{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261013-advance-20261026-r06-graph-isomorphism-0096", "pilot_number": "R0023-12471", "number": 12471, "family_id": "qf-mod26-graphiso-invariant-mismatch", "title": { "zh-Hant": "第 12471 題：圖同構", "en": "Question 12471: Invariant Mismatch Can Refute; a Match Does Not Prove" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261013-advance-20261026-r06-graph-isomorphism-0096", "batch_id": "batch-20261013-advance-20261026-r06-graph-isomorphism-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-graph-isomorphism" ], "title_zh": "圖同構", "stem_zh": "完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,3],[0,5]],\"right_n\":6,\"right_edges\":[[0,1],[0,4],[1,5],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。", "answer": { "kind": "expression", "value": "(6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 1, 1, 2, 2], 是, nonisomorphic_certificate)", "explanation_zh": "結構深度核對=(6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 1, 1, 2, 2], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。" }, "difficulty": { "band": "undergraduate_core", "level": 3, "skills": [ "圖同構" ] }, "variant": { "family_id": "qf-mod26-graphiso-invariant-mismatch", "seed": 202610266096, "parameters": { "left_n": 6, "left_edges": [ [ 0, 1 ], [ 0, 3 ], [ 0, 5 ] ], "right_n": 6, "right_edges": [ [ 0, 1 ], [ 0, 4 ], [ 1, 5 ], [ 2, 3 ] ], "domain": "Complete_finite_simple_graph_isomorphism", "operation": "graphiso-invariant-mismatch", "semantic_template": "qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,3],[0,5]],\"left_n\":6,\"right_edges\":[[0,1],[0,4],[1,5],[2,3]],\"right_n\":6}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_finite_model", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-13", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261013-advance-20261026-r06-graph-isomorphism-0096", "batch_id": "batch-20261013-advance-20261026-r06-graph-isomorphism-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "39a74b438ec0a1bf40925d2a1fb3cb8eb8ceb8ac57190a6e20ee1458583e3dc7", "family_id": "qf-mod26-graphiso-invariant-mismatch", "seed": 202610266096, "semantic_template": "qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,3],[0,5]],\"left_n\":6,\"right_edges\":[[0,1],[0,4],[1,5],[2,3]],\"right_n\":6}" }, "fields": { "title": "Invariant Mismatch Can Refute; a Match Does Not Prove", "stem": "Use complete simple undirected source graph with left_n=6, edges=[[0, 1], [0, 3], [0, 5]], and target with right_n=6, edges=[[0, 1], [0, 4], [1, 5], [2, 3]]. Give (left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch?,conclusion). Sort each degree multiset increasingly. The conclusion is nonisomorphic_certificate for a size or degree mismatch, otherwise necessary-conditions-do-not-prove-isomorphism.", "answer": { "kind": "expression", "value": "(6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 1, 1, 2, 2], Yes, nonisomorphic_certificate)", "explanation": "Different vertex counts or degree multisets refute isomorphism. Equal counts and multisets are necessary conditions only; no mapping has been supplied or checked. An exact finite or explicitly certified slice does not automatically establish a general infinite theorem. The exact result, retaining the requested order, is (6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 1, 1, 2, 2], Yes, nonisomorphic_certificate)." }, "skills": [ "Invariant Mismatch Can Refute; a Match Does Not Prove" ], "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": "完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,3],[0,5]],\"right_n\":6,\"right_edges\":[[0,1],[0,4],[1,5],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。", "en": "Use complete simple undirected source graph with left_n=6, edges=[[0, 1], [0, 3], [0, 5]], and target with right_n=6, edges=[[0, 1], [0, 4], [1, 5], [2, 3]]. Give (left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch?,conclusion). Sort each degree multiset increasingly. The conclusion is nonisomorphic_certificate for a size or degree mismatch, otherwise necessary-conditions-do-not-prove-isomorphism." