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R0054-27712 · q-20261015-advance-20261118-r04-wilson-theorem-0087
Use mode=finite_testing and exact integer n=13. Give (mode, cutoff, tested_modulus_count, tested_range, universal_proof_claim, boundary).
G001 — Use mode=finite_testing and exact integer n=13. Give (mode, cutoff, tested_modulus_count, tested_range, universal_proof_claim, boundary).Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
source roles = [wilson-boundary]
After
derived = [[mode, cutoff, tested_modulus_count, tested_range, universal_proof_claim, boundary]]
Conditions: none
List the complete operation/mode field order without JavaScript or answer-shape inference;Boolean,string,null and an unclaimed result remain distinct.
Rule: source_ordered_fields_without_JS · Uses: G001
Before
source roles = [13]
After
derived = [12, checked_moduli_2_through_13, No]
Conditions: none
This source branch states a finite cutoff/range count,not per-modulus calculation tables.Do not present that description as tests executed for every modulus.Even successful finite checks would not replace a universal equivalence proof.
Rule: Wilson_finite_cutoff_DESCRIPTION_NOT_performed_all_moduli_or_universal_proof · Uses: G001, S001
S002 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S001 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.(finite_testing, 13, 12, checked_moduli_2_through_13, No, finite_cutoff_does_not_prove_the_universal_equivalence)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 721701c1d09cd5997a902d22578360383aaea8c8e108e725fee79c7a2e530f8ccandidate record SHA-256: ae10d6034020b5931ed34944448d17d87257e909e4201cf54f32f34c75a210fdsemantic review receipt SHA-256: 0a76d8e93c08bb16998a0483f3dfc0504f269fc3e1982e6cd868cab0a2856d54question-first witness SHA-256: 09127b736c225714dfa0b7ceb0e6a6e66df27438b480cad8217d3c2f99ce9437Lean: NOT_RUN · human review: NOT_PERFORMED