{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261003-advance-20261004-r01-quantifier-0078", "pilot_number": "R0068-34678", "number": 34678, "family_id": "qf-quantifier-negated-existential", "title": { "zh-Hant": "第 34678 題：有限存在的否定真值", "en": "Question 34678: Negation of a Finite Existential Statement" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261003-advance-20261004-r01-quantifier-0078", "batch_id": "batch-20261003-advance-20261004-r01-quantifier-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-quantifier" ], "title_zh": "有限存在的否定真值", "stem_zh": "採古典真值，明示有限論域 U={1, 2, 3}，整數條件 P(x)：x≥4。¬(∃x∈U P(x)) 是否為真？", "answer": { "kind": "short_text", "value": "是", "explanation_zh": "滿足=0；失敗=3；論域=3。完整檢查明示論域；空論域全稱為真、存在為假，否定後交換真假。不外推到無限論域。" }, "difficulty": { "band": "upper_secondary", "level": 1, "skills": [ "有限存在的否定真值" ] }, "variant": { "family_id": "qf-quantifier-negated-existential", "seed": 202610041078, "parameters": { "U": [ 1, 2, 3 ], "predicate": { "kind": "ge", "value": 4 }, "operation": "not_exists", "semantic_template": "qf-quantifier-negated-existential/{\"U\":[1,2,3],\"operation\":\"not_exists\",\"predicate\":{\"kind\":\"ge\",\"value\":4}}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_integer_rational_arithmetic", "producer_finite_enumeration", "producer_source_snapshot_check", "producer_substantive_template_deduplication" ], "warning_zh": "僅為產生端候選及自檢；主架構者須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "Codex independent peer (inherited model; exact runtime model not exposed)", "generated_at": "2026-10-03", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261003-advance-20261004-r01-quantifier-0078", "batch_id": "batch-20261003-advance-20261004-r01-quantifier-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "1ba624cae6fecf113658d528e6a31433dd2d1600317a13483fee17a81e6edb7e", "family_id": "qf-quantifier-negated-existential", "seed": 202610041078, "semantic_template": "qf-quantifier-negated-existential/{\"U\":[1,2,3],\"operation\":\"not_exists\",\"predicate\":{\"kind\":\"ge\",\"value\":4}}" }, "fields": { "title": "Negation of a Finite Existential Statement", "stem": "Using classical truth semantics, the explicit finite integer domain is U={1, 2, 3} and P(x) means x≥4. Is ¬(∃x∈U P(x)) true? Answer Yes or No.", "answer": { "kind": "short_text", "value": "Yes", "explanation": "There are 0 satisfying and 3 failing elements out of 3; the answer is Yes. On the empty domain, universal truth is true and existential truth is false; negation reverses the corresponding truth value. This exhaustive result concerns only the declared finite domain and does not extend to an infinite domain." }, "skills": [ "Negation of a Finite Existential Statement" ], "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": "採古典真值，明示有限論域 U={1, 2, 3}，整數條件 P(x)：x≥4。¬(∃x∈U P(x)) 是否為真？", "en": "Using classical truth semantics, the explicit finite integer domain is U={1, 2, 3} and P(x) means x≥4. Is ¬(∃x∈U P(x)) true? Answer Yes or No." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-quantifier-negated-existential, [U, operation, predicate]]", "after": "derived = [not_exists, no-invented-domain]", "relation": "implies", "rule_id": "R68_BANK_specific_keys_operations_and_numeric_guards", "conditions": [], "explanation": { "zh-Hant": "按來源分bank：legacy raw SAFE/衍生BigInt無界，BASE Number.isInteger不偷加SAFE/百萬界。underscore operation、domain及寬/嚴keys各依本bank；原JSON完整保存。", "en": "Separate source banks:legacy RAW SAFE with unbounded derived BigInts versus BASE Number.isInteger without invented SAFE/million caps.Operations,domains and permissive/exact keys follow THIS bank.Keep ORIGINAL JSON intact." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [quantifier ORIGINAL U, [1, 2, 3]]", "after": "derived = [[1, 2, 3]]", "relation": "implies", "rule_id": "LDL_RAW_distinct_SAFE_set_empty_allowed", "conditions": [], "explanation": { "zh-Hant": "本LDL set長0..100、元素raw SAFE且不重複，空集合合法；排序只屬衍生表示，原JSON順序不改。不是BASE無上限的另一set協定。", "en": "THIS LDL set has0..100 DISTINCT RAW SAFE labels,with the empty set allowed.Sort only the derived representation;preserve original JSON order.Do not import another BASE set protocol." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [{'kind': 'ge', 'value': 4}]", "after": "derived = [否, validation only;0 is NOT added to U]", "relation": "implies", "rule_id": "Quantifier_SOURCE_predicate_validity_at0_EVEN_empty_U", "conditions": [], "explanation": { "zh-Hant": "SOURCE即使U空也驗predicateValue(0)：kind/value精確兩欄、value SAFE、multiple divisor非0。