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source graph:carrier Fin(6);raw undirected edges=[[0, 1], [0, 3], [0, 5]]", "after": "canonical simple edges=[[0, 1], [0, 3], [0, 5]];loops and repeated undirected edges absent", "relation": "implies", "rule_id": "complete_simple_graph_canonical_edges", "conditions": [], "explanation": { "zh-Hant": "每條邊端點正規化小者在前再排序；反向重複仍是重複，不自行刪掉非法紀錄；保留所有孤立頂點。", "en": "Normalize each edge with its smaller endpoint first,then sort.Reversed duplicates remain invalid rather than being silently removed.Preserve every isolated vertex." }, "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": "target graph:carrier Fin(6);raw undirected edges=[[0, 1], [0, 4], [1, 5], [2, 3]]", "after": "canonical simple edges=[[0, 1], [0, 4], [1, 5], [2, 3]];loops and repeated undirected edges absent", "relation": "implies", "rule_id": "complete_simple_graph_canonical_edges", "conditions": [], "explanation": { "zh-Hant": "每條邊端點正規化小者在前再排序；反向重複仍是重複，不自行刪掉非法紀錄；保留所有孤立頂點。", "en": "Normalize each edge with its smaller endpoint first,then sort.Reversed duplicates remain invalid rather than being silently removed.Preserve every isolated vertex." }, "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": "source graph:vertex=0;complete canonical edges=[[0, 1], [0, 3], [0, 5]]", "after": "neighbors=[1, 3, 5];degree=3", "relation": "implies", "rule_id": "graph_every_vertex_degree_including_isolates", "conditions": [], "explanation": { "zh-Hant": "無圈無重邊後，鄰居數就是度數；即使頂點沒出現在任何邊仍列度0。", "en": "In a loop-free duplicate-free graph,the neighbor count is the degree.Vertices absent from every edge still have degree0." }, "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": "source graph:vertex=1;complete canonical edges=[[0, 1], [0, 3], [0, 5]]", "after": "neighbors=[0];degree=1", "relation": "implies", "rule_id": "graph_every_vertex_degree_including_isolates", "conditions": [], "explanation": { "zh-Hant": "無圈無重邊後，鄰居數就是度數；即使頂點沒出現在任何邊仍列度0。", "en": "In a loop-free duplicate-free graph,the neighbor count is the degree.Vertices absent from every edge still have degree0." }, "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": "source graph:vertex=2;complete canonical edges=[[0, 1], [0, 3], [0, 5]]", "after": "neighbors=[];degree=0", "relation": "implies", "rule_id": "graph_every_vertex_degree_including_isolates", "conditions": [], "explanation": { "zh-Hant": "無圈無重邊後，鄰居數就是度數；即使頂點沒出現在任何邊仍列度0。", "en": "In a loop-free duplicate-free graph,the neighbor count is the degree.Vertices absent from every edge still have degree0." }, "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": "source graph:vertex=3;complete canonical edges=[[0, 1], [0, 3], [0, 5]]", "after": "neighbors=[0];degree=1", "relation": "implies", "rule_id": "graph_every_vertex_degree_including_isolates", "conditions": [], "explanation": { "zh-Hant": "無圈無重邊後，鄰居數就是度數；即使頂點沒出現在任何邊仍列度0。", "en": "In a loop-free duplicate-free graph,the neighbor count is the degree.Vertices absent from every edge still have degree0." }, "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": "source graph:vertex=4;complete canonical edges=[[0, 1], [0, 3], [0, 5]]", "after": "neighbors=[];degree=0", "relation": "implies", "rule_id": "graph_every_vertex_degree_including_isolates", "conditions": [], "explanation": { "zh-Hant": "無圈無重邊後，鄰居數就是度數；即使頂點沒出現在任何邊仍列度0。", "en": "In a loop-free duplicate-free graph,the neighbor count is the degree.Vertices absent from every edge still have