{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0001","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 1, 3, 6], [1, 0, 2, 5], [3, 2, 0, 3], [6, 5, 3, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 1, 3, 6], [1, 0, 2, 5], [3, 2, 0, 3], [6, 5, 3, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226001,"parameters":{"n":4,"distances":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0002","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 2, 5, 9], [2, 0, 3, 7], [5, 3, 0, 4], [9, 7, 4, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 2, 5, 9], [2, 0, 3, 7], [5, 3, 0, 4], [9, 7, 4, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226002,"parameters":{"n":4,"distances":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0003","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 3, 7, 12], [3, 0, 4, 9], [7, 4, 0, 5], [12, 9, 5, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 3, 7, 12], [3, 0, 4, 9], [7, 4, 0, 5], [12, 9, 5, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226003,"parameters":{"n":4,"distances":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0004","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 4, 9, 15], [4, 0, 5, 11], [9, 5, 0, 6], [15, 11, 6, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 4, 9, 15], [4, 0, 5, 11], [9, 5, 0, 6], [15, 11, 6, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226004,"parameters":{"n":4,"distances":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0005","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 5, 11, 18], [5, 0, 6, 13], [11, 6, 0, 7], [18, 13, 7, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 5, 11, 18], [5, 0, 6, 13], [11, 6, 0, 7], [18, 13, 7, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226005,"parameters":{"n":4,"distances":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0006","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 6, 13, 21], [6, 0, 7, 15], [13, 7, 0, 8], [21, 15, 8, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 6, 13, 21], [6, 0, 7, 15], [13, 7, 0, 8], [21, 15, 8, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226006,"parameters":{"n":4,"distances":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0007","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 7, 15, 24], [7, 0, 8, 17], [15, 8, 0, 9], [24, 17, 9, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 7, 15, 24], [7, 0, 8, 17], [15, 8, 0, 9], [24, 17, 9, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226007,"parameters":{"n":4,"distances":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0008","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 8, 17, 27], [8, 0, 9, 19], [17, 9, 0, 10], [27, 19, 10, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 8, 17, 27], [8, 0, 9, 19], [17, 9, 0, 10], [27, 19, 10, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226008,"parameters":{"n":4,"distances":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0009","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 9, 19, 30], [9, 0, 10, 21], [19, 10, 0, 11], [30, 21, 11, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 9, 19, 30], [9, 0, 10, 21], [19, 10, 0, 11], [30, 21, 11, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226009,"parameters":{"n":4,"distances":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0010","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 10, 21, 33], [10, 0, 11, 23], [21, 11, 0, 12], [33, 23, 12, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 10, 21, 33], [10, 0, 11, 23], [21, 11, 0, 12], [33, 23, 12, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226010,"parameters":{"n":4,"distances":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0011","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 11, 23, 36], [11, 0, 12, 25], [23, 12, 0, 13], [36, 25, 13, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 11, 23, 36], [11, 0, 12, 25], [23, 12, 0, 13], [36, 25, 13, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226011,"parameters":{"n":4,"distances":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0012","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 12, 25, 39], [12, 0, 13, 27], [25, 13, 0, 14], [39, 27, 14, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 12, 25, 39], [12, 0, 13, 27], [25, 13, 0, 14], [39, 27, 14, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226012,"parameters":{"n":4,"distances":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0013","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 13, 27, 42], [13, 0, 14, 29], [27, 14, 0, 15], [42, 29, 15, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 13, 27, 42], [13, 0, 14, 29], [27, 14, 0, 15], [42, 29, 15, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226013,"parameters":{"n":4,"distances":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0014","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 14, 29, 45], [14, 0, 15, 31], [29, 15, 0, 16], [45, 31, 16, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 14, 29, 45], [14, 0, 15, 31], [29, 15, 0, 16], [45, 31, 16, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226014,"parameters":{"n":4,"distances":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0015","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 15, 31, 48], [15, 0, 16, 33], [31, 16, 0, 17], [48, 33, 17, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 15, 31, 48], [15, 0, 16, 33], [31, 16, 0, 17], [48, 33, 17, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226015,"parameters":{"n":4,"distances":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0016","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 