{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0001","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[36,49],[6,49],[6,49],[1,49]],\"values\":[-12,-3,2,12],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 36/49, -12], [1, [1, 2], 12/49, -1/2], [2, [3], 1/49, 12]], [-12, -1/2, -1/2, 12])","explanation_zh":"Wave4第三層核對=([[0, [0], 36/49, -12], [1, [1, 2], 12/49, -1/2], [2, [3], 1/49, 12]], [-12, -1/2, -1/2, 12])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294001,"parameters":{"masses":[[36,49],[6,49],[6,49],[1,49]],"values":[-12,-3,2,12],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[36,49],[6,49],[6,49],[1,49]],\"values\":[-12,-3,2,12]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0002","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[30,49],[5,49],[12,49],[2,49]],\"values\":[-11,-2,3,11],\"blocks\":[0,0,1,1]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 5/7, -68/7], [1, [2, 3], 2/7, 29/7]], [-68/7, -68/7, 29/7, 29/7])","explanation_zh":"Wave4第三層核對=([[0, [0, 1], 5/7, -68/7], [1, [2, 3], 2/7, 29/7]], [-68/7, -68/7, 29/7, 29/7])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294002,"parameters":{"masses":[[30,49],[5,49],[12,49],[2,49]],"values":[-11,-2,3,11],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,0,1,1],\"masses\":[[30,49],[5,49],[12,49],[2,49]],\"values\":[-11,-2,3,11]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0003","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[24,49],[4,49],[18,49],[3,49]],\"values\":[-10,-1,4,10],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 24/49, -10], [1, [1, 2], 22/49, 34/11], [2, [3], 3/49, 10]], [-10, 34/11, 34/11, 10])","explanation_zh":"Wave4第三層核對=([[0, [0], 24/49, -10], [1, [1, 2], 22/49, 34/11], [2, [3], 3/49, 10]], [-10, 34/11, 34/11, 10])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294003,"parameters":{"masses":[[24,49],[4,49],[18,49],[3,49]],"values":[-10,-1,4,10],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[24,49],[4,49],[18,49],[3,49]],\"values\":[-10,-1,4,10]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0004","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[18,49],[3,49],[24,49],[4,49]],\"values\":[-9,0,5,9],\"blocks\":[0,0,1,1]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/7, -54/7], [1, [2, 3], 4/7, 39/7]], [-54/7, -54/7, 39/7, 39/7])","explanation_zh":"Wave4第三層核對=([[0, [0, 1], 3/7, -54/7], [1, [2, 3], 4/7, 39/7]], [-54/7, -54/7, 39/7, 39/7])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294004,"parameters":{"masses":[[18,49],[3,49],[24,49],[4,49]],"values":[-9,0,5,9],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,0,1,1],\"masses\":[[18,49],[3,49],[24,49],[4,49]],\"values\":[-9,0,5,9]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0005","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[12,49],[2,49],[30,49],[5,49]],\"values\":[-8,1,6,8],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 12/49, -8], [1, [1, 2], 32/49, 91/16], [2, [3], 5/49, 8]], [-8, 91/16, 91/16, 8])","explanation_zh":"Wave4第三層核對=([[0, [0], 12/49, -8], [1, [1, 2], 32/49, 91/16], [2, [3], 5/49, 8]], [-8, 91/16, 91/16, 8])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294005,"parameters":{"masses":[[12,49],[2,49],[30,49],[5,49]],"values":[-8,1,6,8],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[12,49],[2,49],[30,49],[5,49]],\"values\":[-8,1,6,8]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0006","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[30,49],[12,49],[5,49],[2,49]],\"values\":[-7,2,7,7],\"blocks\":[0,0,1,1]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 6/7, -31/7], [1, [2, 3], 1/7, 7]], [-31/7, -31/7, 7, 7])","explanation_zh":"Wave4第三層核對=([[0, [0, 1], 6/7, -31/7], [1, [2, 3], 1/7, 7]], [-31/7, -31/7, 7, 7])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294006,"parameters":{"masses":[[30,49],[12,49],[5,49],[2,49]],"values":[-7,2,7,7],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,0,1,1],\"masses\":[[30,49],[12,49],[5,49],[2,49]],\"values\":[-7,2,7,7]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0007","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[25,49],[10,49],[10,49],[4,49]],\"values\":[-6,3,8,6],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 25/49, -6], [1, [1, 2], 20/49, 11/2], [2, [3], 4/49, 6]], [-6, 11/2, 11/2, 6])","explanation_zh":"Wave4第三層核對=([[0, [0], 25/49, -6], [1, [1, 2], 20/49, 11/2], [2, [3], 4/49, 6]], [-6, 11/2, 11/2, 6])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294007,"parameters":{"masses":[[25,49],[10,49],[10,49],[4,49]],"values":[-6,3,8,6],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[25,49],[10,49],[10,49],[4,49]],\"values\":[-6,3,8,6]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0008","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[20,49],[8,49],[15,49],[6,49]],\"values\":[-5,-3,9,5],\"blocks\":[0,0,1,1]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 4/7, -31/7], [1, [2, 3], 3/7, 55/7]], [-31/7, -31/7, 55/7, 55/7])","explanation_zh":"Wave4第三層核對=([[0, [0, 1], 4/7, -31/7], [1, [2, 3], 3/7, 55/7]], [-31/7, -31/7, 55/7, 55/7])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294008,"parameters":{"masses":[[20,49],[8,49],[15,49],[6,49]],"values":[-5,-3,9,5],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,0,1,1],\"masses\":[[20,49],[8,49],[15,49],[6,49]],\"values\":[-5,-3,9,5]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0009","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[15,49],[6,49],[20,49],[8,49]],\"values\":[-4,-2,10,4],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 15/49, -4], [1, [1, 2], 26/49, 94/13], [2, [3], 8/49, 4]], [-4, 94/13, 94/13, 4])","explanation_zh":"Wave4第三層核對=([[0, [0], 15/49, -4], [1, [1, 2], 26/49, 94/13], [2, [3], 8/49, 4]], [-4, 94/13, 94/13, 4])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294009,"parameters":{"masses":[[15,49],[6,49],[20,49],[8,49]],"values":[-4,-2,10,4],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[15,49],[6,49],[20,49],[8,49]],\"values\":[-4,-2,10,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0010","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[10,49],[4,49],[25,49],[10,49]],\"values\":[-3,-1,11,3],\"blocks\":[0,0,1,1]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 