{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261015-advance-20261114-r07-vertex-cover-0015", "pilot_number": "R0049-25415", "number": 25415, "family_id": "qf-mod45-vcover-complete-edge-audit", "title": { "zh-Hant": "第 25415 題：頂點覆蓋", "en": "Question 25415: Every Undirected Edge Needs at Least One Selected Endpoint" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261015-advance-20261114-r07-vertex-cover-0015", "batch_id": "batch-20261015-advance-20261114-r07-vertex-cover-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-vertex-cover" ], "title_zh": "頂點覆蓋", "stem_zh": "有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；資料={\"vertices\":[\"v0\",\"v1\",\"v2\",\"v3\",\"v4\",\"v5\",\"v6\",\"v7\",\"v8\"],\"edges\":[[\"v0\",\"v1\"],[\"v1\",\"v2\"],[\"v2\",\"v3\"],[\"v3\",\"v4\"],[\"v4\",\"v5\"],[\"v5\",\"v6\"],[\"v6\",\"v7\"],[\"v7\",\"v8\"],[\"v8\",\"v0\"]],\"candidate\":[\"v0\",\"v1\",\"v2\",\"v3\",\"v4\",\"v6\",\"v7\",\"v8\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "answer": { "kind": "expression", "value": "([v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v0, v8], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8]], [v0, v1, v2, v3, v4, v6, v7, v8], [[[v0, v1], 是], [[v0, v8], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)", "explanation_zh": "Wave6第八層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v0, v8], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8]], [v0, v1, v2, v3, v4, v6, v7, v8], [[[v0, v1], 是], [[v0, v8], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。" }, "difficulty": { "band": "undergraduate_core", "level": 2, "skills": [ "頂點覆蓋" ] }, "variant": { "family_id": "qf-mod45-vcover-complete-edge-audit", "seed": 202611147015, "parameters": { "vertices": [ "v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7", "v8" ], "edges": [ [ "v0", "v1" ], [ "v1", "v2" ], [ "v2", "v3" ], [ "v3", "v4" ], [ "v4", "v5" ], [ "v5", "v6" ], [ "v6", "v7" ], [ "v7", "v8" ], [ "v8", "v0" ] ], "candidate": [ "v0", "v1", "v2", "v3", "v4", "v6", "v7", "v8" ], "domain": "Complete_finite_simple_graph_vertex_cover", "operation": "vcover-complete-edge-audit", "semantic_template": "qf-mod45-vcover-complete-edge-audit/{\"candidate\":[\"v0\",\"v1\",\"v2\",\"v3\",\"v4\",\"v6\",\"v7\",\"v8\"],\"edges\":[[\"v0\",\"v1\"],[\"v0\",\"v8\"],[\"v1\",\"v2\"],[\"v2\",\"v3\"],[\"v3\",\"v4\"],[\"v4\",\"v5\"],[\"v5\",\"v6\"],[\"v6\",\"v7\"],[\"v7\",\"v8\"]],\"vertices\":[\"v0\",\"v1\",\"v2\",\"v3\",\"v4\",\"v5\",\"v6\",\"v7\",\"v8\"]}" } }, "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、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-15", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261015-advance-20261114-r07-vertex-cover-0015", "batch_id": "batch-20261015-advance-20261114-r07-vertex-cover-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "fad2e4a674e878662ab5ad57b690266b131cc36bc407ee1b49fde8d8ddffe217", "family_id": "qf-mod45-vcover-complete-edge-audit", "seed": 202611147015, "semantic_template": "qf-mod45-vcover-complete-edge-audit/{\"candidate\":[\"v0\",\"v1\",\"v2\",\"v3\",\"v4\",\"v6\",\"v7\",\"v8\"],\"edges\":[[\"v0\",\"v1\"],[\"v0\",\"v8\"],[\"v1\",\"v2\"],[\"v2\",\"v3\"],[\"v3\",\"v4\"],[\"v4\",\"v5\"],[\"v5\",\"v6\"],[\"v6\",\"v7\"],[\"v7\",\"v8\"]],\"vertices\":[\"v0\",\"v1\",\"v2\",\"v3\",\"v4\",\"v5\",\"v6\",\"v7\",\"v8\"]}" }, "fields": { "title": "Every Undirected Edge Needs at Least One Selected Endpoint", "stem": "Use complete finite unique vertices=[v0, v1, v2, v3, v4, v5, v6, v7, v8], loop-free simple undirected edges=[[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v0]] and unique candidate subset=[v0, v1, v2, v3, v4, v6, v7, v8]. Edges normalize to sorted unordered pairs and are