{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261111-r03-hausdorff-space-0087", "pilot_number": "R0044-22987", "number": 22987, "family_id": "qf-mod42-hausdorff-sampled-boundary", "title": { "zh-Hant": "第 22987 題：Hausdorff空間", "en": "Question 22987: Successful Pair Samples Do Not Certify Unchecked or Infinite Cases" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261014-advance-20261111-r03-hausdorff-space-0087", "batch_id": "batch-20261014-advance-20261111-r03-hausdorff-space-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-hausdorff-space" ], "title_zh": "Hausdorff空間", "stem_zh": "完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={\"points\":[\"a11\",\"b11\",\"c11\"],\"topology\":[[\"a11\",\"b11\",\"c11\"],[\"a11\",\"b11\"],[\"a11\",\"c11\"],[\"a11\"],[\"c11\"],[]],\"sampled_pairs\":[[\"c11\",\"a11\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "answer": { "kind": "expression", "value": "([[c11, a11, [[c11], [a11, b11]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)", "explanation_zh": "Wave6第五層核對=([[c11, a11, [[c11], [a11, b11]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。" }, "difficulty": { "band": "undergraduate_core", "level": 2, "skills": [ "Hausdorff空間" ] }, "variant": { "family_id": "qf-mod42-hausdorff-sampled-boundary", "seed": 202611113087, "parameters": { "points": [ "a11", "b11", "c11" ], "topology": [ [ "a11", "b11", "c11" ], [ "a11", "b11" ], [ "a11", "c11" ], [ "a11" ], [ "c11" ], [] ], "sampled_pairs": [ [ "c11", "a11" ] ], "domain": "Complete_finite_topology_Hausdorff_audit", "operation": "hausdorff-sampled-boundary", "semantic_template": "qf-mod42-hausdorff-sampled-boundary/{\"points\":[\"a11\",\"b11\",\"c11\"],\"sampled_pairs\":[[\"c11\",\"a11\"]],\"topology\":[[\"a11\",\"b11\",\"c11\"],[\"a11\",\"b11\"],[\"a11\",\"c11\"],[\"a11\"],[\"c11\"],[]]}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_finite_or_symbolic_model", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-14", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261014-advance-20261111-r03-hausdorff-space-0087", "batch_id": "batch-20261014-advance-20261111-r03-hausdorff-space-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "0b78a3bb2282e2f4cd6b364a97c690c770c08daaaf6dc3cd8df4045246ac9e74", "family_id": "qf-mod42-hausdorff-sampled-boundary", "seed": 202611113087, "semantic_template": "qf-mod42-hausdorff-sampled-boundary/{\"points\":[\"a11\",\"b11\",\"c11\"],\"sampled_pairs\":[[\"c11\",\"a11\"]],\"topology\":[[\"a11\",\"b11\",\"c11\"],[\"a11\",\"b11\"],[\"a11\",\"c11\"],[\"a11\"],[\"c11\"],[]]}" }, "fields": { "title": "Successful Pair Samples Do Not Certify Unchecked or Infinite Cases", "stem": "Use finite unique labeled points=[a11, b11, c11] and the complete canonical topology=[[a11, b11, c11], [a11, b11], [a11, c11], [a11], [c11], []]. Every neighborhood witness must be a declared open set containing its assigned point; the two points must be distinct and the witnesses disjoint. The complete topology must qualify before a Hausdorff audit. Supplied sampled_pairs=[[c11, a11]]. Give (sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary).", "answer": { "kind": "expression", "value": "([[c11, a11, [[c11], [a11, b11]]]], Yes, 1, 3, No, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)", "explanation": "Audit each sampled pair and retain sample count and total finite unordered-pair count separately. The fixed No withholds a general sampling certificate, not the preceding separation results. If every finite pair was actually covered, completeness must be established separately rather than inferred from the word sample. The exact result, retaining the requested order, is ([[c11, a11, [[c11], [a11, b11]]]], Yes, 1, 3, No, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)." }, "skills": [ "Successful Pair Samples Do Not Certify Unchecked or Infinite Cases" ], "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": "完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={\"points\":[\"a11\",\"b11\",\"c11\"],\"topology\":[[\"a11\",\"b11\",\"c11\"],[\"a11\",\"b11\"],[\"a11\",\"c11\"],[\"a11\"],[\"c11\"],[]],\"sampled_pairs\":[[\"c11\",\"a11\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "en": "Use finite