{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r06-spanning-tree-0001","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[1,2],[2,3],[3,4]],\"selected\":[0,1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 1, 2, 3], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046001,"parameters":{"n":5,"edges":[[0,1],[1,2],[2,3],[3,4]],"selected":[0,1,2,3],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0002","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[2,3],[3,4]],\"selected\":[0,2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 3, 4], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 2, 3, 4], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046002,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[3,4]],"selected":[0,2,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0003","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[2,3],[3,4]],\"selected\":[0,2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 3, 4], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 2, 3, 4], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046003,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[3,4]],"selected":[0,2,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0004","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],\"selected\":[0,3,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 4, 5], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 3, 4, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046004,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],"selected":[0,3,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0005","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 4], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 1, 3, 4], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046005,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[3,4]],"selected":[0,1,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0006","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 4, 5], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 2, 4, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046006,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0007","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 4, 5], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 2, 4, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046007,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0008","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,3,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 5, 6], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 3, 5, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046008,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,3,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0009","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,4],[2,3],[3,4]],\"selected\":[0,1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 4], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 1, 3, 4], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046009,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[3,4]],"selected":[0,1,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[1,2],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0010","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 4, 5], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 2, 4, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046010,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0011","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 4, 5], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 2, 4, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046011,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0012","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],\"selected\":[0,3,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 5, 6], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 3, 5, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046012,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,3,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0013","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,1,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 4, 5], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 1, 4, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046013,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,1,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0014","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,2,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 5, 6], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 2, 5, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046014,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0015","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,2,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 5, 6], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 2, 5, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046015,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0016","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,3,6,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 6, 7], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 3, 6, 7], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046016,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,3,6,7],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0017","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 4], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 1, 2, 4], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046017,"parameters":{"n":5,"edges":[[0,1],[1,2],[2,3],[2,4],[3,4]],"selected":[0,1,2,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0018","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,2,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 3, 5], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 2, 3, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046018,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0019","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,2,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 3, 5], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 2, 3, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046019,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0020","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,3,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 4, 6], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 3, 4, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046020,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,3,4,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,3,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0021","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,1,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 5], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 1, 3, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046021,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,1,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,1,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0022","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,2,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 4, 6], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 2, 4, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046022,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0023","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,2,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 4, 6], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 2, 4, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046023,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0024","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,3,5,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 5, 7], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 3, 5, 7], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046024,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,3,5,7],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,3,5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0025","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],\"selected\":[0,1,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 5], 是, 是, 是, 是)","explanation_zh":"Wave5第四層核對=([0, 1, 3, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-audit","seed":202611046025,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],"selected":[0,1,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-audit","semantic_template":"qf-mod35-spantree-audit/{\"edges\":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,1,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0026","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[1,2],[2,3],[3,4]],\"selected\":[0,1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046026,"parameters":{"n":5,"edges":[[0,1],[1,2],[2,3],[3,4]],"selected":[0,1,2,3],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0027","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[2,3],[3,4]],\"selected\":[0,2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046027,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[3,4]],"selected":[0,2,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0028","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[2,3],[3,4]],\"selected\":[0,2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046028,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[3,4]],"selected":[0,2,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0029","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],\"selected\":[0,3,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046029,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],"selected":[0,3,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0030","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046030,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[3,4]],"selected":[0,1,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0031","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046031,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0032","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046032,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0033","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,3,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046033,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,3,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0034","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,4],[2,3],[3,4]],\"selected\":[0,1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046034,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[3,4]],"selected":[0,1,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[1,2],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0035","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046035,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0036","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046036,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0037","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],\"selected\":[0,3,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046037,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,3,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0038","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,1,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046038,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,1,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0039","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,2,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046039,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0040","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,2,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046040,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0041","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,3,6,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046041,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,3,6,7],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0042","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046042,"parameters":{"n":5,"edges":[[0,1],[1,2],[2,3],[2,4],[3,4]],"selected":[0,1,2,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0043","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,2,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046043,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0044","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,2,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046044,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0045","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,3,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046045,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,3,4,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,3,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0046","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,1,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046046,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,1,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,1,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0047","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,2,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046047,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0048","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,2,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046048,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0049","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,3,5,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046049,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,3,5,7],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,3,5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0050","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],\"selected\":[0,1,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)","explanation_zh":"Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-n-minus-one-certificate","seed":202611046050,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],"selected":[0,1,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-n-minus-one-certificate","semantic_template":"qf-mod35-spantree-n-minus-one-certificate/{\"edges\":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,1,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0051","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":1,\"edges\":[],\"selected\":[]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [], 