duplicate-free. A cover selects at least one endpoint of every edge; isolated vertices need not be selected. Give (vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, certificate).", "answer": { "kind": "expression", "value": "([v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v0, v8], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8]], [v0, v1, v2, v3, v4, v6, v7, v8], [[[v0, v1], Yes], [[v0, v8], Yes], [[v1, v2], Yes], [[v2, v3], Yes], [[v3, v4], Yes], [[v4, v5], Yes], [[v5, v6], Yes], [[v6, v7], Yes], [[v7, v8], Yes]], Yes, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)", "explanation": "List every [edge,covered] in canonical edge order. A single uncovered edge refutes cover status; report the first such witness or null. A cover is a vertex subset, not an edge cover or a directed orientation condition. The exact result, retaining the requested order, is ([v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v0, v8], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8]], [v0, v1, v2, v3, v4, v6, v7, v8], [[[v0, v1], Yes], [[v0, v8], Yes], [[v1, v2], Yes], [[v2, v3], Yes], [[v3, v4], Yes], [[v4, v5], Yes], [[v5, v6], Yes], [[v6, v7], Yes], [[v7, v8], Yes]], Yes, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)." }, "skills": [ "Every Undirected Edge Needs at Least One Selected Endpoint" ], "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": "有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；資料={\"vertices\":[\"v0\",\"v1\",\"v2\",\"v3\",\"v4\",\"v5\",\"v6\",\"v7\",\"v8\"],\"edges\":[[\"v0\",\"v1\"],[\"v1\",\"v2\"],[\"v2\",\"v3\"],[\"v3\",\"v4\"],[\"v4\",\"v5\"],[\"v5\",\"v6\"],[\"v6\",\"v7\"],[\"v7\",\"v8\"],[\"v8\",\"v0\"]],\"candidate\":[\"v0\",\"v1\",\"v2\",\"v3\",\"v4\",\"v6\",\"v7\",\"v8\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "en": "Use complete finite unique vertices=[v0, v1, v2, v3, v4, v5, v6, v7, v8], loop-free simple undirected edges=[[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v0]] and unique candidate subset=[v0, v1, v2, v3, v4, v6, v7, v8]. Edges normalize to sorted unordered pairs and are duplicate-free. A cover selects at least one endpoint of every edge; isolated vertices need not be selected. Give (vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, certificate)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [vcover-complete-edge-audit]", "after": "derived = [[vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, certificate]]", "relation": "implies", "rule_id": "source_ordered_fields_without_JS", "conditions": [], "explanation": { "zh-Hant": "本頁列完整來源欄序，不需JavaScript；LP三種mode雖同為6欄，角色仍由原mode選，不由答案形狀猜。", "en": "List the full source field order without JavaScript.LP boundary modes all have6 fields but select different roles from the original mode,not answer shape." }, "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": "source roles = [[v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v0]], [v0, v1, v2, v3, v4, v6, v7, v8]]", "after": "derived = [[v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v0, v8], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8]], [v0, v1, v2, v3, v4, v6, v7, v8]]", "relation": "implies", "rule_id": "Vcover_complete_simple_undirected_graph_UTF16_then_English_order", "conditions": [], "explanation": { "zh-Hant": "carrier非空且至多12，edge端點依JS UTF16<排，再按來源English canonical排序；loop或反向重複edge拒絕，不把圖改成有向或edge cover。", "en": "The carrier is nonempty with at most12 vertices.Normalize endpoints by JS UTF16<,then source English canonical edge order.Reject loops/reversed duplicate edges;this is not a directed graph or edge cover." }, "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 roles = [0, [v0, v1], [v0, v1, v2, v3, v4, v6, v7, v8]]", "after": "derived = [[是, 是], 是]", "relation": "implies", "rule_id": "Vcover_EVERY_edge_selected_endpoint_disjunction", "conditions": [], "explanation": { "zh-Hant": "這條edge至少一個endpoint被選才covered，逐完整edge表核對，不用頂點數猜測。", "en": "This edge is covered iff at least one endpoint is selected.Check the entire edge table,not vertex count." }, "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 roles = [1, [v0, v8], [v0, v1, v2, v3, v4, v6, v7, v8]]", "after": "derived = [[是, 是], 是]", "relation": "implies", "rule_id": "Vcover_EVERY_edge_selected_endpoint_disjunction", "conditions": [], "explanation": { "zh-Hant": "這條edge至少一個endpoint被選才covered，逐完整edge表核對，不用頂點數猜測。", "en": "This edge is covered iff at least one endpoint is selected.Check the entire edge table,not vertex count." }, "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 roles = [2, [v1, v2], [v0, v1, v2, v3, v4, v6, v7, v8]]", "after": "derived = [[是, 是], 是]", "relation": "implies", "rule_id": "Vcover_EVERY_edge_selected_endpoint_disjunction", "conditions": [], "explanation": { "zh-Hant": "這條edge至少一個endpoint被選才covered，逐完整edge表核對，不用頂點數猜測。", "en": "This edge is covered iff at least one endpoint is selected.Check the entire edge table,not vertex count." }, "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 roles = [3, [v2, v3], [v0, v1, v2, v3, v4, v6, v7, v8]]", "after": "derived = [[是, 是], 是]", "relation": "implies", "rule_id": "Vcover_EVERY_edge_selected_endpoint_disjunction", "conditions": [], "explanation": { "zh-Hant": "這條edge至少一個endpoint被選才covered，逐完整edge表核對，不用頂點數猜測。", "en": "This edge is covered iff at least one endpoint is selected.Check the entire edge table,not vertex count." }, "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 roles = [4, [v3, v4], [v0, v1, v2, v3, v4, v6, v7, v8]]", "after": "derived = [[是, 是], 是]", "relation": "implies", "rule_id": "Vcover_EVERY_edge_selected_endpoint_disjunction", "conditions": [], "explanation": { "zh-Hant": "這條edge至少一個endpoint被選才covered，逐完整edge表核對，不用頂點數猜測。", "en": "This edge is covered iff at least one endpoint is selected.Check the entire edge table,not vertex count." }, "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 roles = [5, [v4, v5], [v0, v1, v2, v3, v4, v6, v7, v8]]", "after": "derived = [[是, 否], 是]", "relation": "implies", "rule_id": "Vcover_EVERY_edge_selected_endpoint_disjunction", "conditions": [], "explanation": { "zh-Hant": "這條edge至少一個endpoint被選才covered，逐完整edge表核對，不用頂點數猜測。", "en": "This edge is covered iff at least one endpoint is selected.Check the entire edge table,not vertex count." }, "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 roles = [6, [v5, v6], [v0, v1, v2, v3, v4, v6, v7, v8]]", "after": "derived = [[否, 是], 是]", "relation": "implies", "rule_id": "Vcover_EVERY_edge_selected_endpoint_disjunction", "conditions": [], "explanation": { "zh-Hant": "這條edge至少一個endpoint被選才covered，逐完整edge表核對，不用頂點數猜測。", "en": "This edge is covered iff at least one endpoint is selected.Check the entire edge table,not vertex count." }, "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": "source roles = [7, [v6, v7], [v0, v1, v2, v3, v4, v6, v7, v8]]", "after": "derived = [[是, 是], 是]", "relation": "implies", "rule_id": "Vcover_EVERY_edge_selected_endpoint_disjunction", "conditions": [], "explanation": { "zh-Hant": "這條edge至少一個endpoint被選才covered，逐完整edge表核對，不用頂點數猜測。", "en": "This edge is covered iff at least one endpoint is selected.Check the entire edge table,not vertex count." }, "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": "source roles = [8, [v7, v8], [v0, v1, v2, v3, v4, v6, v7, v8]]", "after": "derived = [[是, 是], 是]", "relation": "implies", "rule_id": "Vcover_EVERY_edge_selected_endpoint_disjunction", "conditions": [], "explanation": { "zh-Hant": "這條edge至少一個endpoint被選才covered，逐完整edge表核對，不用頂點數猜測。", "en": "This