{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261101-r05-graph-matching-0092", "pilot_number": "R0031-16392", "number": 16392, "family_id": "qf-mod32-matching-maximum-distinction", "title": { "zh-Hant": "第 16392 題：圖匹配", "en": "Question 16392: A Supplied Larger Valid Matching Refutes Maximum Cardinality" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261014-advance-20261101-r05-graph-matching-0092", "batch_id": "batch-20261014-advance-20261101-r05-graph-matching-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-graph-matching" ], "title_zh": "圖匹配", "stem_zh": "完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[2,3],[4,5]],\"matching\":[0],\"larger_matching\":[0,1]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。", "answer": { "kind": "expression", "value": "([0], [0, 1], 1, 2, 是, supplied_matching_not_maximum)", "explanation_zh": "Wave5根節點核對=([0], [0, 1], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。" }, "difficulty": { "band": "undergraduate_core", "level": 2, "skills": [ "圖匹配" ] }, "variant": { "family_id": "qf-mod32-matching-maximum-distinction", "seed": 202611015092, "parameters": { "n": 6, "edges": [ [ 0, 1 ], [ 2, 3 ], [ 4, 5 ] ], "matching": [ 0 ], "larger_matching": [ 0, 1 ], "domain": "Complete_finite_simple_graph_matching", "operation": "matching-maximum-distinction", "semantic_template": "qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[2,3],[4,5]],\"larger_matching\":[0,1],\"matching\":[0],\"n\":6}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_finite_or_symbolic_model", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式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-20261101-r05-graph-matching-0092", "batch_id": "batch-20261014-advance-20261101-r05-graph-matching-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "b5526effd513fd54213ef3e4323bffaef71e764a64cfaeff7d9b8244d7fefff9", "family_id": "qf-mod32-matching-maximum-distinction", "seed": 202611015092, "semantic_template": "qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[2,3],[4,5]],\"larger_matching\":[0,1],\"matching\":[0],\"n\":6}" }, "fields": { "title": "A Supplied Larger Valid Matching Refutes Maximum Cardinality", "stem": "Use the complete finite undirected loop-free simple graph on Fin(6)={0,…,5} with canonical edges=[[0, 1], [2, 3], [4, 5]], endpoints increasing and the edge list lexicographically sorted. The source rejects noncanonical or duplicate edges. Select original edge indexes matching=[0], sorted increasingly with duplicates forbidden. A matching has pairwise disjoint endpoints; the empty matching is allowed. Keep matching validity, maximality, maximum cardinality and perfect coverage distinct. Compare larger_matching=[0, 1], also normalized as distinct original edge indexes. Give (matching_indexes,larger_indexes,size,larger_size,witness?,conclusion). The conclusion is supplied_matching_not_maximum or no_maximum_conclusion.", "answer": { "kind": "expression", "value": "([0], [0, 1], 1, 2, Yes, supplied_matching_not_maximum)", "explanation": "Validate both selections before comparing their sizes. A strictly larger valid witness disproves maximum cardinality of the first. No witness from this comparison does not prove that the first matching is maximum or perfect. The exact result, retaining the requested order, is ([0], [0, 1], 1, 2, Yes, supplied_matching_not_maximum)." }, "skills": [ "A Supplied Larger Valid Matching Refutes Maximum Cardinality" ], "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": "完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[2,3],[4,5]],\"matching\":[0],\"larger_matching\":[0,1]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。", "en": "Use the complete finite undirected loop-free simple graph on Fin(6)={0,…,5} with canonical edges=[[0, 1], [2, 3], [4, 5]], endpoints increasing and the edge list lexicographically sorted. The source rejects noncanonical or duplicate edges. Select original edge indexes matching=[0], sorted increasingly with duplicates forbidden. A matching has pairwise disjoint endpoints; the empty matching is allowed. Keep matching validity, maximality, maximum cardinality and perfect coverage distinct. Compare larger_matching=[0, 1], also normalized as distinct original edge indexes. Give (matching_indexes,larger_indexes,size,larger_size,witness?,conclusion). The conclusion is supplied_matching_not_maximum or no_maximum_conclusion." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "complete original carrier Fin(6);original edge list=[[0, 1], [2, 3], [4, 5]]", "after": "input ALREADY has increasing endpoints and lexicographic edge order;loop-free unique edges=是;whole carrier=[0, 1, 2, 3, 4, 5]", "relation": "implies", "rule_id": "matching_original_canonical_graph_not_silent_normalization", "conditions": [], "explanation": { "zh-Hant": "這一題族要求原表已正規排序，未排序或反向重複應拒絕，不能套前輪會自動正規化的guard。邊索引綁定此原圖，完整載體保留孤立點。", "en": "This family requires an already canonical input,not silent normalization of unsorted or reversed duplicate edges.Do not reuse the previous round's normalization guard.Edge indices bind to this original graph,and the complete carrier retains isolates." }, "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": "matching:raw original-edge indices=[0];original canonical edges=[[0, 1], [2, 3], [4, 5]]", "after": "sorted duplicate-free selected indices=[0];selected edges=[[0, 1]]", "relation": "implies", "rule_id": "matching_selected_original_edge_indexes_not_new_edges", "conditions": [], "explanation": { "zh-Hant": "排序選取索引但拒重複，只選原邊；空matching合法。不從端點重建新邊或把原索引當頂點標籤。", "en": "Sort the selected indices but reject duplicates and select only original edges.The empty matching is allowed.Do not invent edges from endpoint sets or confuse edge indices with vertex labels." }, "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": "matching edge0 endpoint0 incidence := sum(0, 1)", "after": "matching edge0 endpoint0 incidence = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始欄位角色與已核中間量精確計算，保留分母、正負號、索引及完整載體。", "en": "Compute exactly from original field roles and established intermediates,retaining denominators,signs,indices and the complete carrier." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 matching edge0 endpoint0 incidence，不以小數近似替代。", "en": "Recompute matching edge0 endpoint0 incidence with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "0", "1" ], "output": "1", "label": "matching edge0 endpoint0 incidence" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "matching edge0 endpoint1 incidence := sum(0, 1)", "after": "matching edge0 endpoint1 incidence = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始欄位角色與已核中間量精確計算，保留分母、正負號、索引及完整載體。", "en": "Compute exactly from original field roles and established intermediates,retaining denominators,signs,indices and the complete carrier." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 matching edge0 endpoint1 incidence，不以小數近似替代。", "en": "Recompute matching edge0 endpoint1 incidence with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "0", "1" ], "output": "1", "label": "matching edge0 endpoint1 incidence" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "matching:selected original edge index=0;edge=[0, 1]", "after": "cumulative endpoint counts in first-seen order=[[0, 1], [1, 1]]", "relation": "implies", "rule_id": "matching_every_selected_edge_endpoint_incidence", "conditions": [], "explanation": { "zh-Hant": "每個被選邊的兩端各加一次，計數大於1才是端點衝突；保留首次遇到端點的順序，不能為了好看另排序衝突輸出。", "en": "Increment both endpoints of each selected edge.A count above1 is an endpoint conflict.Keep first-seen endpoint order instead of inventing a numerical sort for the conflict output." }, "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": "matching:final first-seen endpoint counts=[[0, 1], [1, 1]]", "after": "conflicting vertices first-seen=[];matched vertices sorted=[0, 1];matching valid=是", "relation": "implies", "rule_id": "matching_validity_separate_from_coverage_or_optimality", "conditions": [], "explanation": { "zh-Hant": "兩兩端點不交才為matching；即使不合法邊族仍可能覆蓋很多頂點，覆蓋數不替代有效性，更不證maximal、maximum或perfect。", "en": "Pairwise disjoint endpoints define a matching.An invalid selection may still cover many vertices.Coverage does not replace validity or prove maximality,maximum size or perfectness." }, "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": "larger_matching:raw original-edge indices=[0, 1];original canonical edges=[[0, 1], [2, 3], [4, 5]]", "after": "sorted duplicate-free selected indices=[0, 1];selected edges=[[0, 1], [2, 3]]", "relation": "implies", "rule_id": "matching_selected_original_edge_indexes_not_new_edges", "conditions": [], "explanation": { "zh-Hant": "排序選取索引但拒重複，只選原邊；空matching合法。