{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r04-metric-convergence-0001","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],\"center\":0,\"epsilon\":[1,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 0, 1, [0])","explanation_zh":"現代橋梁核對=(4, 0, 1, [0])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234001,"parameters":{"n":4,"distances":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],"center":0,"epsilon":[1,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":0,\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],\"epsilon\":[1,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0002","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],\"center\":1,\"epsilon\":[2,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 1, 2, [1])","explanation_zh":"現代橋梁核對=(4, 1, 2, [1])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234002,"parameters":{"n":4,"distances":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],"center":1,"epsilon":[2,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":1,\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],\"epsilon\":[2,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0003","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],\"center\":2,\"epsilon\":[3,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 2, 3, [2])","explanation_zh":"現代橋梁核對=(4, 2, 3, [2])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234003,"parameters":{"n":4,"distances":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],"center":2,"epsilon":[3,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":2,\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],\"epsilon\":[3,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0004","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],\"center\":3,\"epsilon\":[4,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 4, [3])","explanation_zh":"現代橋梁核對=(4, 3, 4, [3])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234004,"parameters":{"n":4,"distances":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],"center":3,"epsilon":[4,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":3,\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],\"epsilon\":[4,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0005","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],\"center\":0,\"epsilon\":[5,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 0, 5, [0])","explanation_zh":"現代橋梁核對=(4, 0, 5, [0])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234005,"parameters":{"n":4,"distances":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],"center":0,"epsilon":[5,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":0,\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],\"epsilon\":[5,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0006","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],\"center\":1,\"epsilon\":[6,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 1, 6, [1])","explanation_zh":"現代橋梁核對=(4, 1, 6, [1])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234006,"parameters":{"n":4,"distances":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],"center":1,"epsilon":[6,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":1,\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],\"epsilon\":[6,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0007","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],\"center\":2,\"epsilon\":[7,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 2, 7, [2])","explanation_zh":"現代橋梁核對=(4, 2, 7, [2])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234007,"parameters":{"n":4,"distances":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],"center":2,"epsilon":[7,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":2,\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],\"epsilon\":[7,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0008","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],\"center\":3,\"epsilon\":[1,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 1, [3])","explanation_zh":"現代橋梁核對=(4, 3, 1, [3])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234008,"parameters":{"n":4,"distances":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],"center":3,"epsilon":[1,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":3,\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],\"epsilon\":[1,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0009","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],\"center\":0,\"epsilon\":[2,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 0, 2, [0])","explanation_zh":"現代橋梁核對=(4, 0, 2, [0])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234009,"parameters":{"n":4,"distances":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],"center":0,"epsilon":[2,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":0,\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],\"epsilon\":[2,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0010","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],\"center\":1,\"epsilon\":[3,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 1, 3, [1])","explanation_zh":"現代橋梁核對=(4, 1, 3, [1])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234010,"parameters":{"n":4,"distances":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],"center":1,"epsilon":[3,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":1,\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],\"epsilon\":[3,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0011","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],\"center\":2,\"epsilon\":[4,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 2, 4, [2])","explanation_zh":"現代橋梁核對=(4, 2, 4, [2])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234011,"parameters":{"n":4,"distances":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],"center":2,"epsilon":[4,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":2,\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],\"epsilon\":[4,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0012","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],\"center\":3,\"epsilon\":[5,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 5, [3])","explanation_zh":"現代橋梁核對=(4, 3, 5, [3])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234012,"parameters":{"n":4,"distances":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],"center":3,"epsilon":[5,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":3,\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],\"epsilon\":[5,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0013","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],\"center\":0,\"epsilon\":[6,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 0, 6, [0])","explanation_zh":"現代橋梁核對=(4, 0, 6, [0])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234013,"parameters":{"n":4,"distances":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],"center":0,"epsilon":[6,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":0,\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],\"epsilon\":[6,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0014","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],\"center\":1,\"epsilon\":[7,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 1, 7, [1])","explanation_zh":"現代橋梁核對=(4, 1, 7, [1])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234014,"parameters":{"n":4,"distances":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],"center":1,"epsilon":[7,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":1,\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],\"epsilon\":[7,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0015","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],\"center\":2,\"epsilon\":[1,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 