16, 33, 51], [16, 0, 17, 35], [33, 17, 0, 18], [51, 35, 18, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 16, 33, 51], [16, 0, 17, 35], [33, 17, 0, 18], [51, 35, 18, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226016,"parameters":{"n":4,"distances":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0017","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 17, 35, 54], [17, 0, 18, 37], [35, 18, 0, 19], [54, 37, 19, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 17, 35, 54], [17, 0, 18, 37], [35, 18, 0, 19], [54, 37, 19, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226017,"parameters":{"n":4,"distances":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0018","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 18, 37, 57], [18, 0, 19, 39], [37, 19, 0, 20], [57, 39, 20, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 18, 37, 57], [18, 0, 19, 39], [37, 19, 0, 20], [57, 39, 20, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226018,"parameters":{"n":4,"distances":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0019","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 19, 39, 60], [19, 0, 20, 41], [39, 20, 0, 21], [60, 41, 21, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 19, 39, 60], [19, 0, 20, 41], [39, 20, 0, 21], [60, 41, 21, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226019,"parameters":{"n":4,"distances":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0020","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 20, 41, 63], [20, 0, 21, 43], [41, 21, 0, 22], [63, 43, 22, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 20, 41, 63], [20, 0, 21, 43], [41, 21, 0, 22], [63, 43, 22, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226020,"parameters":{"n":4,"distances":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0021","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 21, 43, 66], [21, 0, 22, 45], [43, 22, 0, 23], [66, 45, 23, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 21, 43, 66], [21, 0, 22, 45], [43, 22, 0, 23], [66, 45, 23, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226021,"parameters":{"n":4,"distances":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0022","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 22, 45, 69], [22, 0, 23, 47], [45, 23, 0, 24], [69, 47, 24, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 22, 45, 69], [22, 0, 23, 47], [45, 23, 0, 24], [69, 47, 24, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226022,"parameters":{"n":4,"distances":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0023","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 23, 47, 72], [23, 0, 24, 49], [47, 24, 0, 25], [72, 49, 25, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 23, 47, 72], [23, 0, 24, 49], [47, 24, 0, 25], [72, 49, 25, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226023,"parameters":{"n":4,"distances":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0024","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 24, 49, 75], [24, 0, 25, 51], [49, 25, 0, 26], [75, 51, 26, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 24, 49, 75], [24, 0, 25, 51], [49, 25, 0, 26], [75, 51, 26, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226024,"parameters":{"n":4,"distances":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0025","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-table-qualification；資料={\"n\":4,\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]]}。請依 [n,distances,nonnegative,separation] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 25, 51, 78], [25, 0, 26, 53], [51, 26, 0, 27], [78, 53, 27, 0]], 是, 是)","explanation_zh":"結構基礎核對=(4, [[0, 25, 51, 78], [25, 0, 26, 53], [51, 26, 0, 27], [78, 53, 27, 0]], 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-table-qualification","seed":202610226025,"parameters":{"n":4,"distances":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],"domain":"Complete_finite_metric_table","operation":"metric-table-qualification","semantic_template":"qf-str22-metric-table-qualification/{\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0026","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 1, 3, 6], [1, 0, 2, 5], [3, 2, 0, 3], [6, 5, 3, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 1, 3, 6], [1, 0, 2, 5], [3, 2, 0, 3], [6, 5, 3, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226026,"parameters":{"n":4,"distances":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0027","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 2, 5, 9], [2, 0, 3, 7], [5, 3, 0, 4], [9, 7, 4, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 2, 5, 9], [2, 0, 3, 7], [5, 3, 0, 4], [9, 7, 4, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226027,"parameters":{"n":4,"distances":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0028","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 3, 7, 12], [3, 0, 4, 9], [7, 4, 0, 5], [12, 9, 5, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 3, 7, 12], [3, 0, 4, 9], [7, 4, 0, 5], [12, 9, 5, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226028,"parameters":{"n":4,"distances":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0029","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 4, 9, 15], [4, 0, 5, 11], [9, 5, 0, 6], [15, 11, 6, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 4, 9, 15], [4, 0, 5, 11], [9, 5, 0, 6], [15, 11, 6, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226029,"parameters":{"n":4,"distances":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0030","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 