2/7, -17/7], [1, [2, 3], 5/7, 61/7]], [-17/7, -17/7, 61/7, 61/7])","explanation_zh":"Wave4第三層核對=([[0, [0, 1], 2/7, -17/7], [1, [2, 3], 5/7, 61/7]], [-17/7, -17/7, 61/7, 61/7])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294010,"parameters":{"masses":[[10,49],[4,49],[25,49],[10,49]],"values":[-3,-1,11,3],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,0,1,1],\"masses\":[[10,49],[4,49],[25,49],[10,49]],\"values\":[-3,-1,11,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0011","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[24,49],[18,49],[4,49],[3,49]],\"values\":[-2,0,12,2],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 24/49, -2], [1, [1, 2], 22/49, 24/11], [2, [3], 3/49, 2]], [-2, 24/11, 24/11, 2])","explanation_zh":"Wave4第三層核對=([[0, [0], 24/49, -2], [1, [1, 2], 22/49, 24/11], [2, [3], 3/49, 2]], [-2, 24/11, 24/11, 2])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294011,"parameters":{"masses":[[24,49],[18,49],[4,49],[3,49]],"values":[-2,0,12,2],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[24,49],[18,49],[4,49],[3,49]],\"values\":[-2,0,12,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0012","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[20,49],[15,49],[8,49],[6,49]],\"values\":[-1,1,13,1],\"blocks\":[0,0,1,1]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 5/7, -1/7], [1, [2, 3], 2/7, 55/7]], [-1/7, -1/7, 55/7, 55/7])","explanation_zh":"Wave4第三層核對=([[0, [0, 1], 5/7, -1/7], [1, [2, 3], 2/7, 55/7]], [-1/7, -1/7, 55/7, 55/7])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294012,"parameters":{"masses":[[20,49],[15,49],[8,49],[6,49]],"values":[-1,1,13,1],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,0,1,1],\"masses\":[[20,49],[15,49],[8,49],[6,49]],\"values\":[-1,1,13,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0013","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[16,49],[12,49],[12,49],[9,49]],\"values\":[0,2,14,0],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 16/49, 0], [1, [1, 2], 24/49, 8], [2, [3], 9/49, 0]], [0, 8, 8, 0])","explanation_zh":"Wave4第三層核對=([[0, [0], 16/49, 0], [1, [1, 2], 24/49, 8], [2, [3], 9/49, 0]], [0, 8, 8, 0])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294013,"parameters":{"masses":[[16,49],[12,49],[12,49],[9,49]],"values":[0,2,14,0],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[16,49],[12,49],[12,49],[9,49]],\"values\":[0,2,14,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0014","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[12,49],[9,49],[16,49],[12,49]],\"values\":[1,3,15,-1],\"blocks\":[0,0,1,1]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/7, 13/7], [1, [2, 3], 4/7, 57/7]], [13/7, 13/7, 57/7, 57/7])","explanation_zh":"Wave4第三層核對=([[0, [0, 1], 3/7, 13/7], [1, [2, 3], 4/7, 57/7]], [13/7, 13/7, 57/7, 57/7])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294014,"parameters":{"masses":[[12,49],[9,49],[16,49],[12,49]],"values":[1,3,15,-1],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,0,1,1],\"masses\":[[12,49],[9,49],[16,49],[12,49]],\"values\":[1,3,15,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0015","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[8,49],[6,49],[20,49],[15,49]],\"values\":[2,-3,16,-2],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 8/49, 2], [1, [1, 2], 26/49, 151/13], [2, [3], 15/49, -2]], [2, 151/13, 151/13, -2])","explanation_zh":"Wave4第三層核對=([[0, [0], 8/49, 2], [1, [1, 2], 26/49, 151/13], [2, [3], 15/49, -2]], [2, 151/13, 151/13, -2])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294015,"parameters":{"masses":[[8,49],[6,49],[20,49],[15,49]],"values":[2,-3,16,-2],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[8,49],[6,49],[20,49],[15,49]],\"values\":[2,-3,16,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0016","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[18,49],[24,49],[3,49],[4,49]],\"values\":[3,-2,17,-3],\"blocks\":[0,0,1,1]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 6/7, 1/7], [1, [2, 3], 1/7, 39/7]], [1/7, 1/7, 39/7, 39/7])","explanation_zh":"Wave4第三層核對=([[0, [0, 1], 6/7, 1/7], [1, [2, 3], 1/7, 39/7]], [1/7, 1/7, 39/7, 39/7])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294016,"parameters":{"masses":[[18,49],[24,49],[3,49],[4,49]],"values":[3,-2,17,-3],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,0,1,1],\"masses\":[[18,49],[24,49],[3,49],[4,49]],\"values\":[3,-2,17,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0017","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[15,49],[20,49],[6,49],[8,49]],\"values\":[4,-1,18,-4],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 15/49, 4], [1, [1, 2], 26/49, 44/13], [2, [3], 8/49, -4]], [4, 44/13, 44/13, -4])","explanation_zh":"Wave4第三層核對=([[0, [0], 15/49, 4], [1, [1, 2], 26/49, 44/13], [2, [3], 8/49, -4]], [4, 44/13, 44/13, -4])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294017,"parameters":{"masses":[[15,49],[20,49],[6,49],[8,49]],"values":[4,-1,18,-4],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[15,49],[20,49],[6,49],[8,49]],\"values\":[4,-1,18,-4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0018","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[12,49],[16,49],[9,49],[12,49]],\"values\":[5,0,19,-5],\"blocks\":[0,0,1,1]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 4/7, 15/7], [1, [2, 3], 3/7, 37/7]], [15/7, 15/7, 37/7, 37/7])","explanation_zh":"Wave4第三層核對=([[0, [0, 1], 4/7, 15/7], [1, [2, 3], 3/7, 37/7]], [15/7, 15/7, 37/7, 37/7])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294018,"parameters":{"masses":[[12,49],[16,49],[9,49],[12,49]],"values":[5,0,19,-5],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,0,1,1],\"masses\":[[12,49],[16,49],[9,49],[12,49]],\"values\":[5,0,19,-5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0019","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[9,49],[12,49],[12,49],[16,49]],\"values\":[6,1,20,-6],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 