{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r05-covariance-0001","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[-12,-1],[-11,0],[-10,1],[-9,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(-10, 1, -35/4, 5/4)","explanation_zh":"結構深度核對=(-10, 1, -35/4, 5/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265001,"parameters":{"support":[[-12,-1],[-11,0],[-10,1],[-9,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-12,-1],[-11,0],[-10,1],[-9,2]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0002","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[-11,-1],[-10,0],[-9,1],[-8,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(-9, 3/2, -47/4, 7/4)","explanation_zh":"結構深度核對=(-9, 3/2, -47/4, 7/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265002,"parameters":{"support":[[-11,-1],[-10,0],[-9,1],[-8,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-11,-1],[-10,0],[-9,1],[-8,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0003","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[-10,-1],[-9,0],[-8,1],[-7,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(-8, 2, -55/4, 9/4)","explanation_zh":"結構深度核對=(-8, 2, -55/4, 9/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265003,"parameters":{"support":[[-10,-1],[-9,0],[-8,1],[-7,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-10,-1],[-9,0],[-8,1],[-7,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0004","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[-9,-1],[-8,0],[-7,1],[-6,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(-7, 5/2, -59/4, 11/4)","explanation_zh":"結構深度核對=(-7, 5/2, -59/4, 11/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265004,"parameters":{"support":[[-9,-1],[-8,0],[-7,1],[-6,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-9,-1],[-8,0],[-7,1],[-6,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0005","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[-8,-1],[-7,0],[-6,1],[-5,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(-6, 3, -59/4, 13/4)","explanation_zh":"結構深度核對=(-6, 3, -59/4, 13/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265005,"parameters":{"support":[[-8,-1],[-7,0],[-6,1],[-5,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-8,-1],[-7,0],[-6,1],[-5,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0006","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[-7,-1],[-6,0],[-5,1],[-4,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(-5, 1, -15/4, 5/4)","explanation_zh":"結構深度核對=(-5, 1, -15/4, 5/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265006,"parameters":{"support":[[-7,-1],[-6,0],[-5,1],[-4,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-7,-1],[-6,0],[-5,1],[-4,2]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0007","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[-6,-1],[-5,0],[-4,1],[-3,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(-4, 3/2, -17/4, 7/4)","explanation_zh":"結構深度核對=(-4, 3/2, -17/4, 7/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265007,"parameters":{"support":[[-6,-1],[-5,0],[-4,1],[-3,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-6,-1],[-5,0],[-4,1],[-3,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0008","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[-5,-1],[-4,0],[-3,1],[-2,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(-3, 2, -15/4, 9/4)","explanation_zh":"結構深度核對=(-3, 2, -15/4, 9/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265008,"parameters":{"support":[[-5,-1],[-4,0],[-3,1],[-2,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-5,-1],[-4,0],[-3,1],[-2,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0009","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[-4,-1],[-3,0],[-2,1],[-1,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(-2, 5/2, -9/4, 11/4)","explanation_zh":"結構深度核對=(-2, 5/2, -9/4, 11/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265009,"parameters":{"support":[[-4,-1],[-3,0],[-2,1],[-1,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-4,-1],[-3,0],[-2,1],[-1,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0010","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[-3,-1],[-2,0],[-1,1],[0,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(-1, 3, 1/4, 13/4)","explanation_zh":"結構深度核對=(-1, 3, 1/4, 13/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265010,"parameters":{"support":[[-3,-1],[-2,0],[-1,1],[0,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-3,-1],[-2,0],[-1,1],[0,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0011","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[-2,-1],[-1,0],[0,1],[1,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, 5/4, 5/4)","explanation_zh":"結構深度核對=(0, 1, 5/4, 5/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265011,"parameters":{"support":[[-2,-1],[-1,0],[0,1],[1,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-2,-1],[-1,0],[0,1],[1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0012","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[-1,-1],[0,0],[1,1],[2,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(1, 3/2, 13/4, 7/4)","explanation_zh":"結構深度核對=(1, 3/2, 13/4, 7/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265012,"parameters":{"support":[[-1,-1],[0,0],[1,1],[2,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-1,-1],[0,0],[1,1],[2,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0013","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[0,-1],[1,0],[2,1],[3,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(2, 2, 25/4, 9/4)","explanation_zh":"結構深度核對=(2, 2, 25/4, 9/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265013,"parameters":{"support":[[0,-1],[1,0],[2,1],[3,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[0,-1],[1,0],[2,1],[3,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0014","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[1,-1],[2,0],[3,1],[4,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(3, 5/2, 41/4, 11/4)","explanation_zh":"結構深度核對=(3, 5/2, 41/4, 11/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265014,"parameters":{"support":[[1,-1],[2,0],[3,1],[4,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[1,-1],[2,0],[3,1],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0015","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[2,-1],[3,0],[4,1],[5,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 