5, 11, 18], [5, 0, 6, 13], [11, 6, 0, 7], [18, 13, 7, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 5, 11, 18], [5, 0, 6, 13], [11, 6, 0, 7], [18, 13, 7, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226030,"parameters":{"n":4,"distances":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0031","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 6, 13, 21], [6, 0, 7, 15], [13, 7, 0, 8], [21, 15, 8, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 6, 13, 21], [6, 0, 7, 15], [13, 7, 0, 8], [21, 15, 8, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226031,"parameters":{"n":4,"distances":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0032","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 7, 15, 24], [7, 0, 8, 17], [15, 8, 0, 9], [24, 17, 9, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 7, 15, 24], [7, 0, 8, 17], [15, 8, 0, 9], [24, 17, 9, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226032,"parameters":{"n":4,"distances":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0033","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 8, 17, 27], [8, 0, 9, 19], [17, 9, 0, 10], [27, 19, 10, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 8, 17, 27], [8, 0, 9, 19], [17, 9, 0, 10], [27, 19, 10, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226033,"parameters":{"n":4,"distances":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0034","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 9, 19, 30], [9, 0, 10, 21], [19, 10, 0, 11], [30, 21, 11, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 9, 19, 30], [9, 0, 10, 21], [19, 10, 0, 11], [30, 21, 11, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226034,"parameters":{"n":4,"distances":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0035","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 10, 21, 33], [10, 0, 11, 23], [21, 11, 0, 12], [33, 23, 12, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 10, 21, 33], [10, 0, 11, 23], [21, 11, 0, 12], [33, 23, 12, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226035,"parameters":{"n":4,"distances":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0036","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 11, 23, 36], [11, 0, 12, 25], [23, 12, 0, 13], [36, 25, 13, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 11, 23, 36], [11, 0, 12, 25], [23, 12, 0, 13], [36, 25, 13, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226036,"parameters":{"n":4,"distances":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0037","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 12, 25, 39], [12, 0, 13, 27], [25, 13, 0, 14], [39, 27, 14, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 12, 25, 39], [12, 0, 13, 27], [25, 13, 0, 14], [39, 27, 14, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226037,"parameters":{"n":4,"distances":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0038","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 13, 27, 42], [13, 0, 14, 29], [27, 14, 0, 15], [42, 29, 15, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 13, 27, 42], [13, 0, 14, 29], [27, 14, 0, 15], [42, 29, 15, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226038,"parameters":{"n":4,"distances":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0039","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 14, 29, 45], [14, 0, 15, 31], [29, 15, 0, 16], [45, 31, 16, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 14, 29, 45], [14, 0, 15, 31], [29, 15, 0, 16], [45, 31, 16, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226039,"parameters":{"n":4,"distances":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0040","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 15, 31, 48], [15, 0, 16, 33], [31, 16, 0, 17], [48, 33, 17, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 15, 31, 48], [15, 0, 16, 33], [31, 16, 0, 17], [48, 33, 17, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226040,"parameters":{"n":4,"distances":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0041","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 16, 33, 51], [16, 0, 17, 35], [33, 17, 0, 18], [51, 35, 18, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 16, 33, 51], [16, 0, 17, 35], [33, 17, 0, 18], [51, 35, 18, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226041,"parameters":{"n":4,"distances":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0042","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 17, 35, 54], [17, 0, 18, 37], [35, 18, 0, 19], [54, 37, 19, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 17, 35, 54], [17, 0, 18, 37], [35, 18, 0, 19], [54, 37, 19, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226042,"parameters":{"n":4,"distances":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0043","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 18, 37, 57], [18, 0, 19, 39], [37, 19, 0, 20], [57, 39, 20, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 18, 37, 57], [18, 0, 19, 39], [37, 19, 0, 20], [57, 39, 20, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226043,"parameters":{"n":4,"distances":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0044","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 19, 39, 60], [19, 0, 20, 41], [39, 20, 0, 21], [60, 41, 21, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 19, 39, 60], [19, 0, 20, 41], [39, 20, 0, 21], [60, 41, 21, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226044,"parameters":{"n":4,"distances":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0045","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 