unique labeled points=[a11, b11, c11] and the complete canonical topology=[[a11, b11, c11], [a11, b11], [a11, c11], [a11], [c11], []]. Every neighborhood witness must be a declared open set containing its assigned point; the two points must be distinct and the witnesses disjoint. The complete topology must qualify before a Hausdorff audit. Supplied sampled_pairs=[[c11, a11]]. Give (sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source operation=hausdorff-sampled-boundary;original snapshot and mathematics retained", "after": "explicit ordered source output fields=[sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary]", "relation": "implies", "rule_id": "source_ordered_interface_explicit_without_javascript", "conditions": [], "explanation": { "zh-Hant": "保留原題歷史介面標記，直接列來源欄序，不需JavaScript。tag不是額外證據，固定No依原聲稱範圍解讀；排序輔助只處理協定，不是數學oracle。", "en": "Keep the historical interface marker and list ordered source fields without JavaScript.Tags are not additional evidence;fixed No markers retain their scope.The ordering helper supplies protocol order,not mathematical correctness." }, "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": "ORIGINAL carrier order=[a11, b11, c11];source canonical open family=[[a11, b11, c11], [a11, b11], [a11, c11], [a11], [c11], []];actual open index=0,U=[a11, b11, c11]", "after": "ALL [other_index,union,intersection] rows=[[0, [a11, b11, c11], [a11, b11, c11]], [1, [a11, b11, c11], [a11, b11]], [2, [a11, b11, c11], [a11, c11]], [3, [a11, b11, c11], [a11]], [4, [a11, b11, c11], [c11]], [5, [a11, b11, c11], []]];empty/full present;family qualification passed with exact source English collation", "relation": "implies", "rule_id": "hausdorff_complete_labeled_topology_and_source_order", "conditions": [], "explanation": { "zh-Hant": "點標籤與原carrier次序保留；各open內依來源字串排序，family依固定English collation，不按大小或另一個常見慣例。逐全部open pair核公理，空carrier也有拓撲[[]]。", "en": "Retain labels and original carrier order.Sort elements and the family by the exact declared source conventions,not size or an alternate familiar convention.Check all open pairs;the empty carrier has topology[[]]." }, "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": "ORIGINAL carrier order=[a11, b11, c11];source canonical open family=[[a11, b11, c11], [a11, b11], [a11, c11], [a11], [c11], []];actual open index=1,U=[a11, b11]", "after": "ALL [other_index,union,intersection] rows=[[0, [a11, b11, c11], [a11, b11]], [1, [a11, b11], [a11, b11]], [2, [a11, b11, c11], [a11]], [3, [a11, b11], [a11]], [4, [a11, b11, c11], []], [5, [a11, b11], []]];empty/full present;family qualification passed with exact source English collation", "relation": "implies", "rule_id": "hausdorff_complete_labeled_topology_and_source_order", "conditions": [], "explanation": { "zh-Hant": "點標籤與原carrier次序保留；各open內依來源字串排序，family依固定English collation，不按大小或另一個常見慣例。逐全部open pair核公理，空carrier也有拓撲[[]]。", "en": "Retain labels and original carrier order.Sort elements and the family by the exact declared source conventions,not size or an alternate familiar convention.Check all open pairs;the empty carrier has topology[[]]." }, "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": "ORIGINAL carrier order=[a11, b11, c11];source canonical open family=[[a11, b11, c11], [a11, b11], [a11, c11], [a11], [c11], []];actual open index=2,U=[a11, c11]", "after": "ALL [other_index,union,intersection] rows=[[0, [a11, b11, c11], [a11, c11]], [1, [a11, b11, c11], [a11]], [2, [a11, c11], [a11, c11]], [3, [a11, c11], [a11]], [4, [a11, c11], [c11]], [5, [a11, c11], []]];empty/full present;family qualification passed with exact source English collation", "relation": "implies", "rule_id": "hausdorff_complete_labeled_topology_and_source_order", "conditions": [], "explanation": { "zh-Hant": "點標籤與原carrier次序保留；各open內依來源字串排序，family依固定English collation，不按大小或另一個常見慣例。