61/4, 13/4)","explanation_zh":"結構深度核對=(4, 3, 61/4, 13/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265015,"parameters":{"support":[[2,-1],[3,0],[4,1],[5,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[2,-1],[3,0],[4,1],[5,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0016","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[3,-1],[4,0],[5,1],[6,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(5, 1, 25/4, 5/4)","explanation_zh":"結構深度核對=(5, 1, 25/4, 5/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265016,"parameters":{"support":[[3,-1],[4,0],[5,1],[6,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[3,-1],[4,0],[5,1],[6,2]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0017","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[4,-1],[5,0],[6,1],[7,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(6, 3/2, 43/4, 7/4)","explanation_zh":"結構深度核對=(6, 3/2, 43/4, 7/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265017,"parameters":{"support":[[4,-1],[5,0],[6,1],[7,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[4,-1],[5,0],[6,1],[7,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0018","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[5,-1],[6,0],[7,1],[8,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(7, 2, 65/4, 9/4)","explanation_zh":"結構深度核對=(7, 2, 65/4, 9/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265018,"parameters":{"support":[[5,-1],[6,0],[7,1],[8,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[5,-1],[6,0],[7,1],[8,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0019","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[6,-1],[7,0],[8,1],[9,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(8, 5/2, 91/4, 11/4)","explanation_zh":"結構深度核對=(8, 5/2, 91/4, 11/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265019,"parameters":{"support":[[6,-1],[7,0],[8,1],[9,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[6,-1],[7,0],[8,1],[9,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0020","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[7,-1],[8,0],[9,1],[10,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(9, 3, 121/4, 13/4)","explanation_zh":"結構深度核對=(9, 3, 121/4, 13/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265020,"parameters":{"support":[[7,-1],[8,0],[9,1],[10,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[7,-1],[8,0],[9,1],[10,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0021","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[8,-1],[9,0],[10,1],[11,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(10, 1, 45/4, 5/4)","explanation_zh":"結構深度核對=(10, 1, 45/4, 5/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265021,"parameters":{"support":[[8,-1],[9,0],[10,1],[11,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[8,-1],[9,0],[10,1],[11,2]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0022","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[9,-1],[10,0],[11,1],[12,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(11, 3/2, 73/4, 7/4)","explanation_zh":"結構深度核對=(11, 3/2, 73/4, 7/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265022,"parameters":{"support":[[9,-1],[10,0],[11,1],[12,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[9,-1],[10,0],[11,1],[12,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0023","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[10,-1],[11,0],[12,1],[13,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(12, 2, 105/4, 9/4)","explanation_zh":"結構深度核對=(12, 2, 105/4, 9/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265023,"parameters":{"support":[[10,-1],[11,0],[12,1],[13,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[10,-1],[11,0],[12,1],[13,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0024","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[11,-1],[12,0],[13,1],[14,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(13, 5/2, 141/4, 11/4)","explanation_zh":"結構深度核對=(13, 5/2, 141/4, 11/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265024,"parameters":{"support":[[11,-1],[12,0],[13,1],[14,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[11,-1],[12,0],[13,1],[14,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0025","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-compute；資料={\"support\":[[12,-1],[13,0],[14,1],[15,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [E_X,E_Y,E_XY,covariance] 欄序回答。","answer":{"kind":"expression","value":"(14, 3, 181/4, 13/4)","explanation_zh":"結構深度核對=(14, 3, 181/4, 13/4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-compute","seed":202610265025,"parameters":{"support":[[12,-1],[13,0],[14,1],[15,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-compute","semantic_template":"qf-mod26-covariance-compute/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[12,-1],[13,0],[14,1],[15,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0026","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[-12,-1],[-11,0],[-10,1],[-9,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(5/4, 5/4, 是)","explanation_zh":"結構深度核對=(5/4, 5/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265026,"parameters":{"support":[[-12,-1],[-11,0],[-10,1],[-9,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-12,-1],[-11,0],[-10,1],[-9,2]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0027","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[-11,-1],[-10,0],[-9,1],[-8,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(7/4, 7/4, 是)","explanation_zh":"結構深度核對=(7/4, 7/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265027,"parameters":{"support":[[-11,-1],[-10,0],[-9,1],[-8,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-11,-1],[-10,0],[-9,1],[-8,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0028","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[-10,-1],[-9,0],[-8,1],[-7,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(9/4, 9/4, 是)","explanation_zh":"結構深度核對=(9/4, 