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R0058-29830 · q-20261013-advance-20261020-r04-optimization-problem-0030
Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-6, 4, 8, 4], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).
G001 — Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-6, 4, 8, 4], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).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 = [qf-app20-optimization-argmin, optimization-argmin]
After
derived = [[values, mask, min, best, arg_indices]]
Conditions: none
Follow THIS bank exact keys,domain/frame,operation and answer role.STR22/App20 tuples differ from legacy scalars;retain or omit/1 by the ORIGINAL contract,not a generic visual convention.
Rule: R58_EXACT_source_interface_and_answer_ROLE · Uses: G001
Before
source roles = [[-6, 4, 8, 4], [Yes, Yes, Yes, Yes]]
After
derived = [[0, 1, 2, 3]]
Conditions: none
Require an ACTUAL Boolean mask aligned to original slots and retain zero-based indices with at least one eligible candidate.A better objective cannot change False to True,and0/1 are not Booleans.
Rule: Optimization_EXACT_Boolean_mask_ORIGINAL_zero_indices · Uses: G001, S001
Before
source roles = [explicit Boolean mask, [-6, 4, 8, 4], [0, 1, 2, 3], min]
After
derived = [-6, [0], [[0, -6, Yes, Yes], [1, 4, Yes, No], [2, 8, Yes, No], [3, 4, Yes, No]]]
Conditions: none
Check the corresponding bound for EVERY feasible ORIGINAL index and retain ALL equality indices.The optimal value differs from its arg set.Ignore better infeasible values and do not assume uniqueness.The conclusion is ONLY for this complete declared finite set.
Rule: Optimization_ALL_feasible_objectives_bound_AND_every_tied_index · Uses: G001, S002
S003 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.S002 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.S001 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], min, -6, [0])
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: db78f6ee9edaac99d0029a2bd20ff9130a1062f14c703504d4da9925c43f6250candidate record SHA-256: 396866ce4b1b2a360d6a0f38b3325724df043dc5fa5b57a167b6cc2689fcc5fbsemantic review receipt SHA-256: 66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05dfquestion-first witness SHA-256: b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7Lean: NOT_RUN · human review: NOT_PERFORMED