RUN-039: protocol audit and permutation-orbit admission
Project LOGIC OF KURPISHEV 2. Project and method author: Ivan Borisovich Kurpishev. MASTER-3 / ARBD52, 23 September 2026. This is an English summary; the complete mathematical report is in Russian.
The original OH/alkane preregistration ZIP has been recovered. Its reference code and configuration remain unchanged. No real chemical outcome was read; the original hidden fixture files were not extracted. RUN-038 is fixed as a diagnostic addendum, not an amendment to the primary protocol.
The CLI rejects a nonblank D cell, duplicate positions, a failed source gate and incorrect input hashes. It does not itself check the sealed prediction receipt, enforce one-shot evaluation, exclude extra reconstructable D fields or require distinct reference points. Fourteen synthetic audit checks reproduce these behaviors. PASS means an audit observation was reproduced, not protocol acceptance.
Exact theorem: for visible rational coordinates v1,v2,v3 and an a priori hard domain z∈[a,b], enumerate the twelve affine denominators d=v_i+v_j−2v_c, where c differs from i,j. Every one of the 24 permutations is stable for every z in the domain iff every denominator image has distance at least 1/20 from zero. Endpoint or zero-crossing witnesses attain every minimum. Nondegeneracy additionally requires distinct visible coordinates and no visible coordinate inside the domain.
Conditional rank theorem: under uniformity on a finite orbit Ω, conditioning on a fixed nonempty admission event A yields a uniform law on A. For one common statistic T, p_A(x)=#{y∈A:T(y)≥T(x)}/|A| is super-uniform conditionally on admission. Sorting tied rank blocks proves the claim. This requires the stated joint null law; lineage IDs alone do not establish it.
Exact synthetic witness: values {0,11/1000,22/1000,33/1000}, pole threshold 1/20 and penalty 3. Four of 24 assignments pass. Two have full-orbit upper tail 1/12 but conditional upper tail 1/2. Thus P(full-tail≤0.10 | admitted)=1/2. This concerns the rank mechanism only: one quartet and an effect below 0.10 cannot produce a positive decision under the complete chemical protocol.
The separate exact BigInt module accepts SYNTHETIC and A_PRIORI_HARD_DOMAIN only. It reports all twelve forms and attainable witnesses; it never issues a p-value or empirical certificate. Twelve JS tests passed; an independent Python Fraction implementation checked 80 domains, 17,280 point/permutation evaluations and 960 witnesses. This is an internal implementation cross-check, not external replication.
For R,I,U=(0,1,3), domain [7,8] passes with minimum margin 1. Domain [4,7] contains a pole at D=6. Domain {3} passes the pole gate but fails nondegeneracy. A common additive shift cancels; a general projective transformation need not preserve the fixed numeric threshold.
Unresolved: external registration, independent custodian/verifier, source-bound visible corpus, joint exchangeability and selection-compatible null, rigorous input bounds and external log10 rounding. RUN-040 should specify a new protocol candidate, receipt binding, masking allowlist and append-only reveal control using SE3 before real outcomes. An amended protocol requires a new identifier and fresh holdout.
SCIENCE=ABSTAIN; truth_layer_promotion=0; DHC_chem=OPEN-NOT-CONFIRMED; EXT_RUN=NOT_RUN; real_forecast_trial=NOT_RUN. Physical Android acceptance and empirical bridge remain unverified. The prior source and rollback are RUN-038, site version 47. Neighboring sites were not republished.
Reference: Hemerik J., Goeman J., Exact testing with random permutations, TEST 27 (2018), 811–825; arXiv:1411.7565. The general rank theory is established mathematics; literary priority for this particular application is not claimed.