9/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265028,"parameters":{"support":[[-10,-1],[-9,0],[-8,1],[-7,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-10,-1],[-9,0],[-8,1],[-7,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0029","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[-9,-1],[-8,0],[-7,1],[-6,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(11/4, 11/4, 是)","explanation_zh":"結構深度核對=(11/4, 11/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265029,"parameters":{"support":[[-9,-1],[-8,0],[-7,1],[-6,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-9,-1],[-8,0],[-7,1],[-6,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0030","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[-8,-1],[-7,0],[-6,1],[-5,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(13/4, 13/4, 是)","explanation_zh":"結構深度核對=(13/4, 13/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265030,"parameters":{"support":[[-8,-1],[-7,0],[-6,1],[-5,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-8,-1],[-7,0],[-6,1],[-5,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0031","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[-7,-1],[-6,0],[-5,1],[-4,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(5/4, 5/4, 是)","explanation_zh":"結構深度核對=(5/4, 5/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265031,"parameters":{"support":[[-7,-1],[-6,0],[-5,1],[-4,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-7,-1],[-6,0],[-5,1],[-4,2]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0032","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[-6,-1],[-5,0],[-4,1],[-3,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(7/4, 7/4, 是)","explanation_zh":"結構深度核對=(7/4, 7/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265032,"parameters":{"support":[[-6,-1],[-5,0],[-4,1],[-3,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-6,-1],[-5,0],[-4,1],[-3,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0033","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[-5,-1],[-4,0],[-3,1],[-2,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(9/4, 9/4, 是)","explanation_zh":"結構深度核對=(9/4, 9/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265033,"parameters":{"support":[[-5,-1],[-4,0],[-3,1],[-2,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-5,-1],[-4,0],[-3,1],[-2,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0034","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[-4,-1],[-3,0],[-2,1],[-1,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(11/4, 11/4, 是)","explanation_zh":"結構深度核對=(11/4, 11/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265034,"parameters":{"support":[[-4,-1],[-3,0],[-2,1],[-1,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-4,-1],[-3,0],[-2,1],[-1,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0035","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[-3,-1],[-2,0],[-1,1],[0,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(13/4, 13/4, 是)","explanation_zh":"結構深度核對=(13/4, 13/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265035,"parameters":{"support":[[-3,-1],[-2,0],[-1,1],[0,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-3,-1],[-2,0],[-1,1],[0,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0036","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[-2,-1],[-1,0],[0,1],[1,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(5/4, 5/4, 是)","explanation_zh":"結構深度核對=(5/4, 5/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265036,"parameters":{"support":[[-2,-1],[-1,0],[0,1],[1,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-2,-1],[-1,0],[0,1],[1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0037","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[-1,-1],[0,0],[1,1],[2,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(7/4, 7/4, 是)","explanation_zh":"結構深度核對=(7/4, 7/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265037,"parameters":{"support":[[-1,-1],[0,0],[1,1],[2,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-1,-1],[0,0],[1,1],[2,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0038","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[0,-1],[1,0],[2,1],[3,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(9/4, 9/4, 是)","explanation_zh":"結構深度核對=(9/4, 9/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265038,"parameters":{"support":[[0,-1],[1,0],[2,1],[3,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[0,-1],[1,0],[2,1],[3,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0039","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[1,-1],[2,0],[3,1],[4,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(11/4, 11/4, 是)","explanation_zh":"結構深度核對=(11/4, 11/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265039,"parameters":{"support":[[1,-1],[2,0],[3,1],[4,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[1,-1],[2,0],[3,1],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0040","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[2,-1],[3,0],[4,1],[5,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(13/4, 13/4, 是)","explanation_zh":"結構深度核對=(13/4, 13/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265040,"parameters":{"support":[[2,-1],[3,0],[4,1],[5,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[2,-1],[3,0],[4,1],[5,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0041","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[3,-1],[4,0],[5,1],[6,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(5/4, 5/4, 是)","explanation_zh":"結構深度核對=(5/4, 5/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265041,"parameters":{"support":[[3,-1],[4,0],[5,1],[6,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[3,-1],[4,0],[5,1],[6,2]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0042","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[4,-1],[5,0],[6,1],[7,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(7/4, 7/4, 是)","explanation_zh":"結構深度核對=(7/4, 7/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265042,"parameters":{"support":[[4,-1],[5,0],[6,1],[7,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[4,-1],[5,0],[6,1],[7,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0043","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[5,-1],[6,0],[7,1],[8,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(9/4, 9/4, 是)","explanation_zh":"結構深度核對=(9/4, 