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P1000-0860 · q-20261015-pulse-20261119-r07-0035
Use the complete finite feasible carrier=[A, B, C, D] with aligned exact objective values=[30, 10, 40, 50], candidate=A. The declared feasible challenger is=B. Give (complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope).
G001 — Use the complete finite feasible carrier=[A, B, C, D] with aligned exact objective values=[30, 10, 40, 50], candidate=A. The declared feasible challenger is=B. Give (complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope).Minimization over a complete finite feasible set; one strictly smaller feasible point refutes the candidate's global optimality.
Before
complete feasible domain
After
[[A, 30], [B, 10], [C, 40], [D, 50]]
Conditions: none
Fix the complete table and minimization direction; sampling a few points is not a global certificate.
Rule: complete_objective_data · Uses: G001
Before
candidate=A; challenger=B
After
both feasible; f(candidate)=30, f(challenger)=10
Conditions: none
First check that the challenger is a distinct feasible point.
Rule: feasible_challenger · Uses: G001, S001
Before
challenger minus candidate := sub(10, 30)
After
challenger minus candidate = -20
Conditions: none
Subtract exactly; a strictly negative difference certifies improvement.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
difference=-20<0
After
candidate cannot minimize over all feasible points
Conditions: none
Global minimality requires a value no greater than every feasible value; one strictly better point refutes it.
Rule: strict_improvement_obstruction · Uses: G001, S003
S004 · premise_and_result_audit — Completeness, neighborhoods, attainment and uniqueness are separate obligations; local data do not license a global conclusion.S003 · premise_and_result_audit — Recompute challenger minus candidate with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Completeness, neighborhoods, attainment and uniqueness are separate obligations; local data do not license a global conclusion.S001 · premise_and_result_audit — Completeness, neighborhoods, attainment and uniqueness are separate obligations; local data do not license a global conclusion.([[A, 30], [B, 10], [C, 40], [D, 50]], A, 30, B, 10, Yes, No, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
The full substitutions and premise audits recover the original answer, retaining its field order and verdict meanings.
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: 3c992b6a95c45c750c85386481bc38b21cdd56d68d25f1fe6462b44674e7e08fcandidate record SHA-256: dfe473dc9ad085846e222aa34f842a76c2a842253f6b44bbb6a9e27e7a61bb37semantic review receipt SHA-256: 6c2c6d46aded7582a11ac41a8c0b3bdde2669a53bdb6e796eea2039994a02772question-first witness SHA-256: 77e43898df9efdbf8094ad81fe4ab91cf4b4bd82f481eb9b4699b73cb4da612bLean: NOT_RUN · human review: NOT_PERFORMED