不從端點重建新邊或把原索引當頂點標籤。", "en": "Sort the selected indices but reject duplicates and select only original edges.The empty matching is allowed.Do not invent edges from endpoint sets or confuse edge indices with vertex labels." }, "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": "larger_matching edge0 endpoint0 incidence := sum(0, 1)", "after": "larger_matching edge0 endpoint0 incidence = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始欄位角色與已核中間量精確計算，保留分母、正負號、索引及完整載體。", "en": "Compute exactly from original field roles and established intermediates,retaining denominators,signs,indices and the complete carrier." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 larger_matching edge0 endpoint0 incidence，不以小數近似替代。", "en": "Recompute larger_matching edge0 endpoint0 incidence with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "0", "1" ], "output": "1", "label": "larger_matching edge0 endpoint0 incidence" } }, { "id": "S009", "uses": [ "G001", "S008" ], "before": "larger_matching edge0 endpoint1 incidence := sum(0, 1)", "after": "larger_matching edge0 endpoint1 incidence = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始欄位角色與已核中間量精確計算，保留分母、正負號、索引及完整載體。", "en": "Compute exactly from original field roles and established intermediates,retaining denominators,signs,indices and the complete carrier." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 larger_matching edge0 endpoint1 incidence，不以小數近似替代。", "en": "Recompute larger_matching edge0 endpoint1 incidence with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "0", "1" ], "output": "1", "label": "larger_matching edge0 endpoint1 incidence" } }, { "id": "S010", "uses": [ "G001", "S009" ], "before": "larger_matching:selected original edge index=0;edge=[0, 1]", "after": "cumulative endpoint counts in first-seen order=[[0, 1], [1, 1]]", "relation": "implies", "rule_id": "matching_every_selected_edge_endpoint_incidence", "conditions": [], "explanation": { "zh-Hant": "每個被選邊的兩端各加一次，計數大於1才是端點衝突；保留首次遇到端點的順序，不能為了好看另排序衝突輸出。", "en": "Increment both endpoints of each selected edge.A count above1 is an endpoint conflict.Keep first-seen endpoint order instead of inventing a numerical sort for the conflict output." }, "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": "larger_matching edge1 endpoint2 incidence := sum(0, 1)", "after": "larger_matching edge1 endpoint2 incidence = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始欄位角色與已核中間量精確計算，保留分母、正負號、索引及完整載體。", "en": "Compute exactly from original field roles and established intermediates,retaining denominators,signs,indices and the complete carrier." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 larger_matching edge1 endpoint2 incidence，不以小數近似替代。", "en": "Recompute larger_matching edge1 endpoint2 incidence with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "0", "1" ], "output": "1", "label": "larger_matching edge1 endpoint2 incidence" } }, { "id": "S012", "uses": [ "G001", "S011" ], "before": "larger_matching edge1 endpoint3 incidence := sum(0, 1)", "after": "larger_matching edge1 endpoint3 incidence = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始欄位角色與已核中間量精確計算，保留分母、正負號、索引及完整載體。", "en": "Compute exactly from original field roles and established intermediates,retaining denominators,signs,indices and the complete carrier." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 larger_matching edge1 endpoint3 incidence，不以小數近似替代。", "en": "Recompute larger_matching edge1 endpoint3 incidence with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "0", "1" ], "output": "1", "label": "larger_matching edge1 endpoint3 incidence" } }, { "id": "S013", "uses": [ "G001", "S012" ], "before": "larger_matching:selected original edge index=1;edge=[2, 3]", "after": "cumulative endpoint counts in first-seen order=[[0, 1], [1, 1], [2, 1], [3, 1]]", "relation": "implies", "rule_id": "matching_every_selected_edge_endpoint_incidence", "conditions": [], "explanation": { "zh-Hant": "每個被選邊的兩端各加一次，計數大於1才是端點衝突；保留首次遇到端點的順序，不能為了好看另排序衝突輸出。", "en": "Increment both endpoints of each selected edge.A count above1 is an endpoint conflict.Keep first-seen endpoint order instead of inventing a numerical sort for the conflict output." }, "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": "larger_matching:final first-seen endpoint counts=[[0, 1], [1, 1], [2, 1], [3, 1]]", "after": "conflicting vertices first-seen=[];matched vertices sorted=[0, 1, 2, 3];matching valid=是", "relation": "implies", "rule_id": "matching_validity_separate_from_coverage_or_optimality", "conditions": [], "explanation": { "zh-Hant": "兩兩端點不交才為matching；即使不合法邊族仍可能覆蓋很多頂點，覆蓋數不替代有效性，更不證maximal、maximum或perfect。", "en": "Pairwise disjoint endpoints define a matching.An invalid selection may still cover many vertices.Coverage does not replace validity or prove maximality,maximum size or perfectness." }, "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": "first selection valid=是;comparison selection valid=是;original sizes=[1, 2]", "after": "strictly larger valid witness=是;conclusion=supplied_matching_not_maximum", "relation": "implies", "rule_id": "matching_larger_valid_witness_not_failed_comparison_optimality", "conditions": [], "explanation": { "zh-Hant": "兩份先各自有效，且後者嚴格更多邊，才否證前者最大性；沒有這樣的見證只表示這次比較沒結論，不能改報前者最大或perfect。", "en": "Validate both selections and require strictly more edges in the second to refute maximum size of the first.Without such a witness,this comparison is inconclusive,not a proof that the first is maximum or perfect." }, "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": [ [ 0 ], [ 0, 1 ], 1, 2, true, "supplied_matching_not_maximum" ] }, "conclusion": { "canonical_value": "([0], [0, 1], 1, 2, 是, supplied_matching_not_maximum)", "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-20261101-r05-graph-matching-foundations", "batch_path": "public/data/questions/batches/batch-20261014-advance-20261101-r05-graph-matching-foundations/questions.jsonl", "batch_sha256": "47af5b843502f40de7766913f0ef29756b9fa44ec54934921fd22f2edc194dde", "original_line": 92, "original_line_sha256": "f4d9d9867eb7b0284cdf8e5e2209adad10ce0c09093653937374d0718c910e04", "question_compact_sha256": "b5526effd513fd54213ef3e4323bffaef71e764a64cfaeff7d9b8244d7fefff9", "english_row_compact_sha256": "75290b239a60faa690977896bb8fd2a30de3e5f24e1b31da2165cc6e9b561c3c", "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261101-r05-graph-matching-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261101-r05-graph-matching-foundations.en.jsonl" }, "mko_bindings": { "mko-graph-matching": { "sha256": "a8718b439d32013b3b1b480ad7e54789abe034e6599f18fdc9261be210f5f8ed", "english_sha256": "eadb3898bbba994e1dd449cd4608128cf1c135fc67776de32bd48bcac1df92c7", "original_path": "public/data/mko/graph-matching.json", "english_path": "public/data/i18n/editions/mko-graph-matching.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "633793a5f242dece0a240bd92f77a33c587d12463e0beaedd8f70a14c70cf9e7", "original_candidate_sha256": "e75f0dfa8eab76a93eb9d12a4f6405f56db61700f2634a3e4f9208b058ae5990", "original_candidate_line_sha256": "e75f0dfa8eab76a93eb9d12a4f6405f56db61700f2634a3e4f9208b058ae5990" }, "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-20261026-007-p32", "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": "55bb21783e2125ecf1e67e42f83fd25bec0ccd493f911f4bb937a5e9d6f9369a", "question_first_witness_sha256": "754ddf2a6039c5ef4aae78a538c6e9a1e9a58d4825aee194e869a27b8a4c95bb" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 15, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "9d25f4fe2ecc26ce7c88abefe9547a3c09202b84a8ae188b5fd396b0dac0570b", "arithmetic_steps": 6 }, "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." } }