2, 1, [2])","explanation_zh":"現代橋梁核對=(4, 2, 1, [2])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234015,"parameters":{"n":4,"distances":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],"center":2,"epsilon":[1,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":2,\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],\"epsilon\":[1,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0016","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],\"center\":3,\"epsilon\":[2,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 2, [3])","explanation_zh":"現代橋梁核對=(4, 3, 2, [3])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234016,"parameters":{"n":4,"distances":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],"center":3,"epsilon":[2,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":3,\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],\"epsilon\":[2,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0017","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],\"center\":0,\"epsilon\":[3,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 0, 3, [0])","explanation_zh":"現代橋梁核對=(4, 0, 3, [0])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234017,"parameters":{"n":4,"distances":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],"center":0,"epsilon":[3,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":0,\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],\"epsilon\":[3,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0018","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],\"center\":1,\"epsilon\":[4,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 1, 4, [1])","explanation_zh":"現代橋梁核對=(4, 1, 4, [1])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234018,"parameters":{"n":4,"distances":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],"center":1,"epsilon":[4,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":1,\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],\"epsilon\":[4,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0019","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],\"center\":2,\"epsilon\":[5,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 2, 5, [2])","explanation_zh":"現代橋梁核對=(4, 2, 5, [2])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234019,"parameters":{"n":4,"distances":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],"center":2,"epsilon":[5,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":2,\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],\"epsilon\":[5,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0020","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],\"center\":3,\"epsilon\":[6,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 6, [3])","explanation_zh":"現代橋梁核對=(4, 3, 6, [3])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234020,"parameters":{"n":4,"distances":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],"center":3,"epsilon":[6,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":3,\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],\"epsilon\":[6,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0021","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],\"center\":0,\"epsilon\":[7,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 0, 7, [0])","explanation_zh":"現代橋梁核對=(4, 0, 7, [0])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234021,"parameters":{"n":4,"distances":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],"center":0,"epsilon":[7,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":0,\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],\"epsilon\":[7,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0022","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],\"center\":1,\"epsilon\":[1,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 1, 1, [1])","explanation_zh":"現代橋梁核對=(4, 1, 1, [1])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234022,"parameters":{"n":4,"distances":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],"center":1,"epsilon":[1,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":1,\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],\"epsilon\":[1,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0023","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],\"center\":2,\"epsilon\":[2,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 2, 2, [2])","explanation_zh":"現代橋梁核對=(4, 2, 2, [2])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234023,"parameters":{"n":4,"distances":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],"center":2,"epsilon":[2,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":2,\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],\"epsilon\":[2,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0024","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],\"center\":3,\"epsilon\":[3,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 3, [3])","explanation_zh":"現代橋梁核對=(4, 3, 3, [3])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234024,"parameters":{"n":4,"distances":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],"center":3,"epsilon":[3,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":3,\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],\"epsilon\":[3,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0025","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ball-inventory；資料={\"n\":4,\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],\"center\":0,\"epsilon\":[4,1]}。請依 [n,center,epsilon,ball] 欄序回答。","answer":{"kind":"expression","value":"(4, 0, 4, [0])","explanation_zh":"現代橋梁核對=(4, 0, 4, [0])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ball-inventory","seed":202610234025,"parameters":{"n":4,"distances":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],"center":0,"epsilon":[4,1],"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ball-inventory","semantic_template":"qf-mod23-metricconv-ball-inventory/{\"center\":0,\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],\"epsilon\":[4,1],\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0026","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[1,1],\"N\":1}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 1, 1, [[0, 3, 5, 前綴], [1, 2, 2, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 1, 1, [[0, 3, 5, 前綴], [1, 2, 2, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234026,"parameters":{"n":4,"distances":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[1,1],"N":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":1,\"candidate\":1,\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],\"epsilon\":[1,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0027","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[2,1],\"N\":2}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 2, 2, [[0, 3, 7, 前綴], [1, 2, 3, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 2, 2, [[0, 3, 7, 前綴], [1, 2, 3, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234027,"parameters":{"n":4,"distances":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[2,1],"N":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":2,\"candidate\":1,\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],\"epsilon\":[2,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0028","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[3,1],\"N\":3}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 3, 3, [[0, 3, 9, 前綴], [1, 2, 4, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 3, 3, [[0, 3, 9, 前綴], [1, 2, 4, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234028,"parameters":{"n":4,"distances":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[3,1],"N":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":3,\"candidate\":1,\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],\"epsilon\":[3,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0029","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[4,1],\"N\":1}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 4, 1, [[0, 3, 11, 前綴], [1, 2, 5, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 4, 1, [[0, 3, 11, 前綴], [1, 2, 5, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234029,"parameters":{"n":4,"distances":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[4,1],"N":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":1,\"candidate\":1,\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],\"epsilon\":[4,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0030","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[5,1],\"N\":2}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 5, 2, [[0, 3, 13, 前綴], [1, 2, 6, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 5, 2, [[0, 3, 13, 前綴], [1, 2, 6, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234030,"parameters":{"n":4,"distances":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[5,1],"N":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":2,\"candidate\":1,\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],\"epsilon\":[5,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0031","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[1,1],\"N\":3}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 1, 3, [[0, 3, 15, 前綴], [1, 2, 7, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 1, 3, [[0, 3, 15, 前綴], [1, 2, 7, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234031,"parameters":{"n":4,"distances":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[1,1],"N":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":3,\"candidate\":1,\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],\"epsilon\":[1,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0032","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[2,1],\"N\":1}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 2, 1, [[0, 3, 17, 前綴], [1, 2, 8, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 2, 1, [[0, 3, 17, 前綴], [1, 2, 8, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234032,"parameters":{"n":4,"distances":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[2,1],"N":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":1,\"candidate\":1,\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],\"epsilon\":[2,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0033","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[3,1],\"N\":2}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 3, 2, [[0, 3, 19, 前綴], [1, 2, 9, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 3, 2, [[0, 3, 19, 前綴], [1, 2, 9, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234033,"parameters":{"n":4,"distances":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[3,1],"N":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":2,\"candidate\":1,\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],\"epsilon\":[3,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0034","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[4,1],\"N\":3}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 4, 3, [[0, 3, 21, 前綴], [1, 2, 10, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 4, 3, [[0, 3, 21, 前綴], [1, 2, 10, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234034,"parameters":{"n":4,"distances":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[4,1],"N":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":3,\"candidate\":1,\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],\"epsilon\":[4,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0035","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[5,1],\"N\":1}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 5, 1, [[0, 3, 23, 前綴], [1, 2, 11, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 5, 1, [[0, 3, 23, 前綴], [1, 2, 11, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234035,"parameters":{"n":4,"distances":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[5,1],"N":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":1,\"candidate\":1,\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],\"epsilon\":[5,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0036","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[1,1],\"N\":2}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 1, 2, [[0, 3, 25, 前綴], [1, 2, 12, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 1, 2, [[0, 3, 25, 前綴], [1, 2, 12, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234036,"parameters":{"n":4,"distances":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[1,1],"N":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":2,\"candidate\":1,\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],\"epsilon\":[1,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0037","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[2,1],\"N\":3}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 2, 3, [[0, 3, 27, 前綴], [1, 2, 13, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 2, 3, [[0, 3, 27, 前綴], [1, 2, 13, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234037,"parameters":{"n":4,"distances":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[2,1],"N":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":3,\"candidate\":1,\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],\"epsilon\":[2,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0038","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[3,1],\"N\":1}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 3, 1, [[0, 3, 29, 前綴], [1, 2, 14, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 3, 1, [[0, 3, 29, 前綴], [1, 2, 14, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234038,"parameters":{"n":4,"distances":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[3,1],"N":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":1,\"candidate\":1,\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],\"epsilon\":[3,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0039","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[4,1],\"N\":2}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 4, 2, [[0, 3, 31, 前綴], [1, 2, 15, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 4, 2, [[0, 3, 31, 前綴], [1, 2, 15, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234039,"parameters":{"n":4,"distances":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[4,1],"N":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":2,\"candidate\":1,\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],\"epsilon\":[4,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0040","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[5,1],\"N\":3}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 5, 3, [[0, 3, 33, 前綴], [1, 2, 16, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 5, 3, [[0, 3, 33, 前綴], [1, 2, 16, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234040,"parameters":{"n":4,"distances":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[5,1],"N":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":3,\"candidate\":1,\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],\"epsilon\":[5,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0041","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[1,1],\"N\":1}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 1, 1, [[0, 3, 35, 前綴], [1, 2, 17, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 1, 1, [[0, 3, 35, 前綴], [1, 2, 17, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234041,"parameters":{"n":4,"distances":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[1,1],"N":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":1,\"candidate\":1,\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],\"epsilon\":[1,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0042","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[2,1],\"N\":2}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 2, 2, [[0, 3, 37, 前綴], [1, 2, 18, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 2, 2, [[0, 3, 37, 前綴], [1, 2, 18, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234042,"parameters":{"n":4,"distances":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[2,1],"N":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":2,\"candidate\":1,\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],\"epsilon\":[2,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0043","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[3,1],\"N\":3}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 3, 3, [[0, 3, 39, 前綴], [1, 2, 19, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 3, 3, [[0, 3, 39, 前綴], [1, 2, 19, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234043,"parameters":{"n":4,"distances":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[3,1],"N":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":3,\"candidate\":1,\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],\"epsilon\":[3,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0044","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[4,1],\"N\":1}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 4, 1, [[0, 3, 41, 前綴], [1, 2, 20, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 4, 1, [[0, 3, 41, 前綴], [1, 2, 20, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234044,"parameters":{"n":4,"distances":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[4,1],"N":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":1,\"candidate\":1,\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],\"epsilon\":[4,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0045","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[5,1],\"N\":2}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 5, 2, [[0, 3, 43, 前綴], [1, 2, 21, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 5, 2, [[0, 3, 43, 前綴], [1, 2, 21, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234045,"parameters":{"n":4,"distances":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[5,1],"N":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":2,\"candidate\":1,\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],\"epsilon\":[5,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0046","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[1,1],\"N\":3}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 1, 3, [[0, 3, 45, 前綴], [1, 2, 22, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 1, 3, [[0, 3, 45, 前綴], [1, 2, 22, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234046,"parameters":{"n":4,"distances":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[1,1],"N":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":3,\"candidate\":1,\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],\"epsilon\":[1,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0047","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[2,1],\"N\":1}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 2, 1, [[0, 3, 47, 前綴], [1, 2, 23, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 2, 1, [[0, 3, 47, 前綴], [1, 2, 23, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234047,"parameters":{"n":4,"distances":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[2,1],"N":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":1,\"candidate\":1,\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],\"epsilon\":[2,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0048","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[3,1],\"N\":2}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 3, 2, [[0, 3, 49, 前綴], [1, 2, 24, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 3, 2, [[0, 3, 49, 前綴], [1, 2, 24, 前綴], [2, 1, 0, 內], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234048,"parameters":{"n":4,"distances":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[3,1],"N":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":2,\"candidate\":1,\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],\"epsilon\":[3,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0049","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[4,1],\"N\":3}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 4, 3, [[0, 3, 51, 前綴], [1, 2, 25, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 4, 3, [[0, 3, 51, 前綴], [1, 2, 25, 前綴], [2, 1, 0, 前綴], [3, 1, 0, 內]], 是, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234049,"parameters":{"n":4,"distances":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[4,1],"N":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":3,\"candidate\":1,\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],\"epsilon\":[4,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0050","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-finite-tail-audit；資料={\"n\":4,\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],\"sequence\":[3,2,1,1],\"candidate\":1,\"epsilon\":[5,1],\"N\":1}。請依 [sequence,candidate,epsilon,N,rows,bounded_tail_pass,general_convergence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 1], 1, 5, 1, [[0, 3, 53, 前綴], [1, 2, 26, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)","explanation_zh":"現代橋梁核對=([3, 2, 1, 1], 1, 5, 1, [[0, 3, 53, 前綴], [1, 2, 26, 外], [2, 1, 0, 內], [3, 1, 0, 內]], 否, 否, 有限尾段不足以證一般收斂)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-finite-tail-audit","seed":202610234050,"parameters":{"n":4,"distances":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],"sequence":[3,2,1,1],"candidate":1,"epsilon":[5,1],"N":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-finite-tail-audit","semantic_template":"qf-mod23-metricconv-finite-tail-audit/{\"N\":1,\"candidate\":1,\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],\"epsilon\":[5,1],\"n\":4,\"sequence\":[3,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0051","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate\":3}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 3, 2, 否, 尾值與候選不同)","explanation_zh":"現代橋梁核對=([0, 1], 2, 3, 2, 否, 尾值與候選不同)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234051,"parameters":{"n":4,"distances":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],"prefix":[0,1],"tail_value":2,"candidate":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":3,\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0052","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],\"prefix\":[1,2],\"tail_value\":3,\"candidate\":3}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], 3, 3, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([1, 2], 3, 3, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234052,"parameters":{"n":4,"distances":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],"prefix":[1,2],"tail_value":3,"candidate":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":3,\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],\"n\":4,\"prefix\":[1,2],\"tail_value\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0053","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],\"prefix\":[2,3],\"tail_value\":0,\"candidate\":0}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], 0, 0, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([2, 3], 0, 0, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234053,"parameters":{"n":4,"distances":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],"prefix":[2,3],"tail_value":0,"candidate":0,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":0,\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],\"n\":4,\"prefix\":[2,3],\"tail_value\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0054","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],\"prefix\":[3,0],\"tail_value\":1,\"candidate\":2}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 