{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260913-natural-number-membership-0016", "pilot_number": "R0070-35631", "number": 35631, "family_id": "qf-natural-number-membership", "title": { "zh-Hant": "第 35631 題：自然數隸屬判定", "en": "Question 35631: Natural-Number Membership" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260913-natural-number-membership-0016", "batch_id": "batch-20260913-foundational-language", "language": "zh-Hant", "source_mko_ids": [ "mko-natural-number" ], "title_zh": "自然數隸屬判定", "stem_zh": "依 OCME 本條目「N 包含 0」的慣例，-0.5 是否屬於 N？", "answer": { "kind": "choice", "value": "否", "choices": [ "是", "否" ], "explanation_zh": "-0.5 不符合本條目所用 N 的非負整數範圍；此判定只採 OCME 的包含 0 慣例。" }, "difficulty": { "band": "upper_secondary", "level": 1, "skills": [ "自然數慣例", "集合隸屬" ] }, "variant": { "family_id": "qf-natural-number-membership", "seed": 20260928, "parameters": { "value": -0.5, "scenario": "non_integer", "semantic_template": "natural/non_integer/value--0.5" } }, "verification": { "status": "candidate", "checks": [ "schema_pending", "independent_recomputation_pending" ], "warning_zh": "本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。" }, "provenance": { "generator_role": "question_producer", "generator_model": "GPT-5.6 Terra", "generated_at": "2026-09-13", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20260913-natural-number-membership-0016", "batch_id": "batch-20260913-foundational-language", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "b0444d81e779d947baef87f63a7a4768a79a2227d2ad109366c73bc76c752171", "family_id": "qf-natural-number-membership", "seed": 20260928, "semantic_template": "natural/non_integer/value--0.5" }, "fields": { "title": "Natural-Number Membership", "stem": "Under this OCME entry's convention that N includes 0, does -0.5 belong to N?", "answer": { "kind": "choice", "value": "No", "choices": [ "Yes", "No" ], "explanation": "-0.5 is not a nonnegative integer, so it does not belong to N under this entry's convention." }, "skills": [ "natural-number convention", "set membership" ], "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": "依 OCME 本條目「N 包含 0」的慣例，-0.5 是否屬於 N？", "en": "Under this OCME entry's convention that N includes 0, does -0.5 belong to N?" } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-natural-number-membership, [scenario, value]]", "after": "derived = [natural, 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 = [-0.5, float]", "after": "derived = [是, 否, 否]", "relation": "implies", "rule_id": "Natural_membership_NUMERIC_integrality_not_string_regex", "conditions": [], "explanation": { "zh-Hant": "本條目N含0；先核真數值、整數性與非負，0合法，負數/小數/文字不是此數值域成員。非整數是合法No，不能先當不合格輸入剔除。", "en": "THIS entry’s N includes0.Check actual numeric type,integrality and nonnegativity.Zero belongs;negative,fractional and textual values do not.A noninteger is a LEGAL No,not an input to discard before classification." }, "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 = [否, 否]", "after": "derived = [否]", "relation": "implies", "rule_id": "Natural_membership_INTERSECTION_integer_AND_nonnegative", "conditions": [], "explanation": { "zh-Hant": "N={0,1,2,...}恰為非負整數，兩條件要同時成立；不靠scenario或整數字串格式猜答案。", "en": "N={0,1,2,...}is EXACTLY the nonnegative integers.BOTH conditions must hold;neither scenario metadata nor integer-looking strings determine membership." }, "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": "否" }, "conclusion": { "canonical_value": "否", "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-20260913-foundational-language", "batch_path": "public/data/questions/batches/batch-20260913-foundational-language/questions.jsonl", "batch_sha256": "f9197588b4d22a517e5a50d721638afb80a8f8f03cc65234ee357d2ba1823172", "original_line": 16, "original_line_sha256": "83ce27b00b189272c3eaeaff269d192bd0c4be33183789a9edc7429c365d0ac8", "question_compact_sha256": "b0444d81e779d947baef87f63a7a4768a79a2227d2ad109366c73bc76c752171", "english_row_compact_sha256": "f8309374f0b0d3e0c67ad2caa445c5e6234181b8a0ee40731952658a88fd7591", "english_manifest_path": "public/data/i18n/editions/batch-20260913-foundational-language.en.json", "english_rows_path": "public/data/i18n/questions/batch-20260913-foundational-language.en.jsonl" }, "mko_bindings": { "mko-natural-number": { "sha256": "222b72502fb661f3372012f602fd2f1eeef754b9e2069498c6b24234778730c4", "english_sha256": "f7444a7bfebcfed594478ed5e7c0f36cb1985114de58b5b473beddd1961c0bbc", "original_path": "public/data/mko/natural-number.json", "english_path": "public/data/i18n/editions/mko-natural-number.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "20c37a7e64ee5969e7606c5cc3a00e575002ebebdfe82873521cc3d7c608caff", "original_candidate_sha256": "08c3381285192a1a98c84f085ab3e7cce5e553b534d5397de78e8951085206a8", "original_candidate_line_sha256": "08c3381285192a1a98c84f085ab3e7cce5e553b534d5397de78e8951085206a8" }, "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": 3, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "bca71e82a3b603522a7c8b63fcbc81f6ac763288e5b122c1663da40e54865d65", "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." } }