{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0001","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,1,0,1,1]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0, 1, 1], [[3, 1, 1]], 否)","explanation_zh":"Wave4根節點核對=([0, 1, 0, 1, 1], [[3, 1, 1]], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277001,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,1,0,1,1],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,1,0,1,1]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0002","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,1,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([2, 1, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277002,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0003","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,1,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([3, 1, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277003,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0004","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,1,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([4, 1, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([4, 1, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277004,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0005","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,1,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([5, 1, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([5, 1, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277005,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0006","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,2,0,1,1]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 0, 1, 1], [[3, 1, 1]], 否)","explanation_zh":"Wave4根節點核對=([0, 2, 0, 1, 1], [[3, 1, 1]], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277006,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,2,0,1,1],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,2,0,1,1]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0007","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,2,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([1, 2, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277007,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0008","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,2,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([3, 2, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277008,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0009","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,2,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([4, 2, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([4, 2, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277009,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0010","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,2,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([5, 2, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([5, 2, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277010,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0011","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,3,0,1,1]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 0, 1, 1], [[3, 1, 1]], 否)","explanation_zh":"Wave4根節點核對=([0, 3, 0, 1, 1], [[3, 1, 1]], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277011,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,3,0,1,1],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,3,0,1,1]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0012","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,3,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([1, 3, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277012,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0013","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,3,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([2, 3, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277013,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0014","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,3,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([4, 3, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([4, 3, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277014,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0015","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,3,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([5, 3, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([5, 3, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277015,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0016","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,4,0,1,1]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([0, 4, 0, 1, 1], [[3, 1, 1]], 否)","explanation_zh":"Wave4根節點核對=([0, 4, 0, 1, 1], [[3, 1, 1]], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277016,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,4,0,1,1],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,4,0,1,1]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0017","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,4,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([1, 4, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([1, 4, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277017,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0018","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,4,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([2, 4, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([2, 4, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277018,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0019","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,4,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([3, 4, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([3, 4, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277019,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0020","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,4,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([5, 4, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([5, 4, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277020,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0021","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,5,0,1,1]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([0, 5, 0, 1, 1], [[3, 1, 1]], 否)","explanation_zh":"Wave4根節點核對=([0, 5, 0, 1, 1], [[3, 1, 1]], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277021,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,5,0,1,1],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,5,0,1,1]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0022","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,5,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([1, 5, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([1, 5, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277022,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0023","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,5,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([2, 5, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([2, 5, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277023,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0024","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,5,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([3, 5, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([3, 5, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277024,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0025","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,5,0,1,0]}。請依 [vertices,bad_steps,walk] 欄序回答。","answer":{"kind":"expression","value":"([4, 5, 0, 1, 0], [], 是)","explanation_zh":"Wave4根節點核對=([4, 5, 0, 1, 0], [], 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-qualification","seed":202610277025,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-qualification","semantic_template":"qf-mod27-walk-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0026","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,1,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 否)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277026,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0027","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,1,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 否)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277027,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0028","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,1,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 否)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277028,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0029","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,1,0,1,4]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [1, 4], 否)","explanation_zh":"Wave4根節點核對=(是, [1, 4], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277029,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,1,0,1,4],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,1,0,1,4]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0030","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,1,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 否)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277030,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0031","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,2,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0], 否)","explanation_zh":"Wave4根節點核對=(是, [0], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277031,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0032","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,2,0,1,1]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(否, [1], 否)","explanation_zh":"Wave4根節點核對=(否, [1], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277032,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,2,0,1,1],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,2,0,1,1]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0033","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,2,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0], 否)","explanation_zh":"Wave4根節點核對=(是, [0], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277033,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0034","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,2,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0], 否)","explanation_zh":"Wave4根節點核對=(是, [0], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277034,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0035","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,2,0,1,5]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [5], 否)","explanation_zh":"Wave4根節點核對=(是, [5], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277035,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,2,0,1,5],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,2,0,1,5]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0036","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,3,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0], 否)","explanation_zh":"Wave4根節點核對=(是, [0], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277036,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0037","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,3,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 否)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277037,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0038","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,3,0,1,2]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [2], 否)","explanation_zh":"Wave4根節點核對=(是, [2], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277038,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,3,0,1,2],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,3,0,1,2]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0039","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,3,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0], 否)","explanation_zh":"Wave4根節點核對=(是, [0], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277039,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0040","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,3,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0], 否)","explanation_zh":"Wave4根節點核對=(是, [0], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277040,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0041","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,4,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0], 否)","explanation_zh":"Wave4根節點核對=(是, [0], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277041,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0042","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,4,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 否)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277042,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0043","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,4,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0], 否)","explanation_zh":"Wave4根節點核對=(是, [0], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277043,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0044","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,4,0,1,3]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [3], 否)","explanation_zh":"Wave4根節點核對=(是, [3], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277044,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,4,0,1,3],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,4,0,1,3]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0045","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,4,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0], 否)","explanation_zh":"Wave4根節點核對=(是, [0], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277045,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0046","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,5,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0], 否)","explanation_zh":"Wave4根節點核對=(是, [0], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277046,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0047","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,5,0,1,1]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(否, [1], 否)","explanation_zh":"Wave4根節點核對=(否, [1], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277047,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,5,0,1,1],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,5,0,1,1]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0048","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,5,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0], 否)","explanation_zh":"Wave4根節點核對=(是, [0], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277048,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0049","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,5,0,1,0]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [0], 否)","explanation_zh":"Wave4根節點核對=(是, [0], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277049,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0050","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-simple-path-qualification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,5,0,1,4]}。