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P1000-0864 · q-20261015-pulse-20261119-r07-0039
Use the complete finite feasible carrier=[A, B, C, D] with aligned exact objective values=[42, 14, 56, 70], 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=[42, 14, 56, 70], 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, 42], [B, 14], [C, 56], [D, 70]]
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)=42, f(challenger)=14
Conditions: none
First check that the challenger is a distinct feasible point.
Rule: feasible_challenger · Uses: G001, S001
Before
challenger minus candidate := sub(14, 42)
After
challenger minus candidate = -28
Conditions: none
Subtract exactly; a strictly negative difference certifies improvement.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
difference=-28<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, 42], [B, 14], [C, 56], [D, 70]], A, 42, B, 14, 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: 17524a098ab9bd51d106ac1ba2e4762c72f98f6cf97c8edf9177810e7b4bad6acandidate record SHA-256: cfa32e06c5f6323399e7b59f47da8e5513be96d5c60b3eecab85573fd6621587semantic review receipt SHA-256: 6c2c6d46aded7582a11ac41a8c0b3bdde2669a53bdb6e796eea2039994a02772question-first witness SHA-256: 77e43898df9efdbf8094ad81fe4ab91cf4b4bd82f481eb9b4699b73cb4da612bLean: NOT_RUN · human review: NOT_PERFORMED