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P1000-0865 · q-20261015-pulse-20261119-r07-0040
Use the complete finite feasible carrier=[A, B, C, D] with aligned exact objective values=[45, 15, 60, 75], 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=[45, 15, 60, 75], 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, 45], [B, 15], [C, 60], [D, 75]]
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)=45, f(challenger)=15
Conditions: none
First check that the challenger is a distinct feasible point.
Rule: feasible_challenger · Uses: G001, S001
Before
challenger minus candidate := sub(15, 45)
After
challenger minus candidate = -30
Conditions: none
Subtract exactly; a strictly negative difference certifies improvement.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
difference=-30<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, 45], [B, 15], [C, 60], [D, 75]], A, 45, B, 15, 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.
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