9/49, 6], [1, [1, 2], 24/49, 21/2], [2, [3], 16/49, -6]], [6, 21/2, 21/2, -6])","explanation_zh":"Wave4第三層核對=([[0, [0], 9/49, 6], [1, [1, 2], 24/49, 21/2], [2, [3], 16/49, -6]], [6, 21/2, 21/2, -6])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294019,"parameters":{"masses":[[9,49],[12,49],[12,49],[16,49]],"values":[6,1,20,-6],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[9,49],[12,49],[12,49],[16,49]],\"values\":[6,1,20,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0020","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[6,49],[8,49],[15,49],[20,49]],\"values\":[7,2,21,-7],\"blocks\":[0,0,1,1]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 2/7, 29/7], [1, [2, 3], 5/7, 5]], [29/7, 29/7, 5, 5])","explanation_zh":"Wave4第三層核對=([[0, [0, 1], 2/7, 29/7], [1, [2, 3], 5/7, 5]], [29/7, 29/7, 5, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294020,"parameters":{"masses":[[6,49],[8,49],[15,49],[20,49]],"values":[7,2,21,-7],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,0,1,1],\"masses\":[[6,49],[8,49],[15,49],[20,49]],\"values\":[7,2,21,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0021","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[12,49],[30,49],[2,49],[5,49]],\"values\":[8,3,22,-8],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 12/49, 8], [1, [1, 2], 32/49, 67/16], [2, [3], 5/49, -8]], [8, 67/16, 67/16, -8])","explanation_zh":"Wave4第三層核對=([[0, [0], 12/49, 8], [1, [1, 2], 32/49, 67/16], [2, [3], 5/49, -8]], [8, 67/16, 67/16, -8])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294021,"parameters":{"masses":[[12,49],[30,49],[2,49],[5,49]],"values":[8,3,22,-8],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[12,49],[30,49],[2,49],[5,49]],\"values\":[8,3,22,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0022","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[10,49],[25,49],[4,49],[10,49]],\"values\":[9,-3,23,-9],\"blocks\":[0,0,1,1]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 5/7, 3/7], [1, [2, 3], 2/7, 1/7]], [3/7, 3/7, 1/7, 1/7])","explanation_zh":"Wave4第三層核對=([[0, [0, 1], 5/7, 3/7], [1, [2, 3], 2/7, 1/7]], [3/7, 3/7, 1/7, 1/7])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294022,"parameters":{"masses":[[10,49],[25,49],[4,49],[10,49]],"values":[9,-3,23,-9],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,0,1,1],\"masses\":[[10,49],[25,49],[4,49],[10,49]],\"values\":[9,-3,23,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0023","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[8,49],[20,49],[6,49],[15,49]],\"values\":[10,-2,24,-10],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 8/49, 10], [1, [1, 2], 26/49, 4], [2, [3], 15/49, -10]], [10, 4, 4, -10])","explanation_zh":"Wave4第三層核對=([[0, [0], 8/49, 10], [1, [1, 2], 26/49, 4], [2, [3], 15/49, -10]], [10, 4, 4, -10])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294023,"parameters":{"masses":[[8,49],[20,49],[6,49],[15,49]],"values":[10,-2,24,-10],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[8,49],[20,49],[6,49],[15,49]],\"values\":[10,-2,24,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0024","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[6,49],[15,49],[8,49],[20,49]],\"values\":[11,-1,25,-11],\"blocks\":[0,0,1,1]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/7, 17/7], [1, [2, 3], 4/7, -5/7]], [17/7, 17/7, -5/7, -5/7])","explanation_zh":"Wave4第三層核對=([[0, [0, 1], 3/7, 17/7], [1, [2, 3], 4/7, -5/7]], [17/7, 17/7, -5/7, -5/7])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294024,"parameters":{"masses":[[6,49],[15,49],[8,49],[20,49]],"values":[11,-1,25,-11],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,0,1,1],\"masses\":[[6,49],[15,49],[8,49],[20,49]],\"values\":[11,-1,25,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0025","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-values；資料={\"masses\":[[4,49],[10,49],[10,49],[25,49]],\"values\":[12,0,26,-12],\"blocks\":[0,1,1,2]}。請依 [block_summaries,conditional_values] 欄序回答。","answer":{"kind":"expression","value":"([[0, [0], 4/49, 12], [1, [1, 2], 20/49, 13], [2, [3], 25/49, -12]], [12, 13, 13, -12])","explanation_zh":"Wave4第三層核對=([[0, [0], 4/49, 12], [1, [1, 2], 20/49, 13], [2, [3], 25/49, -12]], [12, 13, 13, -12])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-values","seed":202610294025,"parameters":{"masses":[[4,49],[10,49],[10,49],[25,49]],"values":[12,0,26,-12],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-values","semantic_template":"qf-mod29-condexp-block-values/{\"blocks\":[0,1,1,2],\"masses\":[[4,49],[10,49],[10,49],[25,49]],\"values\":[12,0,26,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0026","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[36,49],[6,49],[6,49],[1,49]],\"values\":[-12,-3,2,12],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([-12, -1/2, -1/2, 12], [[0, [0], [-12], 是], [1, [1, 2], [-1/2], 是], [2, [3], [12], 是]], 是)","explanation_zh":"Wave4第三層核對=([-12, -1/2, -1/2, 12], [[0, [0], [-12], 是], [1, [1, 2], [-1/2], 是], [2, [3], [12], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294026,"parameters":{"masses":[[36,49],[6,49],[6,49],[1,49]],"values":[-12,-3,2,12],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[36,49],[6,49],[6,49],[1,49]],\"values\":[-12,-3,2,12]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0027","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[30,49],[5,49],[12,49],[2,49]],\"values\":[-11,-2,3,11],\"blocks\":[0,0,1,1]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([-68/7, -68/7, 29/7, 29/7], [[0, [0, 1], [-68/7], 是], [1, [2, 3], [29/7], 是]], 是)","explanation_zh":"Wave4第三層核對=([-68/7, -68/7, 29/7, 29/7], [[0, [0, 1], [-68/7], 是], [1, [2, 3], [29/7], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294027,"parameters":{"masses":[[30,49],[5,49],[12,49],[2,49]],"values":[-11,-2,3,11],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,0,1,1],\"masses\":[[30,49],[5,49],[12,49],[2,49]],\"values\":[-11,-2,3,11]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0028","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[24,49],[4,49],[18,49],[3,49]],\"values\":[-10,-1,4,10],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([-10, 