theory(p13): self-dual gadget resume - no-go theorem + explicit counterexample - #751
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September 13, 2026 15:19
…stograms Zero-new-sampling scan of the readable readout family (M at p_ref and on a p-grid, tail derivatives, histogram-native functionals, and the GE-optimal linear combination) for maximal |A4|/se(A4). Pre-registration controls applied: only se(A4) and amplification-vs-M reported; split-half transport control over 40 random splits. Single best readable channel (varKminus) transports (0.83-1.00); the data-snooped GE combination does not (0.37-0.74). Design recommendation with selection-optimism penalty; exact S/D/Sp/Dp declared a buy-back. Full Matching-One repository CI has not been run for this commit.
Positive-control-first graded tangent benchmark for #586. Reuses the exact #581 finite-volume gate (enumerate_torus + covariance_split) for the lattice control: Cov(O,T) = 1/2 Cov(O,B_even) + 1/2 Cov(O,X) is exact (split_is_exact True) for all six observables at L=2 (256) and L=3 (262144 configs); identity gate T-T*=X has 0 failures. open_edges loads purely on X (B_even=0); wrap_either/wrap_cross carry opposite-sign B_even pieces with identical X, confirming B_even and X are physically distinct. Phase A continuum internal check: the Q-tangent of a representative (2,1)-degenerate BPZ ODE satisfies the differentiated inhomogeneous ODE (residual 4.4e-6). Phase B bulk-log numeric declared a buy-back (VJS/Camia-Feng data not in tree). Spin-4 reopening of #263 not yet earned. Full Matching-One repository CI has not been run for this commit.
…uence-function diagnostic) Contract A for #578: freeze nuisance/root, integrate the first-order object m(S)=E[phi|S] over a planar two-terminal cut network under the fixed-cardinality vertex reliability law (no nonlinear ratio/root Rao-Blackwellized). Verified the law of total variance exactly (Var(phi)=Var(E[phi|S])+E[Var(phi|S]), residual 0) on a fully-specified prototype. Variance decomposition S0..S3: S1 removes 31%, S2 (cut-network low-cost invariants) removes 71% at the best wall-clock efficiency, S3 removes 100%. Recommendation: promote S2 as production conditioning level; proceed to Contract B after real-phi buy-back. Saved-prefix asset audit BLOCKED (P334 147-prefix archive not in tree); real original-U phi coefficients declared a buy-back. Full Matching-One repository CI has not been run for this commit.
…erexample Resumes #13 per the 2026-08-31 handoff: deliver a monotone comparison between two specific period diagrams, or a counterexample/theorem that the finite D4-orbit serial class cannot provide it. Outcome (b): a theorem with an explicit counterexample. The finite class (reconstructed via the canonical terminal-partition serial-category machinery) is not a well-defined category: 26/49 orbit pairs are multi-valued under serial composition and 166/343 triples are non-associative (exact). Two specific period diagrams A=[0,0,0,0] (orbit 0) and the two class-2 representatives [0,0,1,1]/[0,1,1,0] glue to two different outputs, so no single composed law and hence no monotone (Strassen) coupling exists. Exact #438 192-state/41-orbit W5 table not in tree -> declared buy-back; result is structural. No new algebra census or generic-certificate task added. Does not edit docs/STATUS.md. Full Matching-One repository CI has not been run for this commit.
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Summary
Resumes #13 per the 2026-08-31 handoff: deliver a monotone comparison between two specific period diagrams, or a counterexample/theorem that the finite D4-orbit serial class cannot provide it. No new adjacent-algebra classification added.
Outcome: (b) theorem + explicit counterexample
The finite D4-orbit serial class does NOT admit a law-preserving monotone (Strassen / stochastic-dominance) comparison between two of its period diagrams. Serial composition — the operation that would define the comparison under gluing — is not a function on the class (exact, recomputed):
Explicit counterexample (two specific period diagrams)
Orbit pair (0,2):
The composed connectivity law of A with the class-2 diagram is not single-valued, so no monotone (Strassen) coupling can be assigned. The finite class cannot provide the comparison.
Honesty / buy-backs
Deliverables
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