這是本協定可定義性責任，不把0加入U，也不宣稱數學上的0整除概念普遍未定義。", "en": "The SOURCE validates predicateValue(0)EVEN for empty U:EXACT kind/value keys,SAFE value and a NONZERO multiple divisor.This is THIS protocol’s qualification,NOT adding0 to U or a universal theorem about divisibility by0." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [1, {'kind': 'ge', 'value': 4}]", "after": "derived = [否]", "relation": "implies", "rule_id": "Quantifier_EACH_original_domain_element_predicate_substitution", "conditions": [], "explanation": { "zh-Hant": "逐明示論域元素代入同一已合格述詞，記滿足或失敗；不能以少數成功樣本取代全部有限核對，也不外推到未列值。", "en": "Substitute EACH explicitly listed domain element into the SAME qualified predicate and record pass/fail.Do not replace complete finite coverage by a successful sample or extrapolate to unlisted values." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "source roles = [2, {'kind': 'ge', 'value': 4}]", "after": "derived = [否]", "relation": "implies", "rule_id": "Quantifier_EACH_original_domain_element_predicate_substitution", "conditions": [], "explanation": { "zh-Hant": "逐明示論域元素代入同一已合格述詞，記滿足或失敗；不能以少數成功樣本取代全部有限核對，也不外推到未列值。", "en": "Substitute EACH explicitly listed domain element into the SAME qualified predicate and record pass/fail.Do not replace complete finite coverage by a successful sample or extrapolate to unlisted values." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "source roles = [3, {'kind': 'ge', 'value': 4}]", "after": "derived = [否]", "relation": "implies", "rule_id": "Quantifier_EACH_original_domain_element_predicate_substitution", "conditions": [], "explanation": { "zh-Hant": "逐明示論域元素代入同一已合格述詞，記滿足或失敗；不能以少數成功樣本取代全部有限核對，也不外推到未列值。", "en": "Substitute EACH explicitly listed domain element into the SAME qualified predicate and record pass/fail.Do not replace complete finite coverage by a successful sample or extrapolate to unlisted values." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "source roles = [[1, 2, 3], [[1, 否], [2, 否], [3, 否]], not_exists]", "after": "derived = [[], [1, 2, 3], 是]", "relation": "implies", "rule_id": "Quantifier_ALL_finite_truth_rows_negation_and_EMPTY_conventions", "conditions": [], "explanation": { "zh-Hant": "∀要求無失敗；∃要求有滿足；¬∀等價有失敗；¬∃等價無滿足。空U的四結果依序True/False/False/True，但只有合格述詞才進此步。不外推到無限論域。", "en": "∀ requires NO failures;∃ requires a passing member;¬∀ means a failing member;¬∃ means NO passing member.For empty U the four results are True/False/False/True,AFTER predicate qualification.No infinite-domain inference follows." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null } ], "math_model": { "result": "是" }, "conclusion": { "canonical_value": "是", "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-20261003-advance-20261004-r01-quantifier-foundations", "batch_path": "public/data/questions/batches/batch-20261003-advance-20261004-r01-quantifier-foundations/questions.jsonl", "batch_sha256": "d661ca45b314766810e5721e9b0b9c2c0c306e15535752937a15e28c8f0cb8c5", "original_line": 78, "original_line_sha256": "1d5eafaa9650e552232521ab8d02d8eacedf878686bebe99ba74a39e64aeef50", "question_compact_sha256": "1ba624cae6fecf113658d528e6a31433dd2d1600317a13483fee17a81e6edb7e", "english_row_compact_sha256": "b706dad099b7a55b98312eeccbfc69002c26a9c34ec4519c6ddf26273cbfb2b9", "english_manifest_path": "public/data/i18n/editions/batch-20261003-advance-20261004-r01-quantifier-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261003-advance-20261004-r01-quantifier-foundations.en.jsonl" }, "mko_bindings": { "mko-quantifier": { "sha256": "3b2f73bd57aa43b5441edef2b27d44470f8cbf04a229fb31e98243708e818341", "english_sha256": "cf34ab77acaa732f1cc6926b00bee27e73188f1108aaad401ca0a12fc391cc57", "original_path": "public/data/mko/quantifier.json", "english_path": "public/data/i18n/editions/mko-quantifier.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "345142be27643acca9d0fec2422ac7311b85bf142709391cd6b5b3a33c03cf8e", "original_candidate_sha256": "6b463245a65d0365ae16a8932d59c597254c521fcede8a6e77a8353ce372d865", "original_candidate_line_sha256": "6b463245a65d0365ae16a8932d59c597254c521fcede8a6e77a8353ce372d865" }, "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-p69", "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": "e7a54104fa02c235f7591329bd6db8d626dd74bf0fae29c557b1f269c85066ed", "question_first_witness_sha256": "8401a3c2064c1275a6a7ea8f00412fa12286cec7b2db6c305ff9dba3724ae229" }, "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": "04d3f7b1b53a2175e0fd8707acf3c0dbdc2b84c660bca89bf8f716e25f5ad050", "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." } }