34/11, 34/11, 10], [[0, [0], [-10], 是], [1, [1, 2], [34/11], 是], [2, [3], [10], 是]], 是)","explanation_zh":"Wave4第三層核對=([-10, 34/11, 34/11, 10], [[0, [0], [-10], 是], [1, [1, 2], [34/11], 是], [2, [3], [10], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294028,"parameters":{"masses":[[24,49],[4,49],[18,49],[3,49]],"values":[-10,-1,4,10],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[24,49],[4,49],[18,49],[3,49]],\"values\":[-10,-1,4,10]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0029","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[18,49],[3,49],[24,49],[4,49]],\"values\":[-9,0,5,9],\"blocks\":[0,0,1,1]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([-54/7, -54/7, 39/7, 39/7], [[0, [0, 1], [-54/7], 是], [1, [2, 3], [39/7], 是]], 是)","explanation_zh":"Wave4第三層核對=([-54/7, -54/7, 39/7, 39/7], [[0, [0, 1], [-54/7], 是], [1, [2, 3], [39/7], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294029,"parameters":{"masses":[[18,49],[3,49],[24,49],[4,49]],"values":[-9,0,5,9],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,0,1,1],\"masses\":[[18,49],[3,49],[24,49],[4,49]],\"values\":[-9,0,5,9]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0030","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[12,49],[2,49],[30,49],[5,49]],\"values\":[-8,1,6,8],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([-8, 91/16, 91/16, 8], [[0, [0], [-8], 是], [1, [1, 2], [91/16], 是], [2, [3], [8], 是]], 是)","explanation_zh":"Wave4第三層核對=([-8, 91/16, 91/16, 8], [[0, [0], [-8], 是], [1, [1, 2], [91/16], 是], [2, [3], [8], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294030,"parameters":{"masses":[[12,49],[2,49],[30,49],[5,49]],"values":[-8,1,6,8],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[12,49],[2,49],[30,49],[5,49]],\"values\":[-8,1,6,8]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0031","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[30,49],[12,49],[5,49],[2,49]],\"values\":[-7,2,7,7],\"blocks\":[0,0,1,1]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([-31/7, -31/7, 7, 7], [[0, [0, 1], [-31/7], 是], [1, [2, 3], [7], 是]], 是)","explanation_zh":"Wave4第三層核對=([-31/7, -31/7, 7, 7], [[0, [0, 1], [-31/7], 是], [1, [2, 3], [7], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294031,"parameters":{"masses":[[30,49],[12,49],[5,49],[2,49]],"values":[-7,2,7,7],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,0,1,1],\"masses\":[[30,49],[12,49],[5,49],[2,49]],\"values\":[-7,2,7,7]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0032","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[25,49],[10,49],[10,49],[4,49]],\"values\":[-6,3,8,6],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([-6, 11/2, 11/2, 6], [[0, [0], [-6], 是], [1, [1, 2], [11/2], 是], [2, [3], [6], 是]], 是)","explanation_zh":"Wave4第三層核對=([-6, 11/2, 11/2, 6], [[0, [0], [-6], 是], [1, [1, 2], [11/2], 是], [2, [3], [6], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294032,"parameters":{"masses":[[25,49],[10,49],[10,49],[4,49]],"values":[-6,3,8,6],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[25,49],[10,49],[10,49],[4,49]],\"values\":[-6,3,8,6]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0033","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[20,49],[8,49],[15,49],[6,49]],\"values\":[-5,-3,9,5],\"blocks\":[0,0,1,1]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([-31/7, -31/7, 55/7, 55/7], [[0, [0, 1], [-31/7], 是], [1, [2, 3], [55/7], 是]], 是)","explanation_zh":"Wave4第三層核對=([-31/7, -31/7, 55/7, 55/7], [[0, [0, 1], [-31/7], 是], [1, [2, 3], [55/7], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294033,"parameters":{"masses":[[20,49],[8,49],[15,49],[6,49]],"values":[-5,-3,9,5],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,0,1,1],\"masses\":[[20,49],[8,49],[15,49],[6,49]],\"values\":[-5,-3,9,5]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0034","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[15,49],[6,49],[20,49],[8,49]],\"values\":[-4,-2,10,4],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([-4, 94/13, 94/13, 4], [[0, [0], [-4], 是], [1, [1, 2], [94/13], 是], [2, [3], [4], 是]], 是)","explanation_zh":"Wave4第三層核對=([-4, 94/13, 94/13, 4], [[0, [0], [-4], 是], [1, [1, 2], [94/13], 是], [2, [3], [4], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294034,"parameters":{"masses":[[15,49],[6,49],[20,49],[8,49]],"values":[-4,-2,10,4],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[15,49],[6,49],[20,49],[8,49]],\"values\":[-4,-2,10,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0035","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[10,49],[4,49],[25,49],[10,49]],\"values\":[-3,-1,11,3],\"blocks\":[0,0,1,1]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([-17/7, -17/7, 61/7, 61/7], [[0, [0, 1], [-17/7], 是], [1, [2, 3], [61/7], 是]], 是)","explanation_zh":"Wave4第三層核對=([-17/7, -17/7, 61/7, 61/7], [[0, [0, 1], [-17/7], 是], [1, [2, 3], [61/7], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294035,"parameters":{"masses":[[10,49],[4,49],[25,49],[10,49]],"values":[-3,-1,11,3],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,0,1,1],\"masses\":[[10,49],[4,49],[25,49],[10,49]],\"values\":[-3,-1,11,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0036","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[24,49],[18,49],[4,49],[3,49]],\"values\":[-2,0,12,2],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([-2, 24/11, 24/11, 2], [[0, [0], [-2], 是], [1, [1, 2], [24/11], 是], [2, [3], [2], 是]], 是)","explanation_zh":"Wave4第三層核對=([-2, 24/11, 24/11, 2], [[0, [0], [-2], 是], [1, [1, 2], [24/11], 是], [2, [3], [2], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294036,"parameters":{"masses":[[24,49],[18,49],[4,49],[3,49]],"values":[-2,0,12,2],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[24,49],[18,49],[4,49],[3,49]],\"values\":[-2,0,12,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0037","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[20,49],[15,49],[8,49],[6,49]],\"values\":[-1,1,13,1],\"blocks\":[0,0,1,1]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([-1/7, -1/7, 