{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261013-advance-20261020-r04-optimization-problem-0033", "pilot_number": "R0058-29833", "number": 29833, "family_id": "qf-app20-optimization-argmin", "title": { "zh-Hant": "第 29833 題：有限候選最佳化", "en": "Question 29833: Finite Minimum Value and Every Original Minimizer Index" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261013-advance-20261020-r04-optimization-problem-0033", "batch_id": "batch-20261013-advance-20261020-r04-optimization-problem-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-optimization-problem" ], "title_zh": "有限候選最佳化", "stem_zh": "完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[-3,-4,5,2],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。", "answer": { "kind": "expression", "value": "([-3, -4, 5, 2], [是, 否, 是, 是], min, -3, [0])", "explanation_zh": "應用基礎核對=([-3, -4, 5, 2], [是, 否, 是, 是], min, -3, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。" }, "difficulty": { "band": "undergraduate_core", "level": 1, "skills": [ "有限候選最佳化" ] }, "variant": { "family_id": "qf-app20-optimization-argmin", "seed": 202610204033, "parameters": { "values": [ -3, -4, 5, 2 ], "feasible": [ true, false, true, true ], "domain": "Finite_declared_optimization", "operation": "optimization-argmin", "semantic_template": "qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[-3,-4,5,2]}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_finite_model", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-13", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261013-advance-20261020-r04-optimization-problem-0033", "batch_id": "batch-20261013-advance-20261020-r04-optimization-problem-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "2be37492b6ab98388da494901592142c3709366f5b2d61ab9a37f95243e7f2c8", "family_id": "qf-app20-optimization-argmin", "seed": 202610204033, "semantic_template": "qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[-3,-4,5,2]}" }, "fields": { "title": "Finite Minimum Value and Every Original Minimizer Index", "stem": "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=[-3, -4, 5, 2], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).", "answer": { "kind": "expression", "value": "([-3, -4, 5, 2], [Yes, No, Yes, Yes], min, -3, [0])", "explanation": "Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-3, -4, 5, 2], [Yes, No, Yes, Yes], min, -3, [0])." }, "skills": [ "Finite Minimum Value and Every Original Minimizer Index" ], "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review." } }, "givens": [ { "id": "G001", "text": { "zh-Hant": "完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[-3,-4,5,2],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。", "en": "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=[-3, -4, 5, 2], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-app20-optimization-argmin, optimization-argmin]", "after": "derived = [[values, mask, min, best, arg_indices]]", "relation": "implies", "rule_id": "R58_EXACT_source_interface_and_answer_ROLE", "conditions": [], "explanation": { "zh-Hant": "依本題銀行的keys、domain或frame、operation與輸出角色。STR22/App20 tuple與legacy scalar不同；分數是否保/1按原契約，不能用共同外觀改題。", "en": "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." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。", "en": "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." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [[-3, -4, 5, 2], [是, 否, 是, 是]]", "after": "derived = [[0, 2, 3]]", "relation": "implies", "rule_id": "Optimization_EXACT_Boolean_mask_ORIGINAL_zero_indices", "conditions": [], "explanation": { "zh-Hant": "feasible必須是真Boolean且逐slot配對；保原0-based index，至少一個合格候選。false不因objective較佳而改true，0/1不冒充Boolean。", "en": "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." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。", "en": "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." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [explicit Boolean mask, [-3, -4, 5, 2], [0, 2, 3], min]", "after": "derived = [-3, [0], [[0, -3, 是, 是], [2, 5, 是, 否], [3, 2, 是, 否]]]", "relation": "implies", "rule_id": "Optimization_ALL_feasible_objectives_bound_AND_every_tied_index", "conditions": [], "explanation": { "zh-Hant": "逐全部feasible原index核對best給相應上下界，且列出所有等號indices；最優value與arg集合不同，不選infeasible較佳值，不假設unique。結論僅限這個完整宣告有限集。", "en": "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." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。", "en": "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." } }, "arithmetic": null } ], "math_model": { "result": [ [ -3, -4, 5, 2 ], [ true, false, true, true ], "min", -3, [ 0 ] ] }, "conclusion": { "canonical_value": "([-3, -4, 5, 2], [是, 否, 是, 是], min, -3, [0])", "explanation": { "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。", "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged." } }, "definition_note": { "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。", "en": "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." }, "source": { "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db", "question_binding": { "batch_id": "batch-20261013-advance-20261020-r04-optimization-problem-foundations", "batch_path": "public/data/questions/batches/batch-20261013-advance-20261020-r04-optimization-problem-foundations/questions.jsonl", "batch_sha256": "81535eb6e80198569e54d036aa76bc021ca6a29840d6f677dc163c2c3367a326", "original_line": 33, "original_line_sha256": "4cca41109dd5baca491fddec0cb31caf5630e05c9af64b602e4285ea5b258c8e", "question_compact_sha256": "2be37492b6ab98388da494901592142c3709366f5b2d61ab9a37f95243e7f2c8", "english_row_compact_sha256": "1cbbfe9ff79f31f4ac2da47ac5399dacfc1b7e6398293caee24efecfc774f495", "english_manifest_path": "public/data/i18n/editions/batch-20261013-advance-20261020-r04-optimization-problem-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261013-advance-20261020-r04-optimization-problem-foundations.en.jsonl" }, "mko_bindings": { "mko-optimization-problem": { "sha256": "55c8accf83a0b3a16cb86f438bdc6575f8dcec45e670f324e863e79a1a233514", "english_sha256": "b6379fa21189b83b931814f4a2acdc266e8f73e8fa2fad6e9d2190456191279e", "original_path": "public/data/mko/optimization-problem.json", "english_path": "public/data/i18n/editions/mko-optimization-problem.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "623c23f45586b08629c5a347ffbc994cf8dbff2133c4f4cdb227b851d74ea6b6", "original_candidate_sha256": "ecd70fcfc82fdcb275e2aecd90b43cb14b54b6cf3fdafa2d71acbcfbd8ca65d6", "original_candidate_line_sha256": "ecd70fcfc82fdcb275e2aecd90b43cb14b54b6cf3fdafa2d71acbcfbd8ca65d6" }, "historical_source_state": { "review_state": { "derivation": "candidate_authored_and_locally_checked", "source_question_state": "candidate", "independent_AI_or_human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN" }, "scope_note": { "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。", "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged." }, "label": "Frozen producer metadata; current per-question review is separate below." }, "revision": { "id": "review-20261026-011-p59", "review_date": "2026-10-26", "owner_authorized_reader_publication": true, "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.", "review_receipts": { "semantic_review_sha256": "66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05df", "question_first_witness_sha256": "b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 3, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "65326c86bb5e285488b166ff38666ccd7a498734463d2c53f6af89d558668e6a", "arithmetic_steps": 0 }, "uses_answer_as_premise": false, "human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN", "Canonical_truth_promotion": false, "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged." } }