[Superseded by #702] Shape rerun — raw-p C3 withdrawn; valid repaired data retained - #666
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…s on repaired inputs (PR #653 bond lab, PR #655 spin-0 N725) - T1 (proved, machine-checked): dual_fail=0 => M antisymmetric, F self-complementing, Z(u)+Z(1-u)=1 exactly on the repaired bond census. Reverses #628's 'duality does not transfer to bonds' (that was the #632 sign bug). - T2 (proved by construction): duality pins Z to the antisymmetric class and nothing more; symmetric-density toy members differ by 0.15 in Z. W2 splits: transfer yes, pinning no. - T3 (observation, 4 sizes, no fit): A/S decomposition of Z; S collapses (-0.0541, -0.0446, 0, -0.0090 at u=0.1) while A drifts monotonically with total spread 0.0475. Shape-limit question localised to A_N. - T4 (conjecture C3, stated to be killable): M_N + M_N(1-.)->0; under C3 the limit shape is antisymmetric. Open; not implied by Theorem L. - g-lift headline of #628 withdrawn to 'undetermined' per #633 retractions (unoriented 20.4 deg on the lab; no N725 deltaZ). - W4 counterexample downgraded per #632 (P11 rescaling leaves simplex); the pointwise-vs-functional kill stands. - Tests: tests/test_rerun_shape_limit_20260908.py new (pass); tests/test_probe_invariant_shape.py updated to repaired census numbers (pass). No STATUS.md, no issue closure, no production, no exponent.
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Superseded on 2026-09-12 by merged #702
Withdraw T4/C3 (
M_N(p)+M_N(1-p)->0on every interior compact) as a normalized-shape hypothesis. With the repository's location limit it forces the centre to be 1/2: at p=1/2 the sum tends to -2 or +2 whenever the limiting centre differs. It is not equivalent to anchored quantile reflection symmetry.The corrected observable is
[Q_N(u)+Q_N(1-u)-Q_N(a)-Q_N(1-a)]/[Q_N(1-a)-Q_N(a)], with fixed symmetric anchors. Its within-model size dependence remains open. Also withdraw the inherited non-intertwining assertion about Aff(1): ordinary affine pushforward and quantile transformation do intertwine.Retain the repaired bond census, corrected spin-0 input, T1 self-duality identities, T2 non-uniqueness within symmetric profiles, and the retractions of covariance-rank and oriented-angle overclaims. Data remain on this branch and their original source branches; they are not erased or turned into new evidence. The mixed site/bond/tiny/large comparison is not an asymptotic size ladder.
Closing this draft because its proposed central new hypothesis is invalid. Existing #622 is the continuation channel for corrected within-model analysis; no duplicate probe or new production is opened by this closure. See
notes/exact-foundations-correction-20260912.md§§3,6.