{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261008-advance-20261011-r01-natural-number-0082", "pilot_number": "R0008-04857", "number": 4857, "family_id": "qf-density11-natural-rational-membership-mask", "title": { "zh-Hant": "第 4857 題：三個有理候選的含零N資格", "en": "Question 4857: Exact Rational Candidates for N" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261008-advance-20261011-r01-natural-number-0082", "batch_id": "batch-20261008-advance-20261011-r01-natural-number-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-natural-number" ], "title_zh": "三個有理候選的含零N資格", "stem_zh": "N包含0；有序有理數候選=[6/1, -6/1, 7/13]。逐項答值是否屬N，以是／否列表表示。", "answer": { "kind": "expression", "value": "[是, 否, 否]", "explanation_zh": "N含0資格=[是, 否, 否]。先精確約分，再要求非負且分母為一；零通過，負整數與非整數分數不通過。" }, "difficulty": { "band": "lower_secondary", "level": 1, "skills": [ "三個有理候選的含零N資格" ] }, "variant": { "family_id": "qf-density11-natural-rational-membership-mask", "seed": 202610111082, "parameters": { "fractions": [ [ 6, 1 ], [ -6, 1 ], [ 7, 13 ] ], "operation": "density11_natural_rational_membership_mask", "domain": "Q_candidates_for_N0", "semantic_template": "qf-density11-natural-rational-membership-mask/[\"6/1\",\"-6/1\",\"7/13\"]" } }, "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": "2026-10-08", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261008-advance-20261011-r01-natural-number-0082", "batch_id": "batch-20261008-advance-20261011-r01-natural-number-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "2b4221dbccf2d967affd8dbef98cdc981442660073d6cf6470b0675fce94f3c4", "family_id": "qf-density11-natural-rational-membership-mask", "seed": 202610111082, "semantic_template": "qf-density11-natural-rational-membership-mask/[\"6/1\",\"-6/1\",\"7/13\"]" }, "fields": { "title": "Exact Rational Candidates for N", "stem": "N includes 0. Ordered rational candidates=[6/1, -6/1, 7/13]. Give the Yes/No membership list for N.", "answer": { "kind": "expression", "value": "[Yes, No, No]", "explanation": "Reduce each rational exactly, then require a nonnegative value and denominator one; zero passes, but negative integers and nonintegers do not. The exact result, retaining the requested order, is [Yes, No, No]." }, "skills": [ "Exact Rational Candidates for N" ], "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": "N包含0；有序有理數候選=[6/1, -6/1, 7/13]。逐項答值是否屬N，以是／否列表表示。", "en": "N includes 0. Ordered rational candidates=[6/1, -6/1, 7/13]. Give the Yes/No membership list for N." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "N={0,1,2,...}", "after": "0 belongs;negative and nonintegral rational values do not", "relation": "implies", "rule_id": "natural_zero_convention", "conditions": [], "explanation": { "zh-Hant": "本題自然數包含0；與有理數值、部分前驅及閉區間的規則分開判定。", "en": "This convention includes0 in N;distinguish membership,rational values,partial predecessors and closed intervals." }, "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 rational=[6, 1];reduced=6/1", "after": "nonnegative integer=是", "relation": "implies", "rule_id": "reduced_rational_natural_membership", "conditions": [], "explanation": { "zh-Hant": "先把分數化為精確值，再看非負且最簡分母1；原分母不是1的表示仍可能是自然數。", "en": "First reduce to its exact value,then require nonnegativity and reduced denominator1.A representation whose original denominator is not1 can still be natural." }, "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 rational=[-6, 1];reduced=-6/1", "after": "nonnegative integer=否", "relation": "implies", "rule_id": "reduced_rational_natural_membership", "conditions": [], "explanation": { "zh-Hant": "先把分數化為精確值，再看非負且最簡分母1；原分母不是1的表示仍可能是自然數。", "en": "First reduce to its exact value,then require nonnegativity and reduced denominator1.A representation whose original denominator is not1 can still be natural." }, "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": "raw rational=[7, 13];reduced=7/13", "after": "nonnegative integer=否", "relation": "implies", "rule_id": "reduced_rational_natural_membership", "conditions": [], "explanation": { "zh-Hant": "先把分數化為精確值，再看非負且最簡分母1；原分母不是1的表示仍可能是自然數。", "en": "First reduce to its exact value,then require nonnegativity and reduced denominator1.A representation whose original denominator is not1 can still be natural." }, "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": [ true, false, false ], "reduced_candidates": [ "6", "-6", "7/13" ] }, "conclusion": { "canonical_value": "[是, 否, 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-20261008-advance-20261011-r01-natural-number-foundations", "batch_path": "public/data/questions/batches/batch-20261008-advance-20261011-r01-natural-number-foundations/questions.jsonl", "batch_sha256": "ccaa1444bd0d6cb142b205d76ade261dd201940cf4971f1370270518e95618a0", "original_line": 82, "original_line_sha256": "9497a43a986d5480f73d5fa832900339fb8bcd10ed73691a7ee5a7158cac9c47", "question_compact_sha256": "2b4221dbccf2d967affd8dbef98cdc981442660073d6cf6470b0675fce94f3c4", "english_row_compact_sha256": "51ab7c35582217a9950c6140b3e65cecf560fb3c70af16a743dc5096683637a4", "english_manifest_path": "public/data/i18n/editions/batch-20261008-advance-20261011-r01-natural-number-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261008-advance-20261011-r01-natural-number-foundations.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": "6dc34e24b0f43c50e49365ca1a1153175f8661d5290c9236df5527bb047157eb", "original_candidate_sha256": "f84169bf01f62f58a2cb6c1fe76d3a4595cc603d6289b019dcd34ccbf8e7631c", "original_candidate_line_sha256": "f84169bf01f62f58a2cb6c1fe76d3a4595cc603d6289b019dcd34ccbf8e7631c" }, "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-20261026-004-p9", "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": "b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289", "question_first_witness_sha256": "caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67" }, "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": "794bff497dd6bec268ccfe038f7d444ea353f716d45ddf5386b2629f55557d3c", "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." } }