[InauguralPhysicist]

Closes #2285

Built by a Codex Cloud task: https://chatgpt.com/codex/tasks/task_e_6ae62dd1daa8832d92534b44d62771c5. Its red/green and gate evidence is in the task log.

[InauguralPhysicist]

@codex review

[InauguralPhysicist]

Reviewer note before merge (for @codex review and the CI round): the eigenvectors_2x2 change replaces abs(x) > 1e-12 with x != 0. For a row that is roundoff-nonzero (e.g. A - λI for a repeated or near-repeated eigenvalue, where the row should be exactly zero), the exact test now picks a nullspace construction from noise. Please show a test where λ comes from the quadratic formula with roundoff (e.g. [[1, 1e-17],[0, 1]], and a symmetric matrix with a near-repeated eigenvalue) and confirm the returned vectors satisfy |A v − λ v| ≤ tol·|A|·|v|; if not, use a scale-relative cutoff there too, consistent with the pivot fix. — Claude DevBox

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Codex Review Summary

This comment shows the latest Codex review activity on this pull request.

Review	Status	Commit	Review trigger
📝 Code Review	✅ Completed 2026-10-31T22:01:30.620109Z	8a9b926	Manual request
🔒 Security Review	✅ Completed 2026-10-31T18:19:29.919602Z	efc884f	PR opened

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Reviewed commit: efc884f8e9

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[codspeed]

Merging this PR will not alter performance

✅ 13 untouched benchmarks

---

_{Comparing cloud-2285 (8a9b926) with main (334d3fc)}

[chatgpt-codex-connector]

Summary

• Updated eigenvectors_2x2 to derive its cutoff from the matrix scale and avoid constructing eigenvectors from roundoff-sized rows of (A-\lambda I). When both rows are negligible, it now returns a stable coordinate direction instead of a nearly zero noise vector. lib/linalg.eigsL459-L490
• Added regression coverage for the repeated triangular matrix [[1, 1e-17], [0, 1]] and a symmetric near-repeated matrix, checking both usable vector magnitude and the relative residual (|Av-\lambda v|\leq tol,|A|,|v|). tests/test_issue_2285.eigsL34-L57
• Updated the suite section to require all 17 regression assertions and expanded the changelog fragment to describe the eigenvector fix. tests/sections/70ed-linalg-scale-2285.shL1-L7 changes/fixed/2285-scale-aware-linalg.mdL1
• Committed the changes as e66410d (Use relative cutoff for 2x2 eigenvectors) and created the requested follow-up PR metadata.

Testing

• ✅ make -j2
• ✅ build/release/eigenscript --lint --json tests/test_issue_2285.eigs
• ✅ build/release/eigenscript tests/test_issue_2285.eigs — 17 passed, 0 failed.
• ✅ git diff --check
• ⚠️ make test-changed — could not derive a test plan because this checkout has no merge base with origin/main.
• ⚠️ make precheck — 16 checks passed, but the aggregate check could not complete because origin/main has no merge base and PyYAML is unavailable; the same missing base also caused dependent enrolment/self-test instrumentation failures.

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[InauguralPhysicist]

@codex Fix the P2 above and the class it reveals: a single matrix-wide scale is the wrong reference for mixed-scale matrices. diag(1e13,1,1,1) is perfectly well-conditioned per row, and the same false-singular verdict will hit mat_inverse and solve_linear, not only mat_det. Use the standard approach: mat_det returns the product of pivots with no numerical-rank cutoff (exact-zero pivot → 0); for mat_inverse/solve_linear, compare each pivot against the scale of its own row (scaled partial pivoting, row scale taken from the original row), not the global max. Add regression rows: diag(1e13,1,1,1) for det, inverse and solve (exact results); the issue's small-entry matrix; a truly singular matrix (still rejected); and a near-singular one built with roundoff (rejected or result verified by residual |Ax−b| ≤ tol·|A|·|x|). Also answer my earlier note on eigenvectors_2x2 (x != 0 picking a construction from roundoff) with a residual-checked test. Red-then-green; update evidence/issue-2285.md. — Claude DevBox

[chatgpt-codex-connector]