9/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265043,"parameters":{"support":[[5,-1],[6,0],[7,1],[8,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[5,-1],[6,0],[7,1],[8,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0044","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[6,-1],[7,0],[8,1],[9,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(11/4, 11/4, 是)","explanation_zh":"結構深度核對=(11/4, 11/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265044,"parameters":{"support":[[6,-1],[7,0],[8,1],[9,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[6,-1],[7,0],[8,1],[9,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0045","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[7,-1],[8,0],[9,1],[10,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(13/4, 13/4, 是)","explanation_zh":"結構深度核對=(13/4, 13/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265045,"parameters":{"support":[[7,-1],[8,0],[9,1],[10,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[7,-1],[8,0],[9,1],[10,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0046","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[8,-1],[9,0],[10,1],[11,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(5/4, 5/4, 是)","explanation_zh":"結構深度核對=(5/4, 5/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265046,"parameters":{"support":[[8,-1],[9,0],[10,1],[11,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[8,-1],[9,0],[10,1],[11,2]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0047","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[9,-1],[10,0],[11,1],[12,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(7/4, 7/4, 是)","explanation_zh":"結構深度核對=(7/4, 7/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265047,"parameters":{"support":[[9,-1],[10,0],[11,1],[12,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[9,-1],[10,0],[11,1],[12,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0048","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[10,-1],[11,0],[12,1],[13,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(9/4, 9/4, 是)","explanation_zh":"結構深度核對=(9/4, 9/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265048,"parameters":{"support":[[10,-1],[11,0],[12,1],[13,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[10,-1],[11,0],[12,1],[13,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0049","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[11,-1],[12,0],[13,1],[14,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(11/4, 11/4, 是)","explanation_zh":"結構深度核對=(11/4, 11/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265049,"parameters":{"support":[[11,-1],[12,0],[13,1],[14,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[11,-1],[12,0],[13,1],[14,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0050","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-symmetry；資料={\"support\":[[12,-1],[13,0],[14,1],[15,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]]}。請依 [Cov_XY,Cov_YX,equal] 欄序回答。","answer":{"kind":"expression","value":"(13/4, 13/4, 是)","explanation_zh":"結構深度核對=(13/4, 13/4, 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-symmetry","seed":202610265050,"parameters":{"support":[[12,-1],[13,0],[14,1],[15,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"domain":"Exact_finite_joint_covariance","operation":"covariance-symmetry","semantic_template":"qf-mod26-covariance-symmetry/{\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[12,-1],[13,0],[14,1],[15,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0051","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[-12,-1],[-11,0],[-10,1],[-9,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":-3,\"b\":-12,\"c\":-2,\"d\":12}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(-3, -12, -2, 12, 5/4, 15/2, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(-3, -12, -2, 12, 5/4, 15/2, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265051,"parameters":{"support":[[-12,-1],[-11,0],[-10,1],[-9,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":-3,"b":-12,"c":-2,"d":12,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":-3,\"b\":-12,\"c\":-2,\"d\":12,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-12,-1],[-11,0],[-10,1],[-9,2]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0052","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[-11,-1],[-10,0],[-9,1],[-8,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":-2,\"b\":-11,\"c\":-1,\"d\":11}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(-2, -11, -1, 11, 7/4, 7/2, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(-2, -11, -1, 11, 7/4, 7/2, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265052,"parameters":{"support":[[-11,-1],[-10,0],[-9,1],[-8,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":-2,"b":-11,"c":-1,"d":11,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":-2,\"b\":-11,\"c\":-1,\"d\":11,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-11,-1],[-10,0],[-9,1],[-8,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0053","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[-10,-1],[-9,0],[-8,1],[-7,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":-1,\"b\":-10,\"c\":0,\"d\":10}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(-1, -10, 0, 10, 9/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(-1, -10, 0, 10, 9/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265053,"parameters":{"support":[[-10,-1],[-9,0],[-8,1],[-7,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":-1,"b":-10,"c":0,"d":10,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":-1,\"b\":-10,\"c\":0,\"d\":10,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-10,-1],[-9,0],[-8,1],[-7,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0054","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[-9,-1],[-8,0],[-7,1],[-6,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":0,\"b\":-9,\"c\":1,\"d\":9}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(0, -9, 1, 9, 11/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(0, -9, 1, 9, 