20, 41, 63], [20, 0, 21, 43], [41, 21, 0, 22], [63, 43, 22, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 20, 41, 63], [20, 0, 21, 43], [41, 21, 0, 22], [63, 43, 22, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226045,"parameters":{"n":4,"distances":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0046","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 21, 43, 66], [21, 0, 22, 45], [43, 22, 0, 23], [66, 45, 23, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 21, 43, 66], [21, 0, 22, 45], [43, 22, 0, 23], [66, 45, 23, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226046,"parameters":{"n":4,"distances":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0047","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 22, 45, 69], [22, 0, 23, 47], [45, 23, 0, 24], [69, 47, 24, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 22, 45, 69], [22, 0, 23, 47], [45, 23, 0, 24], [69, 47, 24, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226047,"parameters":{"n":4,"distances":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0048","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 23, 47, 72], [23, 0, 24, 49], [47, 24, 0, 25], [72, 49, 25, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 23, 47, 72], [23, 0, 24, 49], [47, 24, 0, 25], [72, 49, 25, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226048,"parameters":{"n":4,"distances":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0049","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 24, 49, 75], [24, 0, 25, 51], [49, 25, 0, 26], [75, 51, 26, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 24, 49, 75], [24, 0, 25, 51], [49, 25, 0, 26], [75, 51, 26, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226049,"parameters":{"n":4,"distances":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0050","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-symmetry-audit；資料={\"n\":4,\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]]}。請依 [n,distances,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 25, 51, 78], [25, 0, 26, 53], [51, 26, 0, 27], [78, 53, 27, 0]], 是)","explanation_zh":"結構基礎核對=(4, [[0, 25, 51, 78], [25, 0, 26, 53], [51, 26, 0, 27], [78, 53, 27, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-symmetry-audit","seed":202610226050,"parameters":{"n":4,"distances":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],"domain":"Complete_finite_metric_table","operation":"metric-symmetry-audit","semantic_template":"qf-str22-metric-symmetry-audit/{\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0051","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 1, 3, 6], [1, 0, 2, 5], [3, 2, 0, 3], [6, 5, 3, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 1, 3, 6], [1, 0, 2, 5], [3, 2, 0, 3], [6, 5, 3, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226051,"parameters":{"n":4,"distances":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0052","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 2, 5, 9], [2, 0, 3, 7], [5, 3, 0, 4], [9, 7, 4, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 2, 5, 9], [2, 0, 3, 7], [5, 3, 0, 4], [9, 7, 4, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226052,"parameters":{"n":4,"distances":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0053","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 3, 7, 12], [3, 0, 4, 9], [7, 4, 0, 5], [12, 9, 5, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 3, 7, 12], [3, 0, 4, 9], [7, 4, 0, 5], [12, 9, 5, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226053,"parameters":{"n":4,"distances":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0054","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 4, 9, 15], [4, 0, 5, 11], [9, 5, 0, 6], [15, 11, 6, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 4, 9, 15], [4, 0, 5, 11], [9, 5, 0, 6], [15, 11, 6, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226054,"parameters":{"n":4,"distances":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0055","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 5, 11, 18], [5, 0, 6, 13], [11, 6, 0, 7], [18, 13, 7, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 5, 11, 18], [5, 0, 6, 13], [11, 6, 0, 7], [18, 13, 7, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226055,"parameters":{"n":4,"distances":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0056","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 6, 13, 21], [6, 0, 7, 15], [13, 7, 0, 8], [21, 15, 8, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 6, 13, 21], [6, 0, 7, 15], [13, 7, 0, 8], [21, 15, 8, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226056,"parameters":{"n":4,"distances":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0057","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 7, 15, 24], [7, 0, 8, 17], [15, 8, 0, 9], [24, 17, 9, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 7, 15, 24], [7, 0, 8, 17], [15, 8, 0, 9], [24, 17, 9, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226057,"parameters":{"n":4,"distances":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0058","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 8, 17, 27], [8, 0, 9, 19], [17, 9, 0, 10], [27, 19, 10, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 8, 17, 27], [8, 0, 9, 19], [17, 9, 0, 10], [27, 19, 10, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226058,"parameters":{"n":4,"distances":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0059","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 