7.709% error, while HEX8 remains above 667%. This is retained as a diagnostic result: it corrects the benchmark normalization/load-definition error, does not alter the G08 policy or solver, and does not automatically promote any family. The remaining HEX8 discrepancy is a real analytical-screen limitation requiring separate investigation; it is not converted into a solver defect by this evidence alone.

Euler pre-validation and HEX8 cross-check

The consolidated pre-validation is archived in qualification/0_2_6/g08_euler_prevalidation_evidence.json and qualification/0_2_6/g08_euler_prevalidation_evidence.md. It preserves the historical TET4 evidence and records provisional family decisions without changing the Owner closeout: TET4 PREQUALIFIED_BOUNDED, TET10 and HEX20 PASS_WITH_LIMITATIONS, and HEX8 MORE_EVIDENCE_REQUIRED.

For HEX8, the same-model CalculiX C3D8 cross-check passes at one and two axial cells, with relative QF/CalculiX factor differences of 3.84e-6 and 4.07e-6. Both codes remain much stiffer than the Euler screening value on this solid mesh. The first mode remains a global-bending candidate, the assembled K_G is symmetric with the expected destabilizing negative direction, and the load sum is the same signed compression in both decks. The bounded diagnosis is therefore LOCKING_LIKELY, also described as a low-order solid-discretization limitation for this benchmark. This is diagnostic evidence only: it does not modify the buckling formulation, create a universal locking threshold, or promote HEX8.

Active Owner final review

The active Owner review is archived in qualification/0_2_6/g08_owner_final_review.json, with the readable record in 0_2_6_g08_owner_final_review.md. It confirms PASS_WITH_LIMITATIONS without lowering the contract and makes the family boundary explicit: TET4 is QUALIFIED_BOUNDED, TET10 and HEX20 are PASS_WITH_LIMITATIONS, and HEX8 is MORE_EVIDENCE_REQUIRED. HEX8 remains outside the qualified family subset because its corrected Euler screen is still 298.413% from the continuum oracle, even though the same-model C3D8 check agrees with QF within 0.0003835% and 0.0004065%. That agreement supports a low-order discretization/locking diagnosis; it does not promote HEX8 or prove a QF defect.

The active requirement disposition is six OWNER_APPROVED_FULL requirements (G08-001, G08-002, G08-004, G08-006, G08-007, G08-009) and three OWNER_APPROVED_BOUNDED requirements (G08-003, G08-005, G08-008). The superseded positive-load Euler screen is explicitly excluded from active metrics. The bounded claim remains limited to first linearized factor/first mode, homogeneous isotropic solid, nodal dead loads, sparse SciPy, and the tested domain; it is not a general physical-validation claim.

Historical Owner closeout

The Owner decision is PASS_WITH_LIMITATIONS, with no solver or numerical formulation change. TET4 is QUALIFIED_BOUNDED for the tested first linearized tangent-instability factor and first mode. TET10 and HEX8 are PASS_WITH_LIMITATIONS: their routes and CalculiX rows passed, but their final mesh changes are 3.177% and 2.636%, respectively, above the quantitative 1% eligibility band. HEX20 is MORE_EVIDENCE_REQUIRED because its final mesh change is 13.940% and its CalculiX row is BLOCKED_EXTERNAL_TOOL.

Requirement disposition is six fully satisfied and three satisfied only within bounded limitations (G08-003, G08-005, G08-008). The qualified bounded scope is therefore TET4, homogeneous isotropic 3D material, nodal dead loads, sparse SciPy, first factor and first mode. TET10/HEX8 evidence remains explicitly limited, and HEX20 is not qualified.

The numerical evidence is tied to EXECUTION_SOURCE_SHA = 6589443e1404a2749ac6c0a9b911f00dd9cb8753 with dirty=false. The later documentation/Owner commit is separate and does not replace that execution SHA. This closeout does not claim post-buckling, multi-mode qualification, Code_Aster correlation, or general physical validation.

Case plan

The registry deliberately separates executable definitions from results:

State	Meaning	Count
READY	controlled definition exists and may be executed by the future G08 runner	3
PLANNED	evidence definition exists but execution is deferred to G08	9
NOT_APPLICABLE	outside the current contract or no comparable formulation exists	2
NOT_SUPPORTED	current route explicitly does not support the requested combination	2

The planned mesh work uses coarse/medium/fine/refined where a compatible factory can provide those levels. A future campaign must record DOF, critical factor, mode diagnostics, residuals, mesh quality, timing and provenance at each level. The four-level sequence is a plan, not a claim of convergence.

External correlation

CalculiX is an available supporting route for comparable solid decks and remains subject to the external policy. Code_Aster is retained in the matrix, but the controlled audit currently identifies no equivalent 3D solid eigen-buckling modelisation. Any unavailable or non-comparable external case must be recorded as SKIPPED_NOT_COMPARABLE or an equivalent explicit skip; it cannot be counted as PASS.

Dependencies and closure boundary

G08 execution depends on the clean baseline and V&V foundation gates 026-G00 through 026-G03. It does not require 026-G07 to be silently closed, and G07 evidence cannot be used as a substitute for buckling evidence. The contract itself did not close G08; closeout required archived results, approved policies, final-SHA provenance and the explicit Owner decision now recorded in the closeout artifact.

Out of scope: nonlinear/post-buckling response, imperfection-sensitive collapse, arc-length/path following, finite-kinematic J2, shell/beam/discrete buckling through this route, and general physical validation.