11/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265054,"parameters":{"support":[[-9,-1],[-8,0],[-7,1],[-6,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":0,"b":-9,"c":1,"d":9,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":0,\"b\":-9,\"c\":1,\"d\":9,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-9,-1],[-8,0],[-7,1],[-6,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0055","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[-8,-1],[-7,0],[-6,1],[-5,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":1,\"b\":-8,\"c\":2,\"d\":8}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(1, -8, 2, 8, 13/4, 13/2, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(1, -8, 2, 8, 13/4, 13/2, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265055,"parameters":{"support":[[-8,-1],[-7,0],[-6,1],[-5,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":1,"b":-8,"c":2,"d":8,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":1,\"b\":-8,\"c\":2,\"d\":8,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-8,-1],[-7,0],[-6,1],[-5,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0056","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[-7,-1],[-6,0],[-5,1],[-4,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":2,\"b\":-7,\"c\":-2,\"d\":7}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(2, -7, -2, 7, 5/4, -5, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(2, -7, -2, 7, 5/4, -5, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265056,"parameters":{"support":[[-7,-1],[-6,0],[-5,1],[-4,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":2,"b":-7,"c":-2,"d":7,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":2,\"b\":-7,\"c\":-2,\"d\":7,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-7,-1],[-6,0],[-5,1],[-4,2]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0057","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[-6,-1],[-5,0],[-4,1],[-3,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":3,\"b\":-6,\"c\":-1,\"d\":6}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(3, -6, -1, 6, 7/4, -21/4, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(3, -6, -1, 6, 7/4, -21/4, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265057,"parameters":{"support":[[-6,-1],[-5,0],[-4,1],[-3,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":3,"b":-6,"c":-1,"d":6,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":3,\"b\":-6,\"c\":-1,\"d\":6,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-6,-1],[-5,0],[-4,1],[-3,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0058","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[-5,-1],[-4,0],[-3,1],[-2,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":-3,\"b\":-5,\"c\":0,\"d\":5}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(-3, -5, 0, 5, 9/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(-3, -5, 0, 5, 9/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265058,"parameters":{"support":[[-5,-1],[-4,0],[-3,1],[-2,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":-3,"b":-5,"c":0,"d":5,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":-3,\"b\":-5,\"c\":0,\"d\":5,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-5,-1],[-4,0],[-3,1],[-2,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0059","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[-4,-1],[-3,0],[-2,1],[-1,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":-2,\"b\":-4,\"c\":1,\"d\":4}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(-2, -4, 1, 4, 11/4, -11/2, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(-2, -4, 1, 4, 11/4, -11/2, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265059,"parameters":{"support":[[-4,-1],[-3,0],[-2,1],[-1,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":-2,"b":-4,"c":1,"d":4,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":-2,\"b\":-4,\"c\":1,\"d\":4,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-4,-1],[-3,0],[-2,1],[-1,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0060","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[-3,-1],[-2,0],[-1,1],[0,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":-1,\"b\":-3,\"c\":2,\"d\":3}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(-1, -3, 2, 3, 13/4, -13/2, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(-1, -3, 2, 3, 13/4, -13/2, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265060,"parameters":{"support":[[-3,-1],[-2,0],[-1,1],[0,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":-1,"b":-3,"c":2,"d":3,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":-1,\"b\":-3,\"c\":2,\"d\":3,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-3,-1],[-2,0],[-1,1],[0,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0061","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[-2,-1],[-1,0],[0,1],[1,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":0,\"b\":-2,\"c\":-2,\"d\":2}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(0, -2, -2, 2, 5/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(0, -2, -2, 2, 5/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265061,"parameters":{"support":[[-2,-1],[-1,0],[0,1],[1,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":0,"b":-2,"c":-2,"d":2,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":0,\"b\":-2,\"c\":-2,\"d\":2,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-2,-1],[-1,0],[0,1],[1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0062","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[-1,-1],[0,0],[1,1],[2,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":1,\"b\":-1,\"c\":-1,\"d\":1}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(1, -1, -1, 1, 7/4, -7/4, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(1, -1, -1, 1, 7/4, -7/4, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265062,"parameters":{"support":[[-1,-1],[0,0],[1,1],[2,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":1,"b":-1,"c":-1,"d":1,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":1,\"b\":-1,\"c\":-1,\"d\":1,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[-1,-1],[0,0],[1,1],[2,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0063","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[0,-1],[1,0],[2,1],[3,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":2,\"b\":0,\"c\":0,\"d\":0}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, 0, 0, 9/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(2, 0, 0, 