55/7, 55/7], [[0, [0, 1], [-1/7], 是], [1, [2, 3], [55/7], 是]], 是)","explanation_zh":"Wave4第三層核對=([-1/7, -1/7, 55/7, 55/7], [[0, [0, 1], [-1/7], 是], [1, [2, 3], [55/7], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294037,"parameters":{"masses":[[20,49],[15,49],[8,49],[6,49]],"values":[-1,1,13,1],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,0,1,1],\"masses\":[[20,49],[15,49],[8,49],[6,49]],\"values\":[-1,1,13,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0038","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[16,49],[12,49],[12,49],[9,49]],\"values\":[0,2,14,0],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([0, 8, 8, 0], [[0, [0], [0], 是], [1, [1, 2], [8], 是], [2, [3], [0], 是]], 是)","explanation_zh":"Wave4第三層核對=([0, 8, 8, 0], [[0, [0], [0], 是], [1, [1, 2], [8], 是], [2, [3], [0], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294038,"parameters":{"masses":[[16,49],[12,49],[12,49],[9,49]],"values":[0,2,14,0],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[16,49],[12,49],[12,49],[9,49]],\"values\":[0,2,14,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0039","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[12,49],[9,49],[16,49],[12,49]],\"values\":[1,3,15,-1],\"blocks\":[0,0,1,1]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([13/7, 13/7, 57/7, 57/7], [[0, [0, 1], [13/7], 是], [1, [2, 3], [57/7], 是]], 是)","explanation_zh":"Wave4第三層核對=([13/7, 13/7, 57/7, 57/7], [[0, [0, 1], [13/7], 是], [1, [2, 3], [57/7], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294039,"parameters":{"masses":[[12,49],[9,49],[16,49],[12,49]],"values":[1,3,15,-1],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,0,1,1],\"masses\":[[12,49],[9,49],[16,49],[12,49]],\"values\":[1,3,15,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0040","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[8,49],[6,49],[20,49],[15,49]],\"values\":[2,-3,16,-2],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([2, 151/13, 151/13, -2], [[0, [0], [2], 是], [1, [1, 2], [151/13], 是], [2, [3], [-2], 是]], 是)","explanation_zh":"Wave4第三層核對=([2, 151/13, 151/13, -2], [[0, [0], [2], 是], [1, [1, 2], [151/13], 是], [2, [3], [-2], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294040,"parameters":{"masses":[[8,49],[6,49],[20,49],[15,49]],"values":[2,-3,16,-2],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[8,49],[6,49],[20,49],[15,49]],\"values\":[2,-3,16,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0041","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[18,49],[24,49],[3,49],[4,49]],\"values\":[3,-2,17,-3],\"blocks\":[0,0,1,1]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([1/7, 1/7, 39/7, 39/7], [[0, [0, 1], [1/7], 是], [1, [2, 3], [39/7], 是]], 是)","explanation_zh":"Wave4第三層核對=([1/7, 1/7, 39/7, 39/7], [[0, [0, 1], [1/7], 是], [1, [2, 3], [39/7], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294041,"parameters":{"masses":[[18,49],[24,49],[3,49],[4,49]],"values":[3,-2,17,-3],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,0,1,1],\"masses\":[[18,49],[24,49],[3,49],[4,49]],\"values\":[3,-2,17,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0042","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[15,49],[20,49],[6,49],[8,49]],\"values\":[4,-1,18,-4],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([4, 44/13, 44/13, -4], [[0, [0], [4], 是], [1, [1, 2], [44/13], 是], [2, [3], [-4], 是]], 是)","explanation_zh":"Wave4第三層核對=([4, 44/13, 44/13, -4], [[0, [0], [4], 是], [1, [1, 2], [44/13], 是], [2, [3], [-4], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294042,"parameters":{"masses":[[15,49],[20,49],[6,49],[8,49]],"values":[4,-1,18,-4],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[15,49],[20,49],[6,49],[8,49]],\"values\":[4,-1,18,-4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0043","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[12,49],[16,49],[9,49],[12,49]],\"values\":[5,0,19,-5],\"blocks\":[0,0,1,1]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([15/7, 15/7, 37/7, 37/7], [[0, [0, 1], [15/7], 是], [1, [2, 3], [37/7], 是]], 是)","explanation_zh":"Wave4第三層核對=([15/7, 15/7, 37/7, 37/7], [[0, [0, 1], [15/7], 是], [1, [2, 3], [37/7], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294043,"parameters":{"masses":[[12,49],[16,49],[9,49],[12,49]],"values":[5,0,19,-5],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,0,1,1],\"masses\":[[12,49],[16,49],[9,49],[12,49]],\"values\":[5,0,19,-5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0044","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[9,49],[12,49],[12,49],[16,49]],\"values\":[6,1,20,-6],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([6, 21/2, 21/2, -6], [[0, [0], [6], 是], [1, [1, 2], [21/2], 是], [2, [3], [-6], 是]], 是)","explanation_zh":"Wave4第三層核對=([6, 21/2, 21/2, -6], [[0, [0], [6], 是], [1, [1, 2], [21/2], 是], [2, [3], [-6], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294044,"parameters":{"masses":[[9,49],[12,49],[12,49],[16,49]],"values":[6,1,20,-6],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[9,49],[12,49],[12,49],[16,49]],\"values\":[6,1,20,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0045","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[6,49],[8,49],[15,49],[20,49]],\"values\":[7,2,21,-7],\"blocks\":[0,0,1,1]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([29/7, 29/7, 5, 5], [[0, [0, 1], [29/7], 是], [1, [2, 3], [5], 是]], 是)","explanation_zh":"Wave4第三層核對=([29/7, 29/7, 5, 5], [[0, [0, 1], [29/7], 是], [1, [2, 3], [5], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294045,"parameters":{"masses":[[6,49],[8,49],[15,49],[20,49]],"values":[7,2,21,-7],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,0,1,1],\"masses\":[[6,49],[8,49],[15,49],[20,49]],\"values\":[7,2,21,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0046","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[12,49],[30,49],[2,49],[5,49]],\"values\":[8,3,22,-8],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([8, 67/16, 67/16, -8], [[0, [0], [8], 是], [1, [1, 