edge is covered iff at least one endpoint is selected.Check the entire edge table,not vertex count." }, "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": "source roles = [[[[v0, v1], 是], [[v0, v8], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是]]]", "after": "derived = [是, null, []]", "relation": "implies", "rule_id": "Vcover_COMPLETE_edge_conjunction_FIRST_uncovered_or_NULL", "conditions": [], "explanation": { "zh-Hant": "全邊合取，首uncovered edge保來源canonical次序；沒有則null，不用False代null。isolated點沒有責任edge，故可選可不選。", "en": "Conjoin all edges and retain the first uncovered edge in source order,or null,notFalse.Isolated vertices have no incident coverage obligation and are optional." }, "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": [ [ "v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7", "v8" ], [ [ "v0", "v1" ], [ "v0", "v8" ], [ "v1", "v2" ], [ "v2", "v3" ], [ "v3", "v4" ], [ "v4", "v5" ], [ "v5", "v6" ], [ "v6", "v7" ], [ "v7", "v8" ] ], [ "v0", "v1", "v2", "v3", "v4", "v6", "v7", "v8" ], [ [ [ "v0", "v1" ], true ], [ [ "v0", "v8" ], true ], [ [ "v1", "v2" ], true ], [ [ "v2", "v3" ], true ], [ [ "v3", "v4" ], true ], [ [ "v4", "v5" ], true ], [ [ "v5", "v6" ], true ], [ [ "v6", "v7" ], true ], [ [ "v7", "v8" ], true ] ], true, null, "vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint" ] }, "conclusion": { "canonical_value": "([v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v0, v8], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8]], [v0, v1, v2, v3, v4, v6, v7, v8], [[[v0, v1], 是], [[v0, v8], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)", "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-20261015-advance-20261114-r07-vertex-cover-foundations", "batch_path": "public/data/questions/batches/batch-20261015-advance-20261114-r07-vertex-cover-foundations/questions.jsonl", "batch_sha256": "dcc32dcab475f8f47241521ea888105595fed4813f596fb6b49f2adba6221175", "original_line": 15, "original_line_sha256": "08e480da8a54bf3d3507f12f65a12ed87fae2b3f6a852529cc490fb4f41a13ea", "question_compact_sha256": "fad2e4a674e878662ab5ad57b690266b131cc36bc407ee1b49fde8d8ddffe217", "english_row_compact_sha256": "6b499d17901613bb8a703ef3aa62f291b8a7f91079d1438a81891094fef42fd2", "english_manifest_path": "public/data/i18n/editions/batch-20261015-advance-20261114-r07-vertex-cover-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261015-advance-20261114-r07-vertex-cover-foundations.en.jsonl" }, "mko_bindings": { "mko-vertex-cover": { "sha256": "4e6ca5a6921189d4aac44783f8135dd0f613679ec348ac53ddf8b3fd648ff22b", "english_sha256": "9b80569183079a1991326108c486827298f81d22fc1f370d725462ef96550f0a", "original_path": "public/data/mko/vertex-cover.json", "english_path": "public/data/i18n/editions/mko-vertex-cover.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "991c73df066352bfcfb1142a2492e104cd1d20dafe7e9ecea8cff26a4f9d8e50", "original_candidate_sha256": "1129fe932b0ab0c2f5504aa43c875cdb650fac4160e6d342d839e0ace48a4fd2", "original_candidate_line_sha256": "1129fe932b0ab0c2f5504aa43c875cdb650fac4160e6d342d839e0ace48a4fd2" }, "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-20261026-010-p50", "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": "6212b8b0b3b273f3a514e26ebd17d7e81219c56a8f47e40047ee2b6bf01d1ba3", "question_first_witness_sha256": "f32a23d5e1b66c7794c60def58741bcdfacff24f3cdfc9bc48109c8f71543cf3" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 12, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "2af40cbea4092c8054f7eeca8f2a967b231b82213ca4fc7443bfb8053a44cdfb", "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." } }