1, 2, 2, 否, 尾值與候選不同)","explanation_zh":"現代橋梁核對=([3, 0], 1, 2, 2, 否, 尾值與候選不同)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234054,"parameters":{"n":4,"distances":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],"prefix":[3,0],"tail_value":1,"candidate":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":2,\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],\"n\":4,\"prefix\":[3,0],\"tail_value\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0055","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate\":2}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 2, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([0, 1], 2, 2, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234055,"parameters":{"n":4,"distances":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],"prefix":[0,1],"tail_value":2,"candidate":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":2,\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0056","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],\"prefix\":[1,2],\"tail_value\":3,\"candidate\":3}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], 3, 3, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([1, 2], 3, 3, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234056,"parameters":{"n":4,"distances":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],"prefix":[1,2],"tail_value":3,"candidate":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":3,\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],\"n\":4,\"prefix\":[1,2],\"tail_value\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0057","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],\"prefix\":[2,3],\"tail_value\":0,\"candidate\":1}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], 0, 1, 2, 否, 尾值與候選不同)","explanation_zh":"現代橋梁核對=([2, 3], 0, 1, 2, 否, 尾值與候選不同)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234057,"parameters":{"n":4,"distances":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],"prefix":[2,3],"tail_value":0,"candidate":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":1,\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],\"n\":4,\"prefix\":[2,3],\"tail_value\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0058","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],\"prefix\":[3,0],\"tail_value\":1,\"candidate\":1}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 1, 1, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([3, 0], 1, 1, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234058,"parameters":{"n":4,"distances":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],"prefix":[3,0],"tail_value":1,"candidate":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":1,\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],\"n\":4,\"prefix\":[3,0],\"tail_value\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0059","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate\":2}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 2, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([0, 1], 2, 2, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234059,"parameters":{"n":4,"distances":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],"prefix":[0,1],"tail_value":2,"candidate":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":2,\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0060","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],\"prefix\":[1,2],\"tail_value\":3,\"candidate\":0}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], 3, 0, 2, 否, 尾值與候選不同)","explanation_zh":"現代橋梁核對=([1, 2], 3, 0, 2, 否, 尾值與候選不同)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234060,"parameters":{"n":4,"distances":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],"prefix":[1,2],"tail_value":3,"candidate":0,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":0,\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],\"n\":4,\"prefix\":[1,2],\"tail_value\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0061","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],\"prefix\":[2,3],\"tail_value\":0,\"candidate\":0}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], 0, 0, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([2, 3], 0, 0, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234061,"parameters":{"n":4,"distances":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],"prefix":[2,3],"tail_value":0,"candidate":0,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":0,\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],\"n\":4,\"prefix\":[2,3],\"tail_value\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0062","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],\"prefix\":[3,0],\"tail_value\":1,\"candidate\":1}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 1, 1, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([3, 0], 1, 1, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234062,"parameters":{"n":4,"distances":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],"prefix":[3,0],"tail_value":1,"candidate":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":1,\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],\"n\":4,\"prefix\":[3,0],\"tail_value\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0063","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate\":3}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 3, 2, 否, 尾值與候選不同)","explanation_zh":"現代橋梁核對=([0, 1], 2, 3, 2, 否, 尾值與候選不同)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234063,"parameters":{"n":4,"distances":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],"prefix":[0,1],"tail_value":2,"candidate":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":3,\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0064","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],\"prefix\":[1,2],\"tail_value\":3,\"candidate\":3}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], 3, 3, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([1, 2], 3, 3, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234064,"parameters":{"n":4,"distances":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],"prefix":[1,2],"tail_value":3,"candidate":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":3,\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],\"n\":4,\"prefix\":[1,2],\"tail_value\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0065","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],\"prefix\":[2,3],\"tail_value\":0,\"candidate\":0}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], 0, 0, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([2, 3], 0, 0, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234065,"parameters":{"n":4,"distances":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],"prefix":[2,3],"tail_value":0,"candidate":0,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":0,\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],\"n\":4,\"prefix\":[2,3],\"tail_value\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0066","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],\"prefix\":[3,0],\"tail_value\":1,\"candidate\":2}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 1, 2, 2, 否, 尾值與候選不同)","explanation_zh":"現代橋梁核對=([3, 0], 1, 2, 2, 否, 