2], [67/16], 是], [2, [3], [-8], 是]], 是)","explanation_zh":"Wave4第三層核對=([8, 67/16, 67/16, -8], [[0, [0], [8], 是], [1, [1, 2], [67/16], 是], [2, [3], [-8], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294046,"parameters":{"masses":[[12,49],[30,49],[2,49],[5,49]],"values":[8,3,22,-8],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[12,49],[30,49],[2,49],[5,49]],\"values\":[8,3,22,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0047","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[10,49],[25,49],[4,49],[10,49]],\"values\":[9,-3,23,-9],\"blocks\":[0,0,1,1]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([3/7, 3/7, 1/7, 1/7], [[0, [0, 1], [3/7], 是], [1, [2, 3], [1/7], 是]], 是)","explanation_zh":"Wave4第三層核對=([3/7, 3/7, 1/7, 1/7], [[0, [0, 1], [3/7], 是], [1, [2, 3], [1/7], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294047,"parameters":{"masses":[[10,49],[25,49],[4,49],[10,49]],"values":[9,-3,23,-9],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,0,1,1],\"masses\":[[10,49],[25,49],[4,49],[10,49]],\"values\":[9,-3,23,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0048","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[8,49],[20,49],[6,49],[15,49]],\"values\":[10,-2,24,-10],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([10, 4, 4, -10], [[0, [0], [10], 是], [1, [1, 2], [4], 是], [2, [3], [-10], 是]], 是)","explanation_zh":"Wave4第三層核對=([10, 4, 4, -10], [[0, [0], [10], 是], [1, [1, 2], [4], 是], [2, [3], [-10], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294048,"parameters":{"masses":[[8,49],[20,49],[6,49],[15,49]],"values":[10,-2,24,-10],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[8,49],[20,49],[6,49],[15,49]],\"values\":[10,-2,24,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0049","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[6,49],[15,49],[8,49],[20,49]],\"values\":[11,-1,25,-11],\"blocks\":[0,0,1,1]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([17/7, 17/7, -5/7, -5/7], [[0, [0, 1], [17/7], 是], [1, [2, 3], [-5/7], 是]], 是)","explanation_zh":"Wave4第三層核對=([17/7, 17/7, -5/7, -5/7], [[0, [0, 1], [17/7], 是], [1, [2, 3], [-5/7], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294049,"parameters":{"masses":[[6,49],[15,49],[8,49],[20,49]],"values":[11,-1,25,-11],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,0,1,1],\"masses\":[[6,49],[15,49],[8,49],[20,49]],\"values\":[11,-1,25,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0050","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-measurability；資料={\"masses\":[[4,49],[10,49],[10,49],[25,49]],\"values\":[12,0,26,-12],\"blocks\":[0,1,1,2]}。請依 [conditional_values,block_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"([12, 13, 13, -12], [[0, [0], [12], 是], [1, [1, 2], [13], 是], [2, [3], [-12], 是]], 是)","explanation_zh":"Wave4第三層核對=([12, 13, 13, -12], [[0, [0], [12], 是], [1, [1, 2], [13], 是], [2, [3], [-12], 是]], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-measurability","seed":202610294050,"parameters":{"masses":[[4,49],[10,49],[10,49],[25,49]],"values":[12,0,26,-12],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-measurability","semantic_template":"qf-mod29-condexp-measurability/{\"blocks\":[0,1,1,2],\"masses\":[[4,49],[10,49],[10,49],[25,49]],\"values\":[12,0,26,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0051","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[36,49],[6,49],[6,49],[1,49]],\"values\":[-12,-3,2,12],\"blocks\":[0,1,1,2],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0], -432/49, -432/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0], -432/49, -432/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294051,"parameters":{"masses":[[36,49],[6,49],[6,49],[1,49]],"values":[-12,-3,2,12],"blocks":[0,1,1,2],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,1,1,2],\"masses\":[[36,49],[6,49],[6,49],[1,49]],\"values\":[-12,-3,2,12]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0052","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[30,49],[5,49],[12,49],[2,49]],\"values\":[-11,-2,3,11],\"blocks\":[0,0,1,1],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0, 1], -340/49, -340/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0, 1], -340/49, -340/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294052,"parameters":{"masses":[[30,49],[5,49],[12,49],[2,49]],"values":[-11,-2,3,11],"blocks":[0,0,1,1],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,0,1,1],\"masses\":[[30,49],[5,49],[12,49],[2,49]],\"values\":[-11,-2,3,11]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0053","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[24,49],[4,49],[18,49],[3,49]],\"values\":[-10,-1,4,10],\"blocks\":[0,1,1,2],\"block_label\":1}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2], 68/49, 68/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(1, [1, 2], 68/49, 68/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294053,"parameters":{"masses":[[24,49],[4,49],[18,49],[3,49]],"values":[-10,-1,4,10],"blocks":[0,1,1,2],"block_label":1,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":1,\"blocks\":[0,1,1,2],\"masses\":[[24,49],[4,49],[18,49],[3,49]],\"values\":[-10,-1,4,10]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0054","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[18,49],[3,49],[24,49],[4,49]],\"values\":[-9,0,5,9],\"blocks\":[0,0,1,1],\"block_label\":1}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [2, 3], 156/49, 156/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(1, [2, 3], 156/49, 