是, 是)","explanation_zh":"Wave5第四層核對=(1, [], 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046051,"parameters":{"n":1,"edges":[],"selected":[],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[],\"n\":1,\"selected\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0052","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[1,2],[2,3],[3,4]],\"selected\":[0,1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 1, 2, 3], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 1, 2, 3], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046052,"parameters":{"n":5,"edges":[[0,1],[1,2],[2,3],[3,4]],"selected":[0,1,2,3],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0053","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[2,3],[3,4]],\"selected\":[0,2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 2, 3, 4], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 2, 3, 4], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046053,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[3,4]],"selected":[0,2,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0054","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[2,3],[3,4]],\"selected\":[0,2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 2, 3, 4], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 2, 3, 4], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046054,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[3,4]],"selected":[0,2,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0055","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],\"selected\":[0,3,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 3, 4, 5], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 3, 4, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046055,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],"selected":[0,3,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0056","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 1, 3, 4], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 1, 3, 4], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046056,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[3,4]],"selected":[0,1,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0057","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 2, 4, 5], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 2, 4, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046057,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0058","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 2, 4, 5], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 2, 4, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046058,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0059","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,3,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 3, 5, 6], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 3, 5, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046059,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,3,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r06-spanning-tree-0064","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,1,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 1, 4, 5], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 1, 4, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046064,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,1,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0065","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,2,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 2, 5, 6], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 2, 5, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046065,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0066","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,2,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 2, 5, 6], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 2, 5, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046066,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0067","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,3,6,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 3, 6, 7], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 3, 6, 7], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046067,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,3,6,7],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0068","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 1, 2, 4], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 1, 2, 4], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046068,"parameters":{"n":5,"edges":[[0,1],[1,2],[2,3],[2,4],[3,4]],"selected":[0,1,2,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0069","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,2,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 2, 3, 5], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 2, 3, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046069,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0070","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,2,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 2, 3, 5], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 2, 3, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046070,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0071","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,3,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 3, 4, 6], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 3, 4, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046071,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,3,4,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,3,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0072","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,1,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 1, 3, 5], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 1, 3, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046072,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,1,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,1,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0073","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,2,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 2, 4, 6], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 2, 4, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046073,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0074","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,2,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 2, 4, 6], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 2, 4, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046074,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0075","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,3,5,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, [0, 3, 5, 7], 是, 否)","explanation_zh":"Wave5第四層核對=(5, [0, 3, 5, 7], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-one-vertex","seed":202611046075,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,3,5,7],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-one-vertex","semantic_template":"qf-mod35-spantree-one-vertex/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,3,5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0076","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[1,2],[2,3],[3,4]],\"selected\":[0,1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046076,"parameters":{"n":5,"edges":[[0,1],[1,2],[2,3],[3,4]],"selected":[0,1,2,3],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0077","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[2,3],[3,4]],\"selected\":[0,2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046077,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[3,4]],"selected":[0,2,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0078","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[2,3],[3,4]],\"selected\":[0,2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046078,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[3,4]],"selected":[0,2,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0079","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],\"selected\":[0,3,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046079,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],"selected":[0,3,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0080","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046080,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[3,4]],"selected":[0,1,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0081","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046081,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0082","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046082,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0083","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],\"selected\":[0,3,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046083,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,3,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0084","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,4],[2,3],[3,4]],\"selected\":[0,1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046084,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[3,4]],"selected":[0,1,3,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[1,2],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0085","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046085,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0086","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],\"selected\":[0,2,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046086,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0087","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],\"selected\":[0,3,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046087,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,3,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0088","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,1,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046088,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,1,4,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,1,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0089","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,2,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046089,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0090","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,2,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046090,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,2,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0091","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"selected\":[0,3,6,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046091,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,3,6,7],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":5,\"selected\":[0,3,6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0092","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046092,"parameters":{"n":5,"edges":[[0,1],[1,2],[2,3],[2,4],[3,4]],"selected":[0,1,2,4],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0093","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,2,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046093,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0094","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,2,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046094,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0095","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],\"selected\":[0,3,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046095,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,3,4,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,3,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0096","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,1,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046096,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,1,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,1,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0097","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,2,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046097,"parameters":{"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0098","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,2,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046098,"parameters":{"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,2,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0099","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"selected\":[0,3,5,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046099,"parameters":{"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,3,5,7],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,3,5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r06-spanning-tree-0100","batch_id":"batch-20261014-advance-20261104-r06-spanning-tree-foundations","language":"zh-Hant","source_mko_ids":["mko-spanning-tree"],"title_zh":"生成樹","stem_zh":"完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={\"n\":5,\"edges\":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],\"selected\":[0,1,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)","explanation_zh":"Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["生成樹"]},"variant":{"family_id":"qf-mod35-spantree-non-mst-boundary","seed":202611046100,"parameters":{"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],"selected":[0,1,3,5],"domain":"Complete_finite_graph_spanning_tree","operation":"spantree-non-mst-boundary","semantic_template":"qf-mod35-spantree-non-mst-boundary/{\"edges\":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],\"n\":5,\"selected\":[0,1,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}