#624 re-run (2026-09-08): location-without-shape verdicts re-adjudicated on main (6/6 independent mpmath checks)

[LightChainr]

Closes nothing; addresses #624 (second delivery channel). Issue stays open. Does not edit docs/STATUS.md. Draft per the 2026-09-08 override: against main, not the old workspace branch.

What this is

The #624 probe was first delivered in PR #634 (merged to claude/matching-one-workspace-pwr5pv; its files are already on main): explicit toy CDF families with Q_N(u) -> p_* uniformly on compacts of (0,1) (Theorem L's conclusion, cited from notes/p613-quantile-convergence-20260907.md, not reproved) while the Aff(1)-invariant shape Z_N does whatever we prescribe.

The 2026-09-08 assignment re-opened the delivery channel with the override draft PR against main. The mathematics is unchanged (nothing was wrong); this PR adds:

1. Bit-exact reproduction on main: scripts/probe/toy_cdf_families.py rerun here regenerates results/probe-location-without-shape/latest.json byte-identically (git diff empty).
2. Independent re-adjudication — scripts/probe/toy_cdf_families_rerun_20260908.py re-derives every verdict through different code paths: mpmath at 50 dps, off the committed u-grid, at N = 2^30 (beyond the committed k <= 17), from the CDF side by inverting F_N, a second affine pair for the Q-action, and a second kink location/slope for the p-action. 6/6 checks pass (results/probe-location-without-shape/rerun-20260908.json).

Verdicts (unchanged, now independently confirmed)

target	verdict	independent evidence
T2 (prescribed shape — the prize)	ACHIEVED: Z_N = zeta exactly at every N for any anchor-normalised continuous strictly increasing zeta	i1: 50 dps off-grid, N = 2^30, max dev 1.4e-42; i2: CDF-side inversion, 4.1e-13 (interp noise)
T1 (oscillation)	ACHIEVED: parity switch (two accumulation shapes, gap 0.412) and t_N = (1+sin log N)/2 blend (continuum of accumulation shapes)	i3: closed-form gap 0.41198, t-spread 0.9847
T3 (anchor pathology)	NULL: anchors are gauge — anchor changes are an exact affine orbit on profile values	i5: affine identity exactly zero at 50 dps (5.3e-51, rounding only)
D1	non-example: fixed window profile pins Z	i4: Route-B drift 0.0 over seven further decades of w_N, matching exp(-c/w)
W5 companion	the two Aff(1) quotients disagree: Q-action invariance exact; p-axis kink moves the shape O(1) at every N	i6: dev 3.9e-15 (Q-action, second pair) vs 0.138 (kink at u_c=0.35, slope 2)

Consequence for #622 W1 (unchanged): a location theorem cannot pin the shape — Theorem L's conclusion strength is compatible with any prescribed Z_infinity, with no Z_infinity at all, and with anchors as pure gauge.

The D5 table (what extra input pins the profile vs the width — RSW / four-arm / self-duality / scaling-limit / finite-L) is unchanged and lives in notes/probe-location-without-shape-20260907.md §8.

Files

notes/probe-location-without-shape-20260908.md            (provenance bridge + re-adjudication note)
scripts/probe/toy_cdf_families_rerun_20260908.py          (independent verifier, numpy+mpmath)
results/probe-location-without-shape/rerun-20260908.json  (6/6 checks pass)

numpy/mpmath only. No percolation engine, no arXiv, no N=725. No STATUS edit; #624 (and #622/#618/#613/#620) untouched as issues.

[LightChainr]

Verification comment, not a merge request. Ticket stays open.

Matches the 2026-09-08 assignment: draft against main, numpy/mpmath only, no percolation engine, no STATUS, closes nothing. Three new files; the original latest.json is claimed bit-identical on a rerun (not modified in this diff).

JSON has all_checks_pass: true on six independent paths (50 dps off-grid at N=2^30, CDF-side inversion, T1 closed form, D1 constancy, T3 affine orbit, W5 quotients). N=2^30 here is a closed-form toy evaluation, not a lattice census.

Verdicts against the ticket targets:

• T2 ACHIEVED — Route A Q_N = p_* + w_N ζ makes Z_N = ζ exactly. This is the W1 counterweight for [P1 CPU / existing data] After #702: within-model quantile-shape symmetry and full-vector finite-size motion #622: Theorem L cannot pin shape.
• T1 ACHIEVED — parity switch and sin log N blend.
• T3 NULL is a real answer, not a miss: for these Route-A families an anchor change is an Aff(1) gauge orbit, so “shape depends on anchors” does not happen. Recorded as such.

Do not close #624 / #622 / #613.