0, 9/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265063,"parameters":{"support":[[0,-1],[1,0],[2,1],[3,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":2,"b":0,"c":0,"d":0,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":2,\"b\":0,\"c\":0,\"d\":0,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[0,-1],[1,0],[2,1],[3,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0064","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[1,-1],[2,0],[3,1],[4,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":3,\"b\":1,\"c\":1,\"d\":-1}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, 1, -1, 11/4, 33/4, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(3, 1, 1, -1, 11/4, 33/4, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265064,"parameters":{"support":[[1,-1],[2,0],[3,1],[4,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":3,"b":1,"c":1,"d":-1,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":3,\"b\":1,\"c\":1,\"d\":-1,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[1,-1],[2,0],[3,1],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0065","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[2,-1],[3,0],[4,1],[5,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":-3,\"b\":2,\"c\":2,\"d\":-2}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(-3, 2, 2, -2, 13/4, -39/2, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(-3, 2, 2, -2, 13/4, -39/2, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265065,"parameters":{"support":[[2,-1],[3,0],[4,1],[5,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":-3,"b":2,"c":2,"d":-2,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":-3,\"b\":2,\"c\":2,\"d\":-2,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[2,-1],[3,0],[4,1],[5,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0066","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[3,-1],[4,0],[5,1],[6,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":-2,\"b\":3,\"c\":-2,\"d\":-3}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(-2, 3, -2, -3, 5/4, 5, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(-2, 3, -2, -3, 5/4, 5, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265066,"parameters":{"support":[[3,-1],[4,0],[5,1],[6,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":-2,"b":3,"c":-2,"d":-3,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":-2,\"b\":3,\"c\":-2,\"d\":-3,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[3,-1],[4,0],[5,1],[6,2]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0067","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[4,-1],[5,0],[6,1],[7,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":-1,\"b\":4,\"c\":-1,\"d\":-4}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(-1, 4, -1, -4, 7/4, 7/4, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(-1, 4, -1, -4, 7/4, 7/4, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265067,"parameters":{"support":[[4,-1],[5,0],[6,1],[7,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":-1,"b":4,"c":-1,"d":-4,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":-1,\"b\":4,\"c\":-1,\"d\":-4,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[4,-1],[5,0],[6,1],[7,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0068","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[5,-1],[6,0],[7,1],[8,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":0,\"b\":5,\"c\":0,\"d\":-5}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(0, 5, 0, -5, 9/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(0, 5, 0, -5, 9/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265068,"parameters":{"support":[[5,-1],[6,0],[7,1],[8,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":0,"b":5,"c":0,"d":-5,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":0,\"b\":5,\"c\":0,\"d\":-5,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[5,-1],[6,0],[7,1],[8,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0069","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[6,-1],[7,0],[8,1],[9,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":1,\"b\":6,\"c\":1,\"d\":-6}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(1, 6, 1, -6, 11/4, 11/4, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(1, 6, 1, -6, 11/4, 11/4, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265069,"parameters":{"support":[[6,-1],[7,0],[8,1],[9,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":1,"b":6,"c":1,"d":-6,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":1,\"b\":6,\"c\":1,\"d\":-6,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[6,-1],[7,0],[8,1],[9,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0070","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[7,-1],[8,0],[9,1],[10,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":2,\"b\":7,\"c\":2,\"d\":-7}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(2, 7, 2, -7, 13/4, 13, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(2, 7, 2, -7, 13/4, 13, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265070,"parameters":{"support":[[7,-1],[8,0],[9,1],[10,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":2,"b":7,"c":2,"d":-7,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":2,\"b\":7,\"c\":2,\"d\":-7,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[7,-1],[8,0],[9,1],[10,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0071","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[8,-1],[9,0],[10,1],[11,2]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":3,\"b\":8,\"c\":-2,\"d\":-8}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(3, 8, -2, -8, 5/4, -15/2, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(3, 8, -2, -8, 5/4, -15/2, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265071,"parameters":{"support":[[8,-1],[9,0],[10,1],[11,2]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":3,"b":8,"c":-2,"d":-8,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":3,\"b\":8,\"c\":-2,\"d\":-8,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[8,-1],[9,0],[10,1],[11,2]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0072","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[9,-1],[10,0],[11,1],[12,3]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":-3,\"b\":9,\"c\":-1,\"d\":-9}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(-3, 