156/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294054,"parameters":{"masses":[[18,49],[3,49],[24,49],[4,49]],"values":[-9,0,5,9],"blocks":[0,0,1,1],"block_label":1,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":1,\"blocks\":[0,0,1,1],\"masses\":[[18,49],[3,49],[24,49],[4,49]],\"values\":[-9,0,5,9]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0055","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[12,49],[2,49],[30,49],[5,49]],\"values\":[-8,1,6,8],\"blocks\":[0,1,1,2],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0], -96/49, -96/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0], -96/49, -96/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294055,"parameters":{"masses":[[12,49],[2,49],[30,49],[5,49]],"values":[-8,1,6,8],"blocks":[0,1,1,2],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,1,1,2],\"masses\":[[12,49],[2,49],[30,49],[5,49]],\"values\":[-8,1,6,8]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0056","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[30,49],[12,49],[5,49],[2,49]],\"values\":[-7,2,7,7],\"blocks\":[0,0,1,1],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0, 1], -186/49, -186/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0, 1], -186/49, -186/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294056,"parameters":{"masses":[[30,49],[12,49],[5,49],[2,49]],"values":[-7,2,7,7],"blocks":[0,0,1,1],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,0,1,1],\"masses\":[[30,49],[12,49],[5,49],[2,49]],\"values\":[-7,2,7,7]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0057","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[25,49],[10,49],[10,49],[4,49]],\"values\":[-6,3,8,6],\"blocks\":[0,1,1,2],\"block_label\":1}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2], 110/49, 110/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(1, [1, 2], 110/49, 110/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294057,"parameters":{"masses":[[25,49],[10,49],[10,49],[4,49]],"values":[-6,3,8,6],"blocks":[0,1,1,2],"block_label":1,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":1,\"blocks\":[0,1,1,2],\"masses\":[[25,49],[10,49],[10,49],[4,49]],\"values\":[-6,3,8,6]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0058","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[20,49],[8,49],[15,49],[6,49]],\"values\":[-5,-3,9,5],\"blocks\":[0,0,1,1],\"block_label\":1}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [2, 3], 165/49, 165/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(1, [2, 3], 165/49, 165/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294058,"parameters":{"masses":[[20,49],[8,49],[15,49],[6,49]],"values":[-5,-3,9,5],"blocks":[0,0,1,1],"block_label":1,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":1,\"blocks\":[0,0,1,1],\"masses\":[[20,49],[8,49],[15,49],[6,49]],\"values\":[-5,-3,9,5]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0059","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[15,49],[6,49],[20,49],[8,49]],\"values\":[-4,-2,10,4],\"blocks\":[0,1,1,2],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0], -60/49, -60/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0], -60/49, -60/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294059,"parameters":{"masses":[[15,49],[6,49],[20,49],[8,49]],"values":[-4,-2,10,4],"blocks":[0,1,1,2],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,1,1,2],\"masses\":[[15,49],[6,49],[20,49],[8,49]],\"values\":[-4,-2,10,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0060","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[10,49],[4,49],[25,49],[10,49]],\"values\":[-3,-1,11,3],\"blocks\":[0,0,1,1],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0, 1], -34/49, -34/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0, 1], -34/49, -34/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294060,"parameters":{"masses":[[10,49],[4,49],[25,49],[10,49]],"values":[-3,-1,11,3],"blocks":[0,0,1,1],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,0,1,1],\"masses\":[[10,49],[4,49],[25,49],[10,49]],\"values\":[-3,-1,11,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0061","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[24,49],[18,49],[4,49],[3,49]],\"values\":[-2,0,12,2],\"blocks\":[0,1,1,2],\"block_label\":1}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2], 48/49, 48/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(1, [1, 2], 48/49, 48/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294061,"parameters":{"masses":[[24,49],[18,49],[4,49],[3,49]],"values":[-2,0,12,2],"blocks":[0,1,1,2],"block_label":1,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":1,\"blocks\":[0,1,1,2],\"masses\":[[24,49],[18,49],[4,49],[3,49]],\"values\":[-2,0,12,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0062","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[20,49],[15,49],[8,49],[6,49]],\"values\":[-1,1,13,1],\"blocks\":[0,0,1,1],\"block_label\":1}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [2, 3], 110/49, 110/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(1, [2, 3], 110/49, 110/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294062,"parameters":{"masses":[[20,49],[15,49],[8,49],[6,49]],"values":[-1,1,13,1],"blocks":[0,0,1,1],"block_label":1,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":1,\"blocks\":[0,0,1,1],\"masses\":[[20,49],[15,49],[8,49],[6,49]],\"values\":[-1,1,13,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0063","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[16,49],[12,49],[12,49],[9,49]],\"values\":[0,2,14,0],\"blocks\":[0,1,1,2],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0], 0, 0, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0], 0, 0, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294063,"parameters":{"masses":[[16,49],[12,49],[12,49],[9,49]],"values":[0,2,14,0],"blocks":[0,1,1,2],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,1,1,2],\"masses\":[[16,49],[12,49],[12,49],[9,49]],\"values\":[0,2,14,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0064","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[12,49],[9,49],[16,49],[12,49]],\"values\":[1,3,15,-1],\"blocks\":[0,0,1,1],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0, 1], 39/49, 39/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0, 1], 39/49, 39/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294064,"parameters":{"masses":[[12,49],[9,49],[16,49],[12,49]],"values":[1,3,15,-1],"blocks":[0,0,1,1],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,0,1,1],\"masses\":[[12,49],[9,49],[16,49],[12,49]],\"values\":[1,3,15,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0065","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[8,49],[6,49],[20,49],[15,49]],\"values\":[2,-3,16,-2],\"blocks\":[0,1,1,2],\"block_label\":1}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2], 