{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260914-arithmetic-domain-boundary-0020", "pilot_number": "R0070-35520", "number": 35520, "family_id": "qf-arithmetic-domain-boundary", "title": { "zh-Hant": "第 35520 題：四則運算數系邊界", "en": "Question 35520: Arithmetic Number-System Boundary" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260914-arithmetic-domain-boundary-0020", "batch_id": "batch-20260914-domain-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-arithmetic-operations" ], "title_zh": "四則運算數系邊界", "stem_zh": "在數系 N（包含 0）中，0/0 的結果應如何分類？", "answer": { "kind": "choice", "value": "除數為零，不能給一般數值答案", "choices": [ "在 N 中不封閉", "除數為零，不能給一般數值答案" ], "explanation_zh": "0/0 的除數為零；本題不把它當作一般除法的數值結果。" }, "difficulty": { "band": "upper_secondary", "level": 2, "skills": [ "數系邊界", "四則運算" ] }, "variant": { "family_id": "qf-arithmetic-domain-boundary", "seed": 20260933, "parameters": { "number_system": "N", "operator": "/", "a": 0, "b": 0, "state": "zero_divisor", "semantic_template": "qf-arithmetic-domain-boundary/{\"a\":0,\"b\":0,\"number_system\":\"N\",\"operator\":\"/\"}" } }, "verification": { "status": "candidate", "checks": [ "schema_pending", "independent_recomputation_pending" ], "warning_zh": "本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。" }, "provenance": { "generator_role": "question_producer", "generator_model": "GPT-5.6 Terra", "generated_at": "2026-09-14", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20260914-arithmetic-domain-boundary-0020", "batch_id": "batch-20260914-domain-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "d51e4c2c102fe914f20f76abc2a756d7a52c0aa247d67f561aaf22fa09e0b4cc", "family_id": "qf-arithmetic-domain-boundary", "seed": 20260933, "semantic_template": "qf-arithmetic-domain-boundary/{\"a\":0,\"b\":0,\"number_system\":\"N\",\"operator\":\"/\"}" }, "fields": { "title": "Arithmetic Number-System Boundary", "stem": "In the number system N, including 0, how should the result of 0/0 be classified?", "answer": { "kind": "choice", "value": "Zero divisor; no ordinary numerical result", "choices": [ "Not closed in N", "Zero divisor; no ordinary numerical result" ], "explanation": "The divisor in 0/0 is zero, so this question does not treat it as an ordinary numerical division result." }, "skills": [ "number-system boundaries", "arithmetic operations" ], "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": "在數系 N（包含 0）中，0/0 的結果應如何分類？", "en": "In the number system N, including 0, how should the result of 0/0 be classified?" } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-arithmetic-domain-boundary, [a, b, number_system, operator, state]]", "after": "derived = [arithmetic, null, null]", "relation": "implies", "rule_id": "R70_SOURCE_bank_specific_interface", "conditions": [], "explanation": { "zh-Hant": "只使用此bank真正明示的欄位、operation/domain與型別；BASE容許保留額外metadata，不把LDL SAFE/集合上限或其他bank的去重規則搬來。", "en": "Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [0, 0, /]", "after": "derived = [N={0,1,2,...}]", "relation": "implies", "rule_id": "Natural_arithmetic_GIVEN_N_includes0_and_operands", "conditions": [], "explanation": { "zh-Hant": "先固定本題N含0，兩操作數皆非負整數；問的是此系統內能否給數值，不是擅自換成整數或有理數。", "en": "FIRST fix THIS question’s N={0,1,2,...} and nonnegative integral operands.The question asks for a value WITHIN this system,not a silent change to integers/rationals." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [0, 0]", "after": "derived = [zero_divisor, 除數為零，不能給一般數值答案]", "relation": "implies", "rule_id": "Division_ZERO_never_evaluate_including0over0", "conditions": [], "explanation": { "zh-Hant": "除數0沒有乘法逆元：a≠0時0x=a無解；a=0時0x=0不唯一。所以連0/0也不能給一般唯一商，這條分支不執行除法。", "en": "Zero has no multiplicative inverse:0x=a has no solution for a≠0 and is nonunique for a=0.Thus even0/0 has no ordinary unique quotient;NO division is evaluated in this branch." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [zero_divisor, zero_divisor]", "after": "derived = [除數為零，不能給一般數值答案]", "relation": "implies", "rule_id": "Arithmetic_STATE_checked_AFTER_derivation", "conditions": [], "explanation": { "zh-Hant": "狀態metadata只在完成推導後一致性核對，從未拿它代替計算；除零、非封閉與N內數值三類分開。", "en": "Check state metadata ONLY AFTER deriving the result;never use it instead of calculation.Keep zero divisor,nonclosure and N-valued result distinct." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null } ], "math_model": { "result": "除數為零，不能給一般數值答案" }, "conclusion": { "canonical_value": "除數為零，不能給一般數值答案", "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-20260914-domain-foundations", "batch_path": "public/data/questions/batches/batch-20260914-domain-foundations/questions.jsonl", "batch_sha256": "726b3f94ccd05d8c91cc7e306b42fd71b6d9040e194db91739a250d488fd1de7", "original_line": 20, "original_line_sha256": "0feecfdbc36576780ff8542ec06d63acd3cb25823d8bc2ed9525f6643d9ca1c0", "question_compact_sha256": "d51e4c2c102fe914f20f76abc2a756d7a52c0aa247d67f561aaf22fa09e0b4cc", "english_row_compact_sha256": "c94a80f18b590391d248ed51b444cb7a244d9ff91efe96fe85bf1b3f67db368e", "english_manifest_path": "public/data/i18n/editions/batch-20260914-domain-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20260914-domain-foundations.en.jsonl" }, "mko_bindings": { "mko-arithmetic-operations": { "sha256": "452d77028e2659b860c94200c1de159c4184dde86d6d73950e1998a0080e265a", "english_sha256": "cd55f6d985015e73e560232ec9e4f77f3559c06dc72f0cf006f7083206a54169", "original_path": "public/data/mko/arithmetic-operations.json", "english_path": "public/data/i18n/editions/mko-arithmetic-operations.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "20c37a7e64ee5969e7606c5cc3a00e575002ebebdfe82873521cc3d7c608caff", "original_candidate_sha256": "c74a02040eca3f801efd31b84b480206d125de129f8bcced7ed2e739cca48115", "original_candidate_line_sha256": "c74a02040eca3f801efd31b84b480206d125de129f8bcced7ed2e739cca48115" }, "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-20261026-012-p71", "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": "9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80", "question_first_witness_sha256": "c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dab" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 4, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "b3d38820e5517d401fbe3a4d0210f5e3c7ea9ae07c1d6261a083fc96b030854e", "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." } }