{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261011-advance-20261015-r03-domain-codomain-range-0100", "pilot_number": "R0013-07300", "number": 7300, "family_id": "qf-density15-typed-mapping-table-candidate-audit", "title": { "zh-Hant": "第 7300 題：一列資料協議完整稽核", "en": "Question 7300: Candidate One-Row Protocol and Total-Table Eligibility" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261011-advance-20261015-r03-domain-codomain-range-0100", "batch_id": "batch-20261011-advance-20261015-r03-domain-codomain-range-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-domain-codomain-range" ], "title_zh": "一列資料協議完整稽核", "stem_zh": "Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[2, 0], [2, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。", "answer": { "kind": "expression", "value": "([3, 2], [是, 是], [0, 0, 2], [0, 1], [2], 否, 未成總表)", "explanation_zh": "一列協議候選表完整稽核=([3, 2], [是, 是], [0, 0, 2], [0, 1], [2], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。" }, "difficulty": { "band": "upper_secondary", "level": 3, "skills": [ "一列資料協議完整稽核" ] }, "variant": { "family_id": "qf-density15-typed-mapping-table-candidate-audit", "seed": 202610153100, "parameters": { "n": 3, "m": 2, "rows": [ [ 2, 0 ], [ 2, 0 ] ], "domain": "finite_typed_function_data", "operation": "density15_typed_mapping_table_candidate_audit", "semantic_template": "qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[0,0,2],\"not_total\"]" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_integer_rational_arithmetic", "producer_finite_enumeration", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-11", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261011-advance-20261015-r03-domain-codomain-range-0100", "batch_id": "batch-20261011-advance-20261015-r03-domain-codomain-range-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "39ee03efe6370f3dfb4e9d558c04e47e86edfc5118bc21734a38d060f949bb7d", "family_id": "qf-density15-typed-mapping-table-candidate-audit", "seed": 202610153100, "semantic_template": "qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[0,0,2],\"not_total\"]" }, "fields": { "title": "Candidate One-Row Protocol and Total-Table Eligibility", "stem": "Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[2, 0], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.", "answer": { "kind": "expression", "value": "([3, 2], [Yes, Yes], [0, 0, 2], [0, 1], [2], No, not-total-table)", "explanation": "Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes], [0, 0, 2], [0, 1], [2], No, not-total-table)." }, "skills": [ "Candidate One-Row Protocol and Total-Table Eligibility" ], "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": "Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[2, 0], [2, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。", "en": "Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[2, 0], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "declared types Fin(3)→Fin(2);0-based source labels", "after": "domain,codomain and actual range remain distinct", "relation": "implies", "rule_id": "typed_domain_codomain_data_scope", "conditions": [], "explanation": { "zh-Hant": "Fin(0)是空型別；完整總表不是部分程式函數，實際值域也不自動等於宣告陪域。此處核對有限資料，不冒稱一般無限集合定理。", "en": "Fin(0) is empty;a complete total table is not a partial program function,and its actual range need not equal its declared codomain.This audits finite data,not general infinite-set theorems." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "raw row position=0;input=2;output=0", "after": "both ends typed=是", "relation": "implies", "rule_id": "raw_candidate_table_row_type", "conditions": [], "explanation": { "zh-Hant": "逐列核雙端型別，但只要input合法，就要計入該input的raw出現次數，即使output域外。", "en": "Check both endpoint types row by row,but count every raw occurrence of a legal input even if its output is outside the codomain." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "raw row position=1;input=2;output=0", "after": "both ends typed=是", "relation": "implies", "rule_id": "raw_candidate_table_row_type", "conditions": [], "explanation": { "zh-Hant": "逐列核雙端型別，但只要input合法，就要計入該input的raw出現次數，即使output域外。", "en": "Check both endpoint types row by row,but count every raw occurrence of a legal input even if its output is outside the codomain." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "source input=0;raw row count=0", "after": "exactly one row=否", "relation": "implies", "rule_id": "one_raw_row_per_input_audit", "conditions": [], "explanation": { "zh-Hant": "一列協議要求每個來源恰一raw列；同值重複列也違反此格式，但不等於數學關係經去重後必為多值。", "en": "The one-row protocol requires exactly one raw row per source.Even identical repeated values violate that format,but do not imply the deduplicated mathematical relation is multivalued." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "source input=1;raw row count=0", "after": "exactly one row=否", "relation": "implies", "rule_id": "one_raw_row_per_input_audit", "conditions": [], "explanation": { "zh-Hant": "一列協議要求每個來源恰一raw列；同值重複列也違反此格式，但不等於數學關係經去重後必為多值。", "en": "The one-row protocol requires exactly one raw row per source.Even identical repeated values violate that format,but do not imply the deduplicated mathematical relation is multivalued." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "source input=2;raw row count=2", "after": "exactly one row=否", "relation": "implies", "rule_id": "one_raw_row_per_input_audit", "conditions": [], "explanation": { "zh-Hant": "一列協議要求每個來源恰一raw列；同值重複列也違反此格式，但不等於數學關係經去重後必為多值。", "en": "The one-row protocol requires exactly one raw row per source.Even identical repeated values violate that format,but do not imply the deduplicated mathematical relation is multivalued." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "row typing=[是, 是];input counts=[0, 0, 2]", "after": "complete one-row table=否;ordered images=未成總表", "relation": "implies", "rule_id": "candidate_table_protocol_not_relation_multivaluedness", "conditions": [], "explanation": { "zh-Hant": "兩種條件都過才依來源索引組成orderedImages；空來源空列可成完整空表，非法候選則不求造表。", "en": "Only both conditions permit orderedImages by source index.An empty source with no rows is a complete empty table;do not construct a table for an illegal candidate." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null } ], "math_model": { "result": [ [ 3, 2 ], [ true, true ], [ 0, 0, 2 ], [ 0, 1 ], [ 2 ], false, "未成總表" ] }, "conclusion": { "canonical_value": "([3, 2], [是, 是], [0, 0, 2], [0, 1], [2], 否, 未成總表)", "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-20261011-advance-20261015-r03-domain-codomain-range-foundations", "batch_path": "public/data/questions/batches/batch-20261011-advance-20261015-r03-domain-codomain-range-foundations/questions.jsonl", "batch_sha256": "4c652a7166afbd0ec4ff7932d1aedd85130eb2e1c5b132fd1a6d51ee0824c47e", "original_line": 100, "original_line_sha256": "27bb723a86cbd88f57ed2fd8362b9307b41dbe38e4c96b681f636c9f3d97e091", "question_compact_sha256": "39ee03efe6370f3dfb4e9d558c04e47e86edfc5118bc21734a38d060f949bb7d", "english_row_compact_sha256": "a3cf6731b4dc88af5433f2425f2f74a3d4933b4596a27993354eff91f17fac0d", "english_manifest_path": "public/data/i18n/editions/batch-20261011-advance-20261015-r03-domain-codomain-range-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261011-advance-20261015-r03-domain-codomain-range-foundations.en.jsonl" }, "mko_bindings": { "mko-domain-codomain-range": { "sha256": "94e55c31535caafd763f4e1f805a7da15848c153c844351ec087944dea68d451", "english_sha256": "1e8e497051747d1f535313e0ce98ad171f6ab459c72f0d46af1d1592c667bb58", "original_path": "public/data/mko/domain-codomain-range.json", "english_path": "public/data/i18n/editions/mko-domain-codomain-range.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "944e5a6e7ddc77eb28f9280c1b90da6c7083069b4790cbeb7488d009328efce8", "original_candidate_sha256": "2ca2862a1c9401452eba6fa0965875494009129a6fd54e2c779f4b3e9f48b1b8", "original_candidate_line_sha256": "2ca2862a1c9401452eba6fa0965875494009129a6fd54e2c779f4b3e9f48b1b8" }, "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-20261026-005-p14", "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": "e89fc6d4a50a4a7fc942c6c8939a92f835e30105a9a5850e37dd198f31c1ed59", "question_first_witness_sha256": "0e1039f4cf022bf35af4e5531651c9a2b7ca7a5fdacac34fb1e4bcd9a81f6299" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 7, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "38d09dd55182f9c990a03d1aa3712bc3d379e9e42c596b619de1633fbe41bd86", "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." } }