9, 19, 30], [9, 0, 10, 21], [19, 10, 0, 11], [30, 21, 11, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 9, 19, 30], [9, 0, 10, 21], [19, 10, 0, 11], [30, 21, 11, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226059,"parameters":{"n":4,"distances":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0060","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 10, 21, 33], [10, 0, 11, 23], [21, 11, 0, 12], [33, 23, 12, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 10, 21, 33], [10, 0, 11, 23], [21, 11, 0, 12], [33, 23, 12, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226060,"parameters":{"n":4,"distances":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0061","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 11, 23, 36], [11, 0, 12, 25], [23, 12, 0, 13], [36, 25, 13, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 11, 23, 36], [11, 0, 12, 25], [23, 12, 0, 13], [36, 25, 13, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226061,"parameters":{"n":4,"distances":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0062","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 12, 25, 39], [12, 0, 13, 27], [25, 13, 0, 14], [39, 27, 14, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 12, 25, 39], [12, 0, 13, 27], [25, 13, 0, 14], [39, 27, 14, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226062,"parameters":{"n":4,"distances":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0063","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 13, 27, 42], [13, 0, 14, 29], [27, 14, 0, 15], [42, 29, 15, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 13, 27, 42], [13, 0, 14, 29], [27, 14, 0, 15], [42, 29, 15, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226063,"parameters":{"n":4,"distances":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0064","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 14, 29, 45], [14, 0, 15, 31], [29, 15, 0, 16], [45, 31, 16, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 14, 29, 45], [14, 0, 15, 31], [29, 15, 0, 16], [45, 31, 16, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226064,"parameters":{"n":4,"distances":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0065","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 15, 31, 48], [15, 0, 16, 33], [31, 16, 0, 17], [48, 33, 17, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 15, 31, 48], [15, 0, 16, 33], [31, 16, 0, 17], [48, 33, 17, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226065,"parameters":{"n":4,"distances":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0066","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 16, 33, 51], [16, 0, 17, 35], [33, 17, 0, 18], [51, 35, 18, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 16, 33, 51], [16, 0, 17, 35], [33, 17, 0, 18], [51, 35, 18, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226066,"parameters":{"n":4,"distances":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0067","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 17, 35, 54], [17, 0, 18, 37], [35, 18, 0, 19], [54, 37, 19, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 17, 35, 54], [17, 0, 18, 37], [35, 18, 0, 19], [54, 37, 19, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226067,"parameters":{"n":4,"distances":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0068","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 18, 37, 57], [18, 0, 19, 39], [37, 19, 0, 20], [57, 39, 20, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 18, 37, 57], [18, 0, 19, 39], [37, 19, 0, 20], [57, 39, 20, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226068,"parameters":{"n":4,"distances":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0069","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 19, 39, 60], [19, 0, 20, 41], [39, 20, 0, 21], [60, 41, 21, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 19, 39, 60], [19, 0, 20, 41], [39, 20, 0, 21], [60, 41, 21, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226069,"parameters":{"n":4,"distances":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0070","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 20, 41, 63], [20, 0, 21, 43], [41, 21, 0, 22], [63, 43, 22, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 20, 41, 63], [20, 0, 21, 43], [41, 21, 0, 22], [63, 43, 22, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226070,"parameters":{"n":4,"distances":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0071","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 21, 43, 66], [21, 0, 22, 45], [43, 22, 0, 23], [66, 45, 23, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 21, 43, 66], [21, 0, 22, 45], [43, 22, 0, 23], [66, 45, 23, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226071,"parameters":{"n":4,"distances":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0072","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 22, 45, 69], [22, 0, 23, 47], [45, 23, 0, 24], [69, 47, 24, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 22, 45, 69], [22, 0, 23, 47], [45, 23, 0, 24], [69, 47, 24, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226072,"parameters":{"n":4,"distances":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0073","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 23, 47, 72], [23, 0, 24, 49], [47, 24, 0, 25], [72, 49, 25, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 23, 47, 72], [23, 0, 24, 49], [47, 24, 0, 25], [72, 49, 25, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226073,"parameters":{"n":4,"distances":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0074","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 24, 49, 75], [24, 0, 25, 51], [49, 25, 0, 26], [75, 51, 26, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 24, 49, 75], [24, 0, 25, 51], [49, 25, 0, 26], [75, 51, 26, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226074,"parameters":{"n":4,"distances":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0075","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-triangle-audit；資料={\"n\":4,\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]]}。