degree0." }, "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": "source graph:vertex=5;complete canonical edges=[[0, 1], [0, 3], [0, 5]]", "after": "neighbors=[0];degree=1", "relation": "implies", "rule_id": "graph_every_vertex_degree_including_isolates", "conditions": [], "explanation": { "zh-Hant": "無圈無重邊後，鄰居數就是度數；即使頂點沒出現在任何邊仍列度0。", "en": "In a loop-free duplicate-free graph,the neighbor count is the degree.Vertices absent from every edge still have degree0." }, "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": "source graph:degrees in vertex order=[3, 1, 0, 1, 0, 1]", "after": "sorted degree multiset=[0, 0, 1, 1, 1, 3]", "relation": "implies", "rule_id": "graph_degree_multiset_keeps_repeated_values", "conditions": [], "explanation": { "zh-Hant": "按數值排序成多重集，重複度數不能去重，頂點標籤次序與不變量次序分清。", "en": "Sort numerically into a multiset.Do not deduplicate repeated degrees;distinguish vertex order from invariant order." }, "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": "S010", "uses": [ "G001", "S009" ], "before": "target graph:vertex=0;complete canonical edges=[[0, 1], [0, 4], [1, 5], [2, 3]]", "after": "neighbors=[1, 4];degree=2", "relation": "implies", "rule_id": "graph_every_vertex_degree_including_isolates", "conditions": [], "explanation": { "zh-Hant": "無圈無重邊後，鄰居數就是度數；即使頂點沒出現在任何邊仍列度0。", "en": "In a loop-free duplicate-free graph,the neighbor count is the degree.Vertices absent from every edge still have degree0." }, "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": "S011", "uses": [ "G001", "S010" ], "before": "target graph:vertex=1;complete canonical edges=[[0, 1], [0, 4], [1, 5], [2, 3]]", "after": "neighbors=[0, 5];degree=2", "relation": "implies", "rule_id": "graph_every_vertex_degree_including_isolates", "conditions": [], "explanation": { "zh-Hant": "無圈無重邊後，鄰居數就是度數；即使頂點沒出現在任何邊仍列度0。", "en": "In a loop-free duplicate-free graph,the neighbor count is the degree.Vertices absent from every edge still have degree0." }, "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": "S012", "uses": [ "G001", "S011" ], "before": "target graph:vertex=2;complete canonical edges=[[0, 1], [0, 4], [1, 5], [2, 3]]", "after": "neighbors=[3];degree=1", "relation": "implies", "rule_id": "graph_every_vertex_degree_including_isolates", "conditions": [], "explanation": { "zh-Hant": "無圈無重邊後，鄰居數就是度數；即使頂點沒出現在任何邊仍列度0。", "en": "In a loop-free duplicate-free graph,the neighbor count is the degree.Vertices absent from every edge still have degree0." }, "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": "S013", "uses": [ "G001", "S012" ], "before": "target graph:vertex=3;complete canonical edges=[[0, 1], [0, 4], [1, 5], [2, 3]]", "after": "neighbors=[2];degree=1", "relation": "implies", "rule_id": "graph_every_vertex_degree_including_isolates", "conditions": [], "explanation": { "zh-Hant": "無圈無重邊後，鄰居數就是度數；即使頂點沒出現在任何邊仍列度0。", "en": "In a loop-free duplicate-free graph,the neighbor count is the degree.Vertices absent from every edge still have degree0." }, "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": "S014", "uses": [ "G001", "S013" ], "before": "target graph:vertex=4;complete canonical edges=[[0, 1], [0, 4], [1, 5], [2, 3]]", "after": "neighbors=[0];degree=1", "relation": "implies", "rule_id": "graph_every_vertex_degree_including_isolates", "conditions": [], "explanation": { "zh-Hant": "無圈無重邊後，鄰居數就是度數；即使頂點沒出現在任何邊仍列度0。", "en": "In a loop-free duplicate-free graph,the neighbor count is the degree.Vertices absent from every edge still have degree0." }, "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": "S015", "uses": [ "G001", "S014" ], "before": "target graph:vertex=5;complete canonical edges=[[0, 1], [0, 4], [1, 5], [2, 3]]", "after": "neighbors=[1];degree=1", "relation": "implies", "rule_id": "graph_every_vertex_degree_including_isolates", "conditions": [], "explanation": { "zh-Hant": "無圈無重邊後，鄰居數就是度數；即使頂點沒出現在任何邊仍列度0。", "en": "In