9, -1, -9, 7/4, 21/4, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(-3, 9, -1, -9, 7/4, 21/4, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265072,"parameters":{"support":[[9,-1],[10,0],[11,1],[12,3]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":-3,"b":9,"c":-1,"d":-9,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":-3,\"b\":9,\"c\":-1,\"d\":-9,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[9,-1],[10,0],[11,1],[12,3]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0073","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[10,-1],[11,0],[12,1],[13,4]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":-2,\"b\":10,\"c\":0,\"d\":-10}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(-2, 10, 0, -10, 9/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(-2, 10, 0, -10, 9/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265073,"parameters":{"support":[[10,-1],[11,0],[12,1],[13,4]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":-2,"b":10,"c":0,"d":-10,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":-2,\"b\":10,\"c\":0,\"d\":-10,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[10,-1],[11,0],[12,1],[13,4]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0074","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[11,-1],[12,0],[13,1],[14,5]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":-1,\"b\":11,\"c\":1,\"d\":-11}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(-1, 11, 1, -11, 11/4, -11/4, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(-1, 11, 1, -11, 11/4, -11/4, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265074,"parameters":{"support":[[11,-1],[12,0],[13,1],[14,5]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":-1,"b":11,"c":1,"d":-11,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":-1,\"b\":11,\"c\":1,\"d\":-11,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[11,-1],[12,0],[13,1],[14,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0075","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-affine；資料={\"support\":[[12,-1],[13,0],[14,1],[15,6]],\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"a\":0,\"b\":12,\"c\":2,\"d\":-12}。請依 [a,b,c,d,covariance,transformed_covariance,identity] 欄序回答。","answer":{"kind":"expression","value":"(0, 12, 2, -12, 13/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))","explanation_zh":"結構深度核對=(0, 12, 2, -12, 13/4, 0, Cov(aX+b,cY+d)=ac Cov(X,Y))；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-affine","seed":202610265075,"parameters":{"support":[[12,-1],[13,0],[14,1],[15,6]],"masses":[[1,8],[1,4],[1,8],[1,2]],"a":0,"b":12,"c":2,"d":-12,"domain":"Exact_finite_joint_covariance","operation":"covariance-affine","semantic_template":"qf-mod26-covariance-affine/{\"a\":0,\"b\":12,\"c\":2,\"d\":-12,\"masses\":[[1,8],[1,4],[1,8],[1,2]],\"support\":[[12,-1],[13,0],[14,1],[15,6]]}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0076","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":1}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(1, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265076,"parameters":{"scale":1,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0077","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":2}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(2, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265077,"parameters":{"scale":2,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0078","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":3}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(3, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265078,"parameters":{"scale":3,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0079","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":4}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(4, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265079,"parameters":{"scale":4,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0080","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":5}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(5, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265080,"parameters":{"scale":5,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0081","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":6}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(6, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(6, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265081,"parameters":{"scale":6,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":6}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0082","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":7}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(7, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(7, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265082,"parameters":{"scale":7,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":7}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0083","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":8}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(8, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(8, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265083,"parameters":{"scale":8,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":8}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0084","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":9}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(9, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(9, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265084,"parameters":{"scale":9,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":9}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0085","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":10}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(10, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(10, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265085,"parameters":{"scale":10,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":10}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0086","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":11}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