請依 [n,distances,bad_triples,triangle] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 25, 51, 78], [25, 0, 26, 53], [51, 26, 0, 27], [78, 53, 27, 0]], [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 25, 51, 78], [25, 0, 26, 53], [51, 26, 0, 27], [78, 53, 27, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-triangle-audit","seed":202610226075,"parameters":{"n":4,"distances":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],"domain":"Complete_finite_metric_table","operation":"metric-triangle-audit","semantic_template":"qf-str22-metric-triangle-audit/{\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0076","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 1, 3, 6], [1, 0, 2, 5], [3, 2, 0, 3], [6, 5, 3, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 1, 3, 6], [1, 0, 2, 5], [3, 2, 0, 3], [6, 5, 3, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226076,"parameters":{"n":4,"distances":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0077","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 2, 5, 9], [2, 0, 3, 7], [5, 3, 0, 4], [9, 7, 4, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 2, 5, 9], [2, 0, 3, 7], [5, 3, 0, 4], [9, 7, 4, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226077,"parameters":{"n":4,"distances":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0078","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 3, 7, 12], [3, 0, 4, 9], [7, 4, 0, 5], [12, 9, 5, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 3, 7, 12], [3, 0, 4, 9], [7, 4, 0, 5], [12, 9, 5, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226078,"parameters":{"n":4,"distances":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0079","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 4, 9, 15], [4, 0, 5, 11], [9, 5, 0, 6], [15, 11, 6, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 4, 9, 15], [4, 0, 5, 11], [9, 5, 0, 6], [15, 11, 6, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226079,"parameters":{"n":4,"distances":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0080","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 5, 11, 18], [5, 0, 6, 13], [11, 6, 0, 7], [18, 13, 7, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 5, 11, 18], [5, 0, 6, 13], [11, 6, 0, 7], [18, 13, 7, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226080,"parameters":{"n":4,"distances":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0081","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 6, 13, 21], [6, 0, 7, 15], [13, 7, 0, 8], [21, 15, 8, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 6, 13, 21], [6, 0, 7, 15], [13, 7, 0, 8], [21, 15, 8, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226081,"parameters":{"n":4,"distances":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0082","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 7, 15, 24], [7, 0, 8, 17], [15, 8, 0, 9], [24, 17, 9, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 7, 15, 24], [7, 0, 8, 17], [15, 8, 0, 9], [24, 17, 9, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226082,"parameters":{"n":4,"distances":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0083","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 8, 17, 27], [8, 0, 9, 19], [17, 9, 0, 10], [27, 19, 10, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 8, 17, 27], [8, 0, 9, 19], [17, 9, 0, 10], [27, 19, 10, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226083,"parameters":{"n":4,"distances":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0084","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 9, 19, 30], [9, 0, 10, 21], [19, 10, 0, 11], [30, 21, 11, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 9, 19, 30], [9, 0, 10, 21], [19, 10, 0, 11], [30, 21, 11, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226084,"parameters":{"n":4,"distances":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0085","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 10, 21, 33], [10, 0, 11, 23], [21, 11, 0, 12], [33, 23, 12, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 10, 21, 33], [10, 0, 11, 23], [21, 11, 0, 12], [33, 23, 12, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226085,"parameters":{"n":4,"distances":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0086","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 11, 23, 36], [11, 0, 12, 25], [23, 12, 0, 13], [36, 25, 13, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 11, 23, 36], [11, 0, 12, 25], [23, 12, 0, 13], [36, 25, 13, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226086,"parameters":{"n":4,"distances":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0087","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 12, 25, 39], [12, 0, 13, 27], [25, 13, 0, 14], [39, 27, 14, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 12, 25, 39], [12, 0, 13, 27], [25, 13, 0, 14], [39, 27, 14, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226087,"parameters":{"n":4,"distances":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0088","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 