逐全部open pair核公理，空carrier也有拓撲[[]]。", "en": "Retain labels and original carrier order.Sort elements and the family by the exact declared source conventions,not size or an alternate familiar convention.Check all open pairs;the empty carrier has topology[[]]." }, "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": "ORIGINAL carrier order=[a11, b11, c11];source canonical open family=[[a11, b11, c11], [a11, b11], [a11, c11], [a11], [c11], []];actual open index=3,U=[a11]", "after": "ALL [other_index,union,intersection] rows=[[0, [a11, b11, c11], [a11]], [1, [a11, b11], [a11]], [2, [a11, c11], [a11]], [3, [a11], [a11]], [4, [a11, c11], []], [5, [a11], []]];empty/full present;family qualification passed with exact source English collation", "relation": "implies", "rule_id": "hausdorff_complete_labeled_topology_and_source_order", "conditions": [], "explanation": { "zh-Hant": "點標籤與原carrier次序保留；各open內依來源字串排序，family依固定English collation，不按大小或另一個常見慣例。逐全部open pair核公理，空carrier也有拓撲[[]]。", "en": "Retain labels and original carrier order.Sort elements and the family by the exact declared source conventions,not size or an alternate familiar convention.Check all open pairs;the empty carrier has topology[[]]." }, "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": "ORIGINAL carrier order=[a11, b11, c11];source canonical open family=[[a11, b11, c11], [a11, b11], [a11, c11], [a11], [c11], []];actual open index=4,U=[c11]", "after": "ALL [other_index,union,intersection] rows=[[0, [a11, b11, c11], [c11]], [1, [a11, b11, c11], []], [2, [a11, c11], [c11]], [3, [a11, c11], []], [4, [c11], [c11]], [5, [c11], []]];empty/full present;family qualification passed with exact source English collation", "relation": "implies", "rule_id": "hausdorff_complete_labeled_topology_and_source_order", "conditions": [], "explanation": { "zh-Hant": "點標籤與原carrier次序保留；各open內依來源字串排序，family依固定English collation，不按大小或另一個常見慣例。逐全部open pair核公理，空carrier也有拓撲[[]]。", "en": "Retain labels and original carrier order.Sort elements and the family by the exact declared source conventions,not size or an alternate familiar convention.Check all open pairs;the empty carrier has topology[[]]." }, "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": "ORIGINAL carrier order=[a11, b11, c11];source canonical open family=[[a11, b11, c11], [a11, b11], [a11, c11], [a11], [c11], []];actual open index=5,U=[]", "after": "ALL [other_index,union,intersection] rows=[[0, [a11, b11, c11], []], [1, [a11, b11], []], [2, [a11, c11], []], [3, [a11], []], [4, [c11], []], [5, [], []]];empty/full present;family qualification passed with exact source English collation", "relation": "implies", "rule_id": "hausdorff_complete_labeled_topology_and_source_order", "conditions": [], "explanation": { "zh-Hant": "點標籤與原carrier次序保留；各open內依來源字串排序，family依固定English collation，不按大小或另一個常見慣例。逐全部open pair核公理，空carrier也有拓撲[[]]。", "en": "Retain labels and original carrier order.Sort elements and the family by the exact declared source conventions,not size or an alternate familiar convention.Check all open pairs;the empty carrier has topology[[]]." }, "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": "S008", "uses": [ "G001", "S007" ], "before": "Hausdorff ORIGINAL sampled pair index0:ORIGINAL distinct carrier points x=c11,y=a11;source open order=[[a11, b11, c11], [a11, b11], [a11, c11], [a11], [c11], []]", "after": "ALL tested [U_index,V_index,intersection,disjoint] rows=[[0, 0, [a11, b11, c11], 否], [0, 1, [a11, b11], 否], [0, 2, [a11, c11], 否], [0, 3, [a11], 否], [2, 0, [a11, c11], 否], [2, 1, [a11], 否], [2, 2, [a11, c11], 否], [2, 3, [a11], 否], [4, 0, [c11], 否], [4, 1, [], 是]];FIRST source-order witness=[[c11], [a11, b11]]", "relation": "implies", "rule_id": "hausdorff_FIRST_actual_open_pair_or_EXHAUSTIVE_failure", "conditions": [], "explanation": { "zh-Hant": "只考慮U含x、V含y的真正open；按原U再V順序找第一個不交pair。null表示這個完整有限open-pair域沒有見證，不是抽樣沒看到。", "en": "Use actual opens U containing x and V containing y.Search original U then V order for the first disjoint pair.Null means no witness in this complete finite domain,not a failed sample." }, "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": "S009", "uses": [ "G001", "S008" ], "before": "Hausdorff ORIGINAL sampled positions count := sum(1)", "after": "Hausdorff ORIGINAL sampled positions count = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原題角色、原索引與已證中間量精確代值，不改為浮點近似或其他題目的資料。", "en": "Substitute original roles,indices and established intermediates exactly,not floating-point approximations or another question's data." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Hausdorff ORIGINAL sampled positions count，不以小數近似替代。", "en": "Recompute Hausdorff ORIGINAL sampled positions count with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1" ], "output": "1", "label": "Hausdorff ORIGINAL sampled positions count" } }, { "id": "S010", "uses": [ "G001", "S009" ], "before": "Hausdorff ALL unordered carrier pairs count := sum(1, 1, 1)", "after": "Hausdorff ALL unordered carrier pairs count = 3", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原題角色、原索引與已證中間量精確代值，不改為浮點近似或其他題目的資料。", "en": "Substitute original roles,indices and established intermediates exactly,not floating-point approximations or another question's data." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Hausdorff ALL unordered carrier pairs count，不以小數近似替代。", "en": "Recompute Hausdorff ALL unordered carrier pairs count with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1", "1", "1" ], "output": "3", "label": "Hausdorff ALL unordered carrier pairs count" } }, { "id": "S011", "uses": [ "G001", "S010" ], "before": "ORIGINAL sampled pair rows=[[c11, a11, [[c11], [a11, b11]]]];sample positions count=1;ALL finite pairs=[[a11, b11], [a11, c11], [b11, c11]];total pair count=3", "after": "all_sampled_separated=是;general_sample_certificate fixed No;duplicates/full finite sample allowed;any actual completeness must be established separately", "relation": "implies", "rule_id": "hausdorff_sample_No_not_separation_flag_or_actual_completeness_negation", "conditions": [], "explanation": { "zh-Hant": "sample可空、重複或真的覆蓋全部有限pair；位置數不等於不同pair數。固定No不否定各pair的真分離，也不否認另核完整性後的有限結論，更不從有限抽樣推無窮空間。", "en": "Samples may be empty,repeat pairs or actually cover every finite pair.Position count is not distinct-pair count.The fixed No negates neither true separation results nor a finite conclusion with separately established completeness;finite sampling does not certify an infinite space." }, "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": [ [ [ "c11", "a11", [ [ "c11" ], [ "a11", "b11" ] ] ] ], true, 1, 3, false, "successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces" ] }, "conclusion": { "canonical_value": "([[c11, a11, [[c11], [a11, b11]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)", "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-20261014-advance-20261111-r03-hausdorff-space-foundations", "batch_path": "public/data/questions/batches/batch-20261014-advance-20261111-r03-hausdorff-space-foundations/questions.jsonl", "batch_sha256": "4607ed9d34b4ce6db11c1fe51c7536490da61ae28eb2749cc4916e02df1ec067", "original_line": 87, "original_line_sha256": "aced8ce0ac9ee942f528b66ae126ca0efaa2d10f69ce3c0381b1950a4e54226f", "question_compact_sha256": "0b78a3bb2282e2f4cd6b364a97c690c770c08daaaf6dc3cd8df4045246ac9e74", "english_row_compact_sha256": "e927452c8db09e2e0971a924b3c0862b1107e48d405886222737b2bc921ff8d5", "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261111-r03-hausdorff-space-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261111-r03-hausdorff-space-foundations.en.jsonl" }, "mko_bindings": { "mko-hausdorff-space": { "sha256": "084615a021bcdce41165bfa9dd88865f68a94405aa7108b97c7353e8f40ac5b3", "english_sha256": "a145da737e1f922a302fc3731116b71d26eb726e2ce1196d7c1ae73b4f07b46d", "original_path": "public/data/mko/hausdorff-space.json", "english_path": "public/data/i18n/editions/mko-hausdorff-space.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "4db6f09f48d29a15f89787c4aac3ae0abe7981d9f906e3fbecc88b60dd686db5", "original_candidate_sha256": "c0b9b0f1dda500eef31c7895b884426341b251f495d99d00256586eeda516b40", "original_candidate_line_sha256": "c0b9b0f1dda500eef31c7895b884426341b251f495d99d00256586eeda516b40" }, "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-20261026-009-p45", "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": "89b8e810eced1a69dbfef28d4b112e829edf156c7905a86e39a3f4958cd75e81", "question_first_witness_sha256": "b2e8b769c463242f05172564ae96e310403eae151e1ec30bcb50be3ffe12cfc7" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 11, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "8f474480a50f545ab3a70e59a09b00511d80c0518b2f67000c1cf908b5d4e0f9", "arithmetic_steps": 2 }, "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." } }