P3: enforce covariance support and recover the N580 matrix without new sampling

[LightChainr]

Completed and integration-checked — 2026-09-12

Head 909d4b3. This PR now includes the saturated-design repair that was previously reported as local-only.

Statistical repair

• Validate positive semidefiniteness before covariance truncation.
• Require explicit singular/truncated covariance semantics. Empirical low rank does not establish a deterministic constraint.
• exact_support enforces U0^T(y-Va)=0 and uses df=rank(S)-rank(W V Z). The old D=0,p=1 support contradiction now raises an explicit incompatibility; a deterministic amplitude constraint gives D=1,df=2.
• Saturated df=0 models have algebraic residual zero after a scale-relative numerical consistency check. Roundoff no longer produces p=0/infinite sigma. Positive-df residuals are not clipped. Six new targeted mathematical tests cover both support modes and retained Fieller behavior.
• Historical positive-df output arithmetic remains unchanged. The extreme-tail inverse-erf display limitation is NOT fixed in this patch; the recovered summary reports its unresolved sigma as null rather than infinite evidence.

Executed N580 recovery — no new samples

The existing 100 aligned delete-one shard rows recover corr(r2,r4)=0.11001108422637242; covariance rank 3, condition 1.96789. Bare aspect pure line: D=10.86445991488253/2, p=.004373332575404287, equivalent 2.84989746 sigma: NOT rejected at the declared nominal 3-sigma threshold. Seven other pure lines are rejected under that model contract. Raw curvature z=-3.11061597.

Initial executed recovery: run 34679359201, job 103514945963. Current bounded recovery workflow run 34681074144 also passed after the saturated-design change. results/research-control-20260912/n580-complete-covariance-summary.json and notes/n580-complete-covariance-20260912.md retain the original executed result and provenance.

Full CI read, not inferred

Run 34681074153: all four jobs succeeded, including Tests job 103519701485. Its log records 1626 tests, OK (skipped=3) in 762.584s, plus a passing smoke check. Tested merge checkout 9a005e9, merging this head into main d435f30.

The prior CI failure was the existing P598 test importing NumPy while CI installed only the lightweight runtime requirements. requirements-test.txt now installs NumPy/SciPy for the complete suite; no test was removed or newly skipped to make CI pass. Python 3.9/3.13 compilation and C++17 build/self-tests also passed.

Scientific boundary

Same-block retrospective three-rung analysis, not a change to the frozen two-rung test and not independent evidence. All p-values are nominal Gaussian-reference values using estimated covariance, not exact finite-sample coverage. Original production artifacts and freezes are unchanged.

P3 manuscript corrections and a genuinely new rung-specific bounded-H8 sensitivity are in child #704. Neither PR claims publication readiness or field/threshold identification. No further N580 replay is needed merely to recover this covariance.