尾值與候選不同)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234066,"parameters":{"n":4,"distances":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],"prefix":[3,0],"tail_value":1,"candidate":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":2,\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],\"n\":4,\"prefix\":[3,0],\"tail_value\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0067","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate\":2}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 2, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([0, 1], 2, 2, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234067,"parameters":{"n":4,"distances":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],"prefix":[0,1],"tail_value":2,"candidate":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":2,\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0068","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],\"prefix\":[1,2],\"tail_value\":3,\"candidate\":3}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], 3, 3, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([1, 2], 3, 3, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234068,"parameters":{"n":4,"distances":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],"prefix":[1,2],"tail_value":3,"candidate":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":3,\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],\"n\":4,\"prefix\":[1,2],\"tail_value\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0069","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],\"prefix\":[2,3],\"tail_value\":0,\"candidate\":1}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], 0, 1, 2, 否, 尾值與候選不同)","explanation_zh":"現代橋梁核對=([2, 3], 0, 1, 2, 否, 尾值與候選不同)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234069,"parameters":{"n":4,"distances":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],"prefix":[2,3],"tail_value":0,"candidate":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":1,\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],\"n\":4,\"prefix\":[2,3],\"tail_value\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0070","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],\"prefix\":[3,0],\"tail_value\":1,\"candidate\":1}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 1, 1, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([3, 0], 1, 1, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234070,"parameters":{"n":4,"distances":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],"prefix":[3,0],"tail_value":1,"candidate":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":1,\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],\"n\":4,\"prefix\":[3,0],\"tail_value\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0071","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate\":2}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 2, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([0, 1], 2, 2, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234071,"parameters":{"n":4,"distances":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],"prefix":[0,1],"tail_value":2,"candidate":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":2,\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0072","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],\"prefix\":[1,2],\"tail_value\":3,\"candidate\":0}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], 3, 0, 2, 否, 尾值與候選不同)","explanation_zh":"現代橋梁核對=([1, 2], 3, 0, 2, 否, 尾值與候選不同)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234072,"parameters":{"n":4,"distances":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],"prefix":[1,2],"tail_value":3,"candidate":0,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":0,\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],\"n\":4,\"prefix\":[1,2],\"tail_value\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0073","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],\"prefix\":[2,3],\"tail_value\":0,\"candidate\":0}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], 0, 0, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([2, 3], 0, 0, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234073,"parameters":{"n":4,"distances":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],"prefix":[2,3],"tail_value":0,"candidate":0,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":0,\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],\"n\":4,\"prefix\":[2,3],\"tail_value\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0074","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],\"prefix\":[3,0],\"tail_value\":1,\"candidate\":1}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 1, 1, 2, 是, 任意epsilon>0取N=prefix長度)","explanation_zh":"現代橋梁核對=([3, 0], 1, 1, 2, 是, 任意epsilon>0取N=prefix長度)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234074,"parameters":{"n":4,"distances":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],"prefix":[3,0],"tail_value":1,"candidate":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":1,\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],\"n\":4,\"prefix\":[3,0],\"tail_value\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0075","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-ultimately-constant-limit；資料={\"n\":4,\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate\":3}。請依 [prefix,tail,candidate,N,converges,witness] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 3, 2, 否, 尾值與候選不同)","explanation_zh":"現代橋梁核對=([0, 1], 2, 3, 2, 否, 尾值與候選不同)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-ultimately-constant-limit","seed":202610234075,"parameters":{"n":4,"distances":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],"prefix":[0,1],"tail_value":2,"candidate":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-ultimately-constant-limit","semantic_template":"qf-mod23-metricconv-ultimately-constant-limit/{\"candidate\":3,\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0076","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate_a\":2,\"candidate_b\":2}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 2, 2, 0, 是, 是, 是)","explanation_zh":"現代橋梁核對=([0, 1], 2, 2, 2, 0, 是, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234076,"parameters":{"n":4,"distances":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],"prefix":[0,1],"tail_value":2,"candidate_a":2,"candidate_b":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":2,\"candidate_b\":2,\"distances\":[[0,1,3,6],[1,0,2,5],[3,2,0,3],[6,5,3,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0077","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],\"prefix\":[1,2],\"tail_value\":3,\"candidate_a\":3,\"candidate_b\":0}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], 3, 3, 0, 9, 是, 否, 是)","explanation_zh":"現代橋梁核對=([1, 2], 3, 3, 0, 9, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234077,"parameters":{"n":4,"distances":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],"prefix":[1,2],"tail_value":3,"candidate_a":3,"candidate_b":0,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":3,\"candidate_b\":0,\"distances\":[[0,2,5,9],[2,0,3,7],[5,3,0,4],[9,7,4,0]],\"n\":4,\"prefix\":[1,2],\"tail_value\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0078","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],\"prefix\":[2,3],\"tail_value\":0,\"candidate_a\":0,\"candidate_b\":1}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], 0, 0, 1, 3, 是, 否, 是)","explanation_zh":"現代橋梁核對=([2, 3], 0, 0, 1, 3, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234078,"parameters":{"n":4,"distances":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],"prefix":[2,3],"tail_value":0,"candidate_a":0,"candidate_b":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":0,\"candidate_b\":1,\"distances\":[[0,3,7,12],[3,0,4,9],[7,4,0,5],[12,9,5,0]],\"n\":4,\"prefix\":[2,3],\"tail_value\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0079","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],\"prefix\":[3,0],\"tail_value\":1,\"candidate_a\":1,\"candidate_b\":1}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 