請依 [walk,repeated_vertices,simple_path] 欄序回答。","answer":{"kind":"expression","value":"(是, [4], 否)","explanation_zh":"Wave4根節點核對=(是, [4], 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-simple-path-qualification","seed":202610277050,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,5,0,1,4],"domain":"Complete_finite_undirected_walk","operation":"walk-simple-path-qualification","semantic_template":"qf-mod27-walk-simple-path-qualification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,5,0,1,4]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0051","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,1,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 0, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 0, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277051,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0052","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,1,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 2, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 2, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277052,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0053","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,1,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 3, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 3, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277053,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0054","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,1,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 4, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 4, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277054,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0055","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,1,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 5, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 5, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277055,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0056","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,2,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 0, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 0, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277056,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0057","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,2,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 1, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 1, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277057,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0058","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,2,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 3, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 3, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277058,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0059","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,2,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 4, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 4, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277059,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0060","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,2,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 5, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 5, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277060,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0061","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,3,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 0, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 0, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277061,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0062","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,3,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 1, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 1, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277062,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0063","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,3,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 2, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 2, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277063,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0064","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,3,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 4, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 4, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277064,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0065","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,3,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 5, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 5, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277065,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0066","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,4,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 0, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 0, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277066,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0067","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,4,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 1, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 1, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277067,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0068","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,4,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 2, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 2, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277068,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0069","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,4,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 3, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 3, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277069,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0070","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,4,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 5, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 5, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277070,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0071","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,5,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 0, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 0, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277071,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0072","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,5,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 1, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 1, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277072,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0073","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,5,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 2, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 2, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277073,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0074","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,5,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 3, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 3, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277074,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0075","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-length-endpoints；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,5,0,1,0]}。請依 [walk,edge_length,start,end,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, 4, 0, edge_length_equals_vertex_count_minus_one)","explanation_zh":"Wave4根節點核對=(是, 4, 4, 0, edge_length_equals_vertex_count_minus_one)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-length-endpoints","seed":202610277075,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-length-endpoints","semantic_template":"qf-mod27-walk-length-endpoints/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0076","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,1,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0, 1], [[0, 1]], 否, 否, 是)","explanation_zh":"Wave4根節點核對=(是, 4, [0, 1], [[0, 1]], 否, 否, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277076,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0077","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,1,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0, 1], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0, 1], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277077,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0078","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,1,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0, 1], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0, 1], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277078,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0079","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,1,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0, 1], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0, 1], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277079,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0080","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,1,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0, 1], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0, 1], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277080,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,1,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,1,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0081","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,2,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 2], [0, 1]], 否, 否, 是)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 2], [0, 1]], 否, 否, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277081,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0082","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,2,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0, 1], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0, 1], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277082,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0083","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,2,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277083,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0084","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,2,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277084,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0085","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,2,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277085,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,2,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,2,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0086","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,3,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 3], [0, 1]], 否, 否, 是)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 3], [0, 1]], 否, 否, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277086,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0087","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,3,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0, 1], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0, 1], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277087,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0088","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,3,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277088,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0089","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,3,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277089,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0090","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,3,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277090,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,3,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,3,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0091","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,4,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 4], [0, 1]], 否, 否, 是)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 4], [0, 1]], 否, 否, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277091,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0092","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,4,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0, 1], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0, 1], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277092,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0093","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,4,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277093,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0094","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,4,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277094,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0095","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[5,4,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277095,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[5,4,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[5,4,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0096","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[0,5,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 5], [0, 1]], 否, 否, 是)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 5], [0, 1]], 否, 否, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277096,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[0,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[0,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0097","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[1,5,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0, 1], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0, 1], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277097,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[1,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[1,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0098","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[2,5,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277098,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[2,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[2,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0099","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[3,5,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277099,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[3,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[3,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r07-graph-walk-simple-path-0100","batch_id":"batch-20261014-advance-20261027-r07-graph-walk-simple-path-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-walk-simple-path"],"title_zh":"圖walk與simple path","stem_zh":"有限無向無loop簡單圖與完整頂點序列。操作=walk-repetition-classification；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"vertices\":[4,5,0,1,0]}。請依 [walk,edge_length,repeated_vertices,repeated_edges,trail,simple_path,closed] 欄序回答。","answer":{"kind":"expression","value":"(是, 4, [0], [[0, 1]], 否, 否, 否)","explanation_zh":"Wave4根節點核對=(是, 4, [0], [[0, 1]], 否, 否, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；每對連續頂點都須相鄰且長度是邊數；walk可重複但simple path不得重複頂點。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖walk與simple path"]},"variant":{"family_id":"qf-mod27-walk-repetition-classification","seed":202610277100,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],"vertices":[4,5,0,1,0],"domain":"Complete_finite_undirected_walk","operation":"walk-repetition-classification","semantic_template":"qf-mod27-walk-repetition-classification/{\"edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],\"n\":6,\"vertices\":[4,5,0,1,0]}"}},"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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}