Summary

• Updated mat_det to return the signed product of all nonzero pivots, using only an exact-zero pivot to report a zero determinant. This prevents mixed-scale matrices such as diag(1e13,1,1,1) from being misclassified. lib/linalg.eigsL159-L209
• Changed mat_inverse and solve_linear to use scaled partial pivoting based on each original row’s maximum magnitude, with row scales following their rows through swaps. lib/linalg.eigsL215-L277 lib/linalg.eigsL375-L431
• Updated eigenvectors_2x2 to ignore roundoff-sized entries of (A-\lambda I), avoiding unstable eigenvector constructions for repeated and near-repeated eigenvalues. lib/linalg.eigsL485-L523
• Expanded issue lib/linalg: mat_inverse and solve_linear refuse a well-conditioned matrix with small entries (absolute 1e-12 pivot), while mat_det now calls it nonsingular #2285 regressions to cover the original small-entry matrix, exact mixed-scale determinant/inverse/solve results, exact singular rejection, roundoff-exposed singularity, and residual-checked eigenvectors for triangular and symmetric matrices. tests/test_issue_2285.eigsL4-L68
• Added the requested red-then-green record and documented the resulting numerical policy. evidence/issue-2285.mdL3-L46
• Updated the changelog fragment, committed the changes as 8a90b06, and created follow-up PR metadata titled “Follow-up: fix mixed-scale linalg pivot handling.” changes/fixed/2285-scale-aware-linalg.mdL1

Testing

• ✅ make -j2
• ✅ build/release/eigenscript --lint --json lib/linalg.eigs
• ✅ build/release/eigenscript --lint --json tests/test_issue_2285.eigs
• ✅ build/release/eigenscript tests/test_issue_2285.eigs — 15 passed, 0 failed.
• ✅ EIGS_SUITE_SECTIONS=70ed bash tests/run_all_tests.sh — 2/2 suite checks passed.
• ✅ git diff --check
• ⚠️ make test-changed — unable to derive a test plan because this checkout has no merge base with origin/main.
• ⚠️ make precheck — 16 checks passed, but the aggregate check could not complete because origin/main has no usable merge base, PyYAML is unavailable, and dependent enrolment/self-test instrumentation failed in this environment.

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[InauguralPhysicist]

@codex review

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💡 Codex Review

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Reviewed commit: c46c3b89da

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[InauguralPhysicist]

@codex Fix the two open P2s on c46c3b8: (1) if mat_det still returns 0 for diag(1e13,1,1,1), it must not apply any rank cutoff (product of pivots; exact-zero pivot only); show the 4x4 result; (2) break scaled-pivot ties by the larger absolute pivot; regression A=[[1,1],[1e20,0]], b=[1,1] must give a residual-verified solution ([1e-20, 1]). Add both as tests; keep every earlier case green. Update evidence/issue-2285.md. — Claude DevBox

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Summary

• Updated scaled partial pivoting in both mat_inverse and solve_linear so equal scaled ratios are resolved using the larger absolute pivot, preventing catastrophic cancellation for rows with very different magnitudes. lib/linalg.eigsL245-L262 lib/linalg.eigsL408-L423
• Added regression coverage for A = [[1,1],[1e20,0]], verifying the solution [1e-20,1] component-wise and checking the resulting residual. The existing 4×4 diag(1e13,1,1,1) determinant, inverse, and solve regressions remain explicit. tests/test_issue_2285.eigsL12-L33
• Updated the focused suite gate from 15 to 18 assertions. tests/sections/70ed-linalg-scale-2285.shL1-L7
• Added red/green evidence documenting the no-cutoff determinant policy, the original failure, the exact 4×4 determinant result 10000000000000, the corrected solution [1e-20,1], and zero residual. evidence/issue-2285.mdL3-L43
• Updated the changelog fragment to mention absolute-pivot tie-breaking. changes/fixed/2285-scale-aware-linalg.mdL1
• Committed the changes as 66b2513 (Fix scaled pivot tie handling) and created follow-up PR metadata titled “Follow-up: fix absolute pivot tie-breaking for lib/linalg: mat_inverse and solve_linear refuse a well-conditioned matrix with small entries (absolute 1e-12 pivot), while mat_det now calls it nonsingular #2285.”

Testing

• ✅ make -j2
• ✅ build/release/eigenscript --lint --json lib/linalg.eigs
• ✅ build/release/eigenscript --lint --json tests/test_issue_2285.eigs
• ✅ build/release/eigenscript tests/test_issue_2285.eigs — 18 passed, 0 failed.
• ✅ build/release/eigenscript /tmp/issue2285_probe.eigs — determinant 10000000000000, solution [1e-20, 1], residual [0, 0].
• ✅ EIGS_SUITE_SECTIONS=70ed bash tests/run_all_tests.sh — 2/2 suite checks passed.
• ✅ git diff --check
• ⚠️ make test-changed — the checkout has no merge base between origin/main and HEAD, so the test planner refused to derive an empty plan.

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[InauguralPhysicist]

@codex review

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Codex Review: Didn't find any major issues. Delightful!

Reviewed commit: 8a9b92646c

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