1, 1, 1, 0, 是, 是, 是)","explanation_zh":"現代橋梁核對=([3, 0], 1, 1, 1, 0, 是, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234079,"parameters":{"n":4,"distances":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],"prefix":[3,0],"tail_value":1,"candidate_a":1,"candidate_b":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":1,\"candidate_b\":1,\"distances\":[[0,4,9,15],[4,0,5,11],[9,5,0,6],[15,11,6,0]],\"n\":4,\"prefix\":[3,0],\"tail_value\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0080","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate_a\":2,\"candidate_b\":3}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 2, 3, 7, 是, 否, 是)","explanation_zh":"現代橋梁核對=([0, 1], 2, 2, 3, 7, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234080,"parameters":{"n":4,"distances":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],"prefix":[0,1],"tail_value":2,"candidate_a":2,"candidate_b":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":2,\"candidate_b\":3,\"distances\":[[0,5,11,18],[5,0,6,13],[11,6,0,7],[18,13,7,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0081","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],\"prefix\":[1,2],\"tail_value\":3,\"candidate_a\":3,\"candidate_b\":0}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], 3, 3, 0, 21, 是, 否, 是)","explanation_zh":"現代橋梁核對=([1, 2], 3, 3, 0, 21, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234081,"parameters":{"n":4,"distances":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],"prefix":[1,2],"tail_value":3,"candidate_a":3,"candidate_b":0,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":3,\"candidate_b\":0,\"distances\":[[0,6,13,21],[6,0,7,15],[13,7,0,8],[21,15,8,0]],\"n\":4,\"prefix\":[1,2],\"tail_value\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0082","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],\"prefix\":[2,3],\"tail_value\":0,\"candidate_a\":0,\"candidate_b\":0}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], 0, 0, 0, 0, 是, 是, 是)","explanation_zh":"現代橋梁核對=([2, 3], 0, 0, 0, 0, 是, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234082,"parameters":{"n":4,"distances":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],"prefix":[2,3],"tail_value":0,"candidate_a":0,"candidate_b":0,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":0,\"candidate_b\":0,\"distances\":[[0,7,15,24],[7,0,8,17],[15,8,0,9],[24,17,9,0]],\"n\":4,\"prefix\":[2,3],\"tail_value\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0083","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],\"prefix\":[3,0],\"tail_value\":1,\"candidate_a\":1,\"candidate_b\":2}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 1, 1, 2, 9, 是, 否, 是)","explanation_zh":"現代橋梁核對=([3, 0], 1, 1, 2, 9, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234083,"parameters":{"n":4,"distances":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],"prefix":[3,0],"tail_value":1,"candidate_a":1,"candidate_b":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":1,\"candidate_b\":2,\"distances\":[[0,8,17,27],[8,0,9,19],[17,9,0,10],[27,19,10,0]],\"n\":4,\"prefix\":[3,0],\"tail_value\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0084","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate_a\":2,\"candidate_b\":3}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 2, 3, 11, 是, 否, 是)","explanation_zh":"現代橋梁核對=([0, 1], 2, 2, 3, 11, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234084,"parameters":{"n":4,"distances":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],"prefix":[0,1],"tail_value":2,"candidate_a":2,"candidate_b":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":2,\"candidate_b\":3,\"distances\":[[0,9,19,30],[9,0,10,21],[19,10,0,11],[30,21,11,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0085","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],\"prefix\":[1,2],\"tail_value\":3,\"candidate_a\":3,\"candidate_b\":3}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], 3, 3, 3, 0, 是, 是, 是)","explanation_zh":"現代橋梁核對=([1, 2], 3, 3, 3, 0, 是, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234085,"parameters":{"n":4,"distances":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],"prefix":[1,2],"tail_value":3,"candidate_a":3,"candidate_b":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":3,\"candidate_b\":3,\"distances\":[[0,10,21,33],[10,0,11,23],[21,11,0,12],[33,23,12,0]],\"n\":4,\"prefix\":[1,2],\"tail_value\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0086","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],\"prefix\":[2,3],\"tail_value\":0,\"candidate_a\":0,\"candidate_b\":1}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], 0, 0, 1, 11, 是, 否, 是)","explanation_zh":"現代橋梁核對=([2, 3], 0, 0, 1, 11, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234086,"parameters":{"n":4,"distances":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],"prefix":[2,3],"tail_value":0,"candidate_a":0,"candidate_b":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":0,\"candidate_b\":1,\"distances\":[[0,11,23,36],[11,0,12,25],[23,12,0,13],[36,25,13,0]],\"n\":4,\"prefix\":[2,3],\"tail_value\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0087","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],\"prefix\":[3,0],\"tail_value\":1,\"candidate_a\":1,\"candidate_b\":2}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 1, 1, 2, 13, 是, 否, 是)","explanation_zh":"現代橋梁核對=([3, 0], 1, 1, 2, 13, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234087,"parameters":{"n":4,"distances":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],"prefix":[3,0],"tail_value":1,"candidate_a":1,"candidate_b":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":1,\"candidate_b\":2,\"distances\":[[0,12,25,39],[12,0,13,27],[25,13,0,14],[39,27,14,0]],\"n\":4,\"prefix\":[3,0],\"tail_value\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0088","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate_a\":2,\"candidate_b\":2}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 2, 2, 0, 是, 是, 是)","explanation_zh":"現代橋梁核對=([0, 1], 2, 2, 2, 0, 是, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234088,"parameters":{"n":4,"distances":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],"prefix":[0,1],"tail_value":2,"candidate_a":2,"candidate_b":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":2,\"candidate_b\":2,\"distances\":[[0,13,27,42],[13,0,14,29],[27,14,0,15],[42,29,15,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0089","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],\"prefix\":[1,2],\"tail_value\":3,\"candidate_a\":3,\"candidate_b\":0}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], 3, 3, 0, 45, 是, 否, 是)","explanation_zh":"現代橋梁核對=([1, 2], 3, 3, 0, 45, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234089,"parameters":{"n":4,"distances":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],"prefix":[1,2],"tail_value":3,"candidate_a":3,"candidate_b":0,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":3,\"candidate_b\":0,\"distances\":[[0,14,29,45],[14,0,15,31],[29,15,0,16],[45,31,16,0]],\"n\":4,\"prefix\":[1,2],\"tail_value\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0090","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],\"prefix\":[2,3],\"tail_value\":0,\"candidate_a\":0,\"candidate_b\":1}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], 0, 0, 1, 15, 是, 否, 是)","explanation_zh":"現代橋梁核對=([2, 3], 0, 0, 1, 15, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234090,"parameters":{"n":4,"distances":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],"prefix":[2,3],"tail_value":0,"candidate_a":0,"candidate_b":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":0,\"candidate_b\":1,\"distances\":[[0,15,31,48],[15,0,16,33],[31,16,0,17],[48,33,17,0]],\"n\":4,\"prefix\":[2,3],\"tail_value\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0091","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],\"prefix\":[3,0],\"tail_value\":1,\"candidate_a\":1,\"candidate_b\":1}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 1, 1, 1, 0, 是, 是, 是)","explanation_zh":"現代橋梁核對=([3, 0], 1, 1, 1, 0, 是, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234091,"parameters":{"n":4,"distances":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],"prefix":[3,0],"tail_value":1,"candidate_a":1,"candidate_b":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":1,\"candidate_b\":1,\"distances\":[[0,16,33,51],[16,0,17,35],[33,17,0,18],[51,35,18,0]],\"n\":4,\"prefix\":[3,0],\"tail_value\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0092","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate_a\":2,\"candidate_b\":3}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 2, 3, 19, 是, 否, 是)","explanation_zh":"現代橋梁核對=([0, 1], 2, 2, 3, 19, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234092,"parameters":{"n":4,"distances":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],"prefix":[0,1],"tail_value":2,"candidate_a":2,"candidate_b":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":2,\"candidate_b\":3,\"distances\":[[0,17,35,54],[17,0,18,37],[35,18,0,19],[54,37,19,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0093","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],\"prefix\":[1,2],\"tail_value\":3,\"candidate_a\":3,\"candidate_b\":0}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], 3, 3, 0, 57, 是, 否, 是)","explanation_zh":"現代橋梁核對=([1, 2], 3, 3, 0, 57, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234093,"parameters":{"n":4,"distances":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],"prefix":[1,2],"tail_value":3,"candidate_a":3,"candidate_b":0,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":3,\"candidate_b\":0,\"distances\":[[0,18,37,57],[18,0,19,39],[37,19,0,20],[57,39,20,0]],\"n\":4,\"prefix\":[1,2],\"tail_value\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0094","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],\"prefix\":[2,3],\"tail_value\":0,\"candidate_a\":0,\"candidate_b\":0}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], 0, 0, 0, 0, 是, 是, 是)","explanation_zh":"現代橋梁核對=([2, 3], 0, 0, 0, 0, 是, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234094,"parameters":{"n":4,"distances":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],"prefix":[2,3],"tail_value":0,"candidate_a":0,"candidate_b":0,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":0,\"candidate_b\":0,\"distances\":[[0,19,39,60],[19,0,20,41],[39,20,0,21],[60,41,21,0]],\"n\":4,\"prefix\":[2,3],\"tail_value\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0095","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],\"prefix\":[3,0],\"tail_value\":1,\"candidate_a\":1,\"candidate_b\":2}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 1, 1, 2, 21, 是, 否, 是)","explanation_zh":"現代橋梁核對=([3, 0], 1, 1, 2, 21, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234095,"parameters":{"n":4,"distances":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],"prefix":[3,0],"tail_value":1,"candidate_a":1,"candidate_b":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":1,\"candidate_b\":2,\"distances\":[[0,20,41,63],[20,0,21,43],[41,21,0,22],[63,43,22,0]],\"n\":4,\"prefix\":[3,0],\"tail_value\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0096","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate_a\":2,\"candidate_b\":3}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 2, 3, 23, 是, 否, 是)","explanation_zh":"現代橋梁核對=([0, 1], 2, 2, 3, 23, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234096,"parameters":{"n":4,"distances":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],"prefix":[0,1],"tail_value":2,"candidate_a":2,"candidate_b":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":2,\"candidate_b\":3,\"distances\":[[0,21,43,66],[21,0,22,45],[43,22,0,23],[66,45,23,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0097","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],\"prefix\":[1,2],\"tail_value\":3,\"candidate_a\":3,\"candidate_b\":3}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], 3, 3, 3, 0, 是, 是, 是)","explanation_zh":"現代橋梁核對=([1, 2], 3, 3, 3, 0, 是, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234097,"parameters":{"n":4,"distances":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],"prefix":[1,2],"tail_value":3,"candidate_a":3,"candidate_b":3,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":3,\"candidate_b\":3,\"distances\":[[0,22,45,69],[22,0,23,47],[45,23,0,24],[69,47,24,0]],\"n\":4,\"prefix\":[1,2],\"tail_value\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0098","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],\"prefix\":[2,3],\"tail_value\":0,\"candidate_a\":0,\"candidate_b\":1}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], 0, 0, 1, 23, 是, 否, 是)","explanation_zh":"現代橋梁核對=([2, 3], 0, 0, 1, 23, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234098,"parameters":{"n":4,"distances":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],"prefix":[2,3],"tail_value":0,"candidate_a":0,"candidate_b":1,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":0,\"candidate_b\":1,\"distances\":[[0,23,47,72],[23,0,24,49],[47,24,0,25],[72,49,25,0]],\"n\":4,\"prefix\":[2,3],\"tail_value\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0099","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],\"prefix\":[3,0],\"tail_value\":1,\"candidate_a\":1,\"candidate_b\":2}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 1, 1, 2, 25, 是, 否, 是)","explanation_zh":"現代橋梁核對=([3, 0], 1, 1, 2, 25, 是, 否, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234099,"parameters":{"n":4,"distances":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],"prefix":[3,0],"tail_value":1,"candidate_a":1,"candidate_b":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":1,\"candidate_b\":2,\"distances\":[[0,24,49,75],[24,0,25,51],[49,25,0,26],[75,51,26,0]],\"n\":4,\"prefix\":[3,0],\"tail_value\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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-20261023-r04-metric-convergence-0100","batch_id":"batch-20261013-advance-20261023-r04-metric-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-metric-convergence"],"title_zh":"度量收斂證書","stem_zh":"完整有限度量與明示序列模型。操作=metricconv-limit-uniqueness-audit；資料={\"n\":4,\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],\"prefix\":[0,1],\"tail_value\":2,\"candidate_a\":2,\"candidate_b\":2}。請依 [prefix,tail,candidate_a,candidate_b,distance,a_limit,b_limit,uniqueness_consistent] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 2, 2, 2, 0, 是, 是, 是)","explanation_zh":"現代橋梁核對=([0, 1], 2, 2, 2, 0, 是, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；保留forall epsilon exists N forall n>=N；有限尾段本身不證一般收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["度量收斂證書"]},"variant":{"family_id":"qf-mod23-metricconv-limit-uniqueness-audit","seed":202610234100,"parameters":{"n":4,"distances":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],"prefix":[0,1],"tail_value":2,"candidate_a":2,"candidate_b":2,"domain":"Finite_metric_convergence_certificates","operation":"metricconv-limit-uniqueness-audit","semantic_template":"qf-mod23-metricconv-limit-uniqueness-audit/{\"candidate_a\":2,\"candidate_b\":2,\"distances\":[[0,25,51,78],[25,0,26,53],[51,26,0,27],[78,53,27,0]],\"n\":4,\"prefix\":[0,1],\"tail_value\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、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"}}