a loop-free duplicate-free graph,the neighbor count is the degree.Vertices absent from every edge still have degree0." }, "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": "S016", "uses": [ "G001", "S015" ], "before": "target graph:degrees in vertex order=[2, 2, 1, 1, 1, 1]", "after": "sorted degree multiset=[1, 1, 1, 1, 2, 2]", "relation": "implies", "rule_id": "graph_degree_multiset_keeps_repeated_values", "conditions": [], "explanation": { "zh-Hant": "按數值排序成多重集，重複度數不能去重，頂點標籤次序與不變量次序分清。", "en": "Sort numerically into a multiset.Do not deduplicate repeated degrees;distinguish vertex order from invariant order." }, "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": "S017", "uses": [ "G001", "S016" ], "before": "source size=6;degree multiset=[0, 0, 1, 1, 1, 3];target size=6;degree multiset=[1, 1, 1, 1, 2, 2]", "after": "invariant mismatch=是;conclusion=nonisomorphic_certificate", "relation": "implies", "rule_id": "graph_necessary_invariants_not_sufficient_match", "conditions": [], "explanation": { "zh-Hant": "同構雙射保頂點數，也把每個頂點鄰居雙射到像點鄰居，因此保度多重集。任一不同即否證；相同只過必要條件，沒有給可用映射，不可宣稱同構。", "en": "An isomorphism preserves vertex count and bijects each vertex's neighbors with its image's neighbors,hence preserves the degree multiset.Any mismatch refutes it.A match passes necessary conditions only and supplies no isomorphism map." }, "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": [ 6, [ 0, 0, 1, 1, 1, 3 ], 6, [ 1, 1, 1, 1, 2, 2 ], true, "nonisomorphic_certificate" ] }, "conclusion": { "canonical_value": "(6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 1, 1, 2, 2], 是, nonisomorphic_certificate)", "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-20261013-advance-20261026-r06-graph-isomorphism-foundations", "batch_path": "public/data/questions/batches/batch-20261013-advance-20261026-r06-graph-isomorphism-foundations/questions.jsonl", "batch_sha256": "894a25ae8120f126dba0bbf73c146628348596e72b997643fe14c5a5779a1fee", "original_line": 96, "original_line_sha256": "a13f572fe588c32170a5172fcedfbc74492e0af07f8162914fb78a773dab8c8f", "question_compact_sha256": "39a74b438ec0a1bf40925d2a1fb3cb8eb8ceb8ac57190a6e20ee1458583e3dc7", "english_row_compact_sha256": "751b9e34608bc8eab97a121f7d9e16edfda240a9869d62457a5fc15594b1e5bc", "english_manifest_path": "public/data/i18n/editions/batch-20261013-advance-20261026-r06-graph-isomorphism-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261013-advance-20261026-r06-graph-isomorphism-foundations.en.jsonl" }, "mko_bindings": { "mko-graph-isomorphism": { "sha256": "36b491efcb2f7e6297c71cc86792ccbd2cc61cace4f61f1b9324257b32a5d09f", "english_sha256": "ec4fb7d7ac3e76e9a33d43225389ae22fde71112b0fa77885b4a4282b89c7c54", "original_path": "public/data/mko/graph-isomorphism.json", "english_path": "public/data/i18n/editions/mko-graph-isomorphism.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "c6ae588be9bc8b3dd8461be32c073abfa25a0f827b4602cf28bf291ce532d507", "original_candidate_sha256": "599ec3fb22199c69990bf8e63d1d34eb15ef5a8a450ffdbc9ecec263d25bd17a", "original_candidate_line_sha256": "599ec3fb22199c69990bf8e63d1d34eb15ef5a8a450ffdbc9ecec263d25bd17a" }, "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-20261026-006-p24", "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": "f783e81f44ff0faa13dbf948657e9187244a59a809ebdf96f22cca24966649ff", "question_first_witness_sha256": "49a50ed0550be55124d6562260c2ccf4fa6d3f316d7ad9d0d32174400e362e18" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 17, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "cd2f9111d2f713920e6577720c64fa6b24f468a4b2810fbeaa1d3c4098f7c581", "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." } }