13, 27, 42], [13, 0, 14, 29], [27, 14, 0, 15], [42, 29, 15, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 13, 27, 42], [13, 0, 14, 29], [27, 14, 0, 15], [42, 29, 15, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226088,"parameters":{"n":4,"distances":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0089","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 14, 29, 45], [14, 0, 15, 31], [29, 15, 0, 16], [45, 31, 16, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 14, 29, 45], [14, 0, 15, 31], [29, 15, 0, 16], [45, 31, 16, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226089,"parameters":{"n":4,"distances":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0090","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 15, 31, 48], [15, 0, 16, 33], [31, 16, 0, 17], [48, 33, 17, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 15, 31, 48], [15, 0, 16, 33], [31, 16, 0, 17], [48, 33, 17, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226090,"parameters":{"n":4,"distances":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0091","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 16, 33, 51], [16, 0, 17, 35], [33, 17, 0, 18], [51, 35, 18, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 16, 33, 51], [16, 0, 17, 35], [33, 17, 0, 18], [51, 35, 18, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226091,"parameters":{"n":4,"distances":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0092","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 17, 35, 54], [17, 0, 18, 37], [35, 18, 0, 19], [54, 37, 19, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 17, 35, 54], [17, 0, 18, 37], [35, 18, 0, 19], [54, 37, 19, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226092,"parameters":{"n":4,"distances":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0093","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 18, 37, 57], [18, 0, 19, 39], [37, 19, 0, 20], [57, 39, 20, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 18, 37, 57], [18, 0, 19, 39], [37, 19, 0, 20], [57, 39, 20, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226093,"parameters":{"n":4,"distances":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0094","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 19, 39, 60], [19, 0, 20, 41], [39, 20, 0, 21], [60, 41, 21, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 19, 39, 60], [19, 0, 20, 41], [39, 20, 0, 21], [60, 41, 21, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226094,"parameters":{"n":4,"distances":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0095","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 20, 41, 63], [20, 0, 21, 43], [41, 21, 0, 22], [63, 43, 22, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 20, 41, 63], [20, 0, 21, 43], [41, 21, 0, 22], [63, 43, 22, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226095,"parameters":{"n":4,"distances":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0096","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 21, 43, 66], [21, 0, 22, 45], [43, 22, 0, 23], [66, 45, 23, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 21, 43, 66], [21, 0, 22, 45], [43, 22, 0, 23], [66, 45, 23, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226096,"parameters":{"n":4,"distances":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0097","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 22, 45, 69], [22, 0, 23, 47], [45, 23, 0, 24], [69, 47, 24, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 22, 45, 69], [22, 0, 23, 47], [45, 23, 0, 24], [69, 47, 24, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226097,"parameters":{"n":4,"distances":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0098","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 23, 47, 72], [23, 0, 24, 49], [47, 24, 0, 25], [72, 49, 25, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 23, 47, 72], [23, 0, 24, 49], [47, 24, 0, 25], [72, 49, 25, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226098,"parameters":{"n":4,"distances":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0099","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 24, 49, 75], [24, 0, 25, 51], [49, 25, 0, 26], [75, 51, 26, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 24, 49, 75], [24, 0, 25, 51], [49, 25, 0, 26], [75, 51, 26, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226099,"parameters":{"n":4,"distances":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r06-metric-space-0100","batch_id":"batch-20261013-advance-20261022-r06-metric-space-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-space"],"title_zh":"完整有限度量表","stem_zh":"完整有限距離表。操作=metric-full-metric-audit；資料={\"n\":4,\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]]}。請依 [n,distances,nonnegative,separation,symmetric,bad_triples,metric] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 25, 51, 78], [25, 0, 26, 53], [51, 26, 0, 27], [78, 53, 27, 0]], 是, 是, 是, [], 是)","explanation_zh":"結構基礎核對=(4, [[0, 25, 51, 78], [25, 0, 26, 53], [51, 26, 0, 27], [78, 53, 27, 0]], 是, 是, 是, [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；三角不等式逐三元組核對；有限模型不外推任意度量空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限度量表"]},"variant":{"family_id":"qf-str22-metric-full-metric-audit","seed":202610226100,"parameters":{"n":4,"distances":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],"domain":"Complete_finite_metric_table","operation":"metric-full-metric-audit","semantic_template":"qf-str22-metric-full-metric-audit/{\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}