W7 · CP-4 follow-up: the NaN-under-both draws and all-transect non-finite gradients — singular systems or a formula-independent overflow?

[Jammy2211]

From phase_08_regularization/RESULTS.md (human call 2026-08-24: adopt slogdet, chase the rest).

Questions

1. The 32 (A100) / 20 (CPU) delaunay_adapt_split draws that are NaN under both cholesky and slogdet: are the curvature+reg matrices genuinely singular (λ⁴ fragility, feat(jax_compile): make warm compile machine-identifiable via cache_state #104 — eigen-spectrum at those draws), or does the NaN arise upstream (mapping matrix, data-vector overflow, the sqrt(dual_area) grad hazard) so no log-det formula could help? Replay from slogdet_ab/draws/*.npz with per-term instrumentation.
2. The λ-transect gradients are non-finite under both arms on all 128 draws on both tiers (while prior/truth-bar draws mostly are finite): identify the term (is it the transect's log-coefficient axis itself?) — this may be a driver artefact rather than a likelihood hazard.
3. The marginal-band disagreement (up to 9,619 nats on A100 vs 2.27 on CPU): tier-dependent — characterise the coefficient range and whether it is fp64 LU pivoting on GPU.

Deliverable

RESULTS.md addendum with attribution per draw class; a recommendation on whether the PyAutoArray default should flip (feeds W9).

[Jammy2211]

Approved 2026-08-24 as planned, plus a formal CP-4 re-score on the clean replay subset (DECISIONS.md amendment). Reconnaissance on the stored per_draw arrays already shows two driver artefacts contaminated the A/B: (1) 10 A100 'NaN-under-both' draws have NaN input vectors (dead descent lanes) and 6 more carry negative coefficients — the coefficient_min=-5.2 ops note is a harvest bug; (2) all 128 λ-transect draws sit at the prior-median anchor where ell_comps/shear are exactly (0,0) → sqrt-at-zero gradient NaN under both arms regardless of log-det. The genuine λ⁴ candidates are the 22/20 prior draws with coefficients 4e5–9e5; the 9,619-nat tier outlier is draw 96 (NaN under both on CPU). Implementation in progress on feature/w7-slogdet-nan-attribution.

[Jammy2211]

Shipped: PR #171 merged — per-draw NaN attribution (slogdet_nan_attribution.py, 170 draws classified), two driver artefacts fixed in the slogdet_ab harvest, tier flips explained by cond(F+λ⁴H) up to 4.5e18. CP-4 re-scored on the clean subset: FAIL unchanged on both tiers (residual 22/20 NaN = genuine λ⁴ population). W9 (#166) unblocked: cond ≥ 1e16 → trust neither arm; slogdet-on-GPU / cholesky-on-CPU (3.7×); harvest guards shipped.