(11, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(11, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265086,"parameters":{"scale":11,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":11}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0087","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":12}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(12, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(12, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265087,"parameters":{"scale":12,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":12}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0088","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":13}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(13, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(13, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265088,"parameters":{"scale":13,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":13}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0089","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":14}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(14, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(14, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265089,"parameters":{"scale":14,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":14}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0090","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":15}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(15, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(15, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265090,"parameters":{"scale":15,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":15}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0091","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":16}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(16, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(16, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265091,"parameters":{"scale":16,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":16}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0092","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":17}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(17, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(17, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265092,"parameters":{"scale":17,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":17}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0093","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":18}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(18, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(18, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265093,"parameters":{"scale":18,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":18}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0094","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":19}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(19, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(19, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265094,"parameters":{"scale":19,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":19}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0095","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":20}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(20, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(20, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265095,"parameters":{"scale":20,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":20}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0096","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":21}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(21, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(21, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265096,"parameters":{"scale":21,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":21}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0097","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":22}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(22, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(22, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265097,"parameters":{"scale":22,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":22}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0098","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":23}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(23, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(23, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265098,"parameters":{"scale":23,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":23}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0099","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":24}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(24, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(24, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265099,"parameters":{"scale":24,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":24}"}},"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、獨立性、一般圖同構、不限維分析、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-20261026-r05-covariance-0100","batch_id":"batch-20261013-advance-20261026-r05-covariance-foundations","language":"zh-Hant","source_mko_ids":["mko-covariance"],"title_zh":"協方差","stem_zh":"協方差必須綁定同一完整有限joint law。操作=covariance-zero-counterexample；資料={\"scale\":25}。請依 [scale,covariance,joint_zero,product_zero,zero_covariance,dependent,boundary] 欄序回答。","answer":{"kind":"expression","value":"(25, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)","explanation_zh":"結構深度核對=(25, 0, 1/3, 1/9, 是, 是, 零協方差但不獨立)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；非零協方差可否證獨立；零協方差通常不推出獨立。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["協方差"]},"variant":{"family_id":"qf-mod26-covariance-zero-counterexample","seed":202610265100,"parameters":{"scale":25,"domain":"Exact_finite_joint_covariance","operation":"covariance-zero-counterexample","semantic_template":"qf-mod26-covariance-zero-counterexample/{\"scale\":25}"}},"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、獨立性、一般圖同構、不限維分析、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"}}