N580: seven exclusions survive rung-specific bounded H8; correct P3 inference claims

[LightChainr]

Completed analysis — 2026-09-12

Retargeted to main after #703 merged at d84fc48. Head: 1a6c9da. No production request or duplicate issue was opened for this completed work.

Scientific question and result

A uniform bound on H8/H4 does not imply one common ratio across moduli. This analysis uses mu_i=a*v_i*(1+lambda_i*rho_i), signed a, independently varying |rho_i|<=B, rather than the old common-ratio assumption.

Both amplitude signs are solved as two cones generated by eight vertices each. Supports up to size three suffice in R^3. Selected solutions are independently re-solved at 60 dps and checked against the KKT inequalities of ALL eight rays of BOTH cones.

Against ONE full three-dimensional nominal 99.73% Gaussian mean ellipsoid (cutoff 14.1564136091), seven of eight candidate images remain disjoint even at B=1; bare aspect intersects already at B=0. First intersection occurs at B about 5.49417 for Q4 weight-4, 5.71612 for area scaling, and 6.55584 for no modulus dependence. These are conditional uncertainty-region sensitivity bounds, NOT actual H8 measurements or fitted-cone chi-square p-values. Bare aspect is not established as a physical law.

Files

• scripts/n580_rungwise_leakage.py: complete reader/solver, fitted witnesses or compact summary; refuses result-file overwriting.
• results/research-control-20260912/n580-rungwise-leakage-summary.json: executed result using the P3: enforce covariance support and recover the N580 matrix without new sampling #703 recovered mean/matrix/rays; not another shard replay.
• notes/n580-rungwise-leakage-20260912.md: projection argument, shared confidence-region argument, result and limits.
• tests/test_n580_rungwise_leakage.py: three mathematical controls (exact toy D=2/11; zero bound=GLS; sign/nesting).
• P3 correction addendum and current README: covariance support/df, signed-line vs ray, curvature sign, Fieller equivalence, recovered covariance, independent vs common nuisance, and why unanchored cone-to-cone minimum distance is zero. Historical manuscript/tables/data/freezes retained. The manuscript is explicitly NOT submission-ready; this is not a full prose rewrite.

Validation actually executed

All three new tests passed locally; together with #703's six saturated/support regression tests, nine local tests passed. The full bounded analysis was rerun from the input mean/matrix: all 24 fixed-bound fits and every positive-threshold bracket endpoint passed 60-dps KKT checks. Fixed-bound relative maxima 1.76e-61 (KKT) and 5.10e-61 (complementarity). Numerical checks, not exact rational certificates.

The parent #703 completed full CI (1626 tests, 3 existing skips, compile/C++ all green). A new complete suite has NOT yet been observed for this six-file analysis-only delta; do not substitute parent CI for child CI. The delta adds a standalone analysis/tests and documentation, without changing the repaired inference module or historical scorers.

Decision

Same-block C2, not new evidence; estimated jackknife covariance gives nominal/asymptotic coverage. No new N580 replay or automatic N650/N2210 purchase. #575 recovery closed completed; #583's saturated pure-H8 acquisition retired into #589's identifiable-design channel. The two current delegated analyses are #622's within-model shape motion and #681's restricted torus/cylinder bridge; no GPU job is justified by these questions.