302/49, 302/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(1, [1, 2], 302/49, 302/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294065,"parameters":{"masses":[[8,49],[6,49],[20,49],[15,49]],"values":[2,-3,16,-2],"blocks":[0,1,1,2],"block_label":1,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":1,\"blocks\":[0,1,1,2],\"masses\":[[8,49],[6,49],[20,49],[15,49]],\"values\":[2,-3,16,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0066","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[18,49],[24,49],[3,49],[4,49]],\"values\":[3,-2,17,-3],\"blocks\":[0,0,1,1],\"block_label\":1}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [2, 3], 39/49, 39/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(1, [2, 3], 39/49, 39/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294066,"parameters":{"masses":[[18,49],[24,49],[3,49],[4,49]],"values":[3,-2,17,-3],"blocks":[0,0,1,1],"block_label":1,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":1,\"blocks\":[0,0,1,1],\"masses\":[[18,49],[24,49],[3,49],[4,49]],\"values\":[3,-2,17,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0067","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[15,49],[20,49],[6,49],[8,49]],\"values\":[4,-1,18,-4],\"blocks\":[0,1,1,2],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0], 60/49, 60/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0], 60/49, 60/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294067,"parameters":{"masses":[[15,49],[20,49],[6,49],[8,49]],"values":[4,-1,18,-4],"blocks":[0,1,1,2],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,1,1,2],\"masses\":[[15,49],[20,49],[6,49],[8,49]],\"values\":[4,-1,18,-4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0068","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[12,49],[16,49],[9,49],[12,49]],\"values\":[5,0,19,-5],\"blocks\":[0,0,1,1],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0, 1], 60/49, 60/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0, 1], 60/49, 60/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294068,"parameters":{"masses":[[12,49],[16,49],[9,49],[12,49]],"values":[5,0,19,-5],"blocks":[0,0,1,1],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,0,1,1],\"masses\":[[12,49],[16,49],[9,49],[12,49]],\"values\":[5,0,19,-5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0069","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[9,49],[12,49],[12,49],[16,49]],\"values\":[6,1,20,-6],\"blocks\":[0,1,1,2],\"block_label\":1}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2], 36/7, 36/7, 是, positive_block)","explanation_zh":"Wave4第三層核對=(1, [1, 2], 36/7, 36/7, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294069,"parameters":{"masses":[[9,49],[12,49],[12,49],[16,49]],"values":[6,1,20,-6],"blocks":[0,1,1,2],"block_label":1,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":1,\"blocks\":[0,1,1,2],\"masses\":[[9,49],[12,49],[12,49],[16,49]],\"values\":[6,1,20,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0070","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[6,49],[8,49],[15,49],[20,49]],\"values\":[7,2,21,-7],\"blocks\":[0,0,1,1],\"block_label\":1}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [2, 3], 25/7, 25/7, 是, positive_block)","explanation_zh":"Wave4第三層核對=(1, [2, 3], 25/7, 25/7, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294070,"parameters":{"masses":[[6,49],[8,49],[15,49],[20,49]],"values":[7,2,21,-7],"blocks":[0,0,1,1],"block_label":1,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":1,\"blocks\":[0,0,1,1],\"masses\":[[6,49],[8,49],[15,49],[20,49]],\"values\":[7,2,21,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0071","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[12,49],[30,49],[2,49],[5,49]],\"values\":[8,3,22,-8],\"blocks\":[0,1,1,2],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0], 96/49, 96/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0], 96/49, 96/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294071,"parameters":{"masses":[[12,49],[30,49],[2,49],[5,49]],"values":[8,3,22,-8],"blocks":[0,1,1,2],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,1,1,2],\"masses\":[[12,49],[30,49],[2,49],[5,49]],\"values\":[8,3,22,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0072","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[10,49],[25,49],[4,49],[10,49]],\"values\":[9,-3,23,-9],\"blocks\":[0,0,1,1],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0, 1], 15/49, 15/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0, 1], 15/49, 15/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294072,"parameters":{"masses":[[10,49],[25,49],[4,49],[10,49]],"values":[9,-3,23,-9],"blocks":[0,0,1,1],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,0,1,1],\"masses\":[[10,49],[25,49],[4,49],[10,49]],\"values\":[9,-3,23,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0073","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[8,49],[20,49],[6,49],[15,49]],\"values\":[10,-2,24,-10],\"blocks\":[0,1,1,2],\"block_label\":1}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2], 104/49, 104/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(1, [1, 2], 104/49, 104/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294073,"parameters":{"masses":[[8,49],[20,49],[6,49],[15,49]],"values":[10,-2,24,-10],"blocks":[0,1,1,2],"block_label":1,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":1,\"blocks\":[0,1,1,2],\"masses\":[[8,49],[20,49],[6,49],[15,49]],\"values\":[10,-2,24,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0074","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[6,49],[15,49],[8,49],[20,49]],\"values\":[11,-1,25,-11],\"blocks\":[0,0,1,1],\"block_label\":1}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [2, 3], -20/49, -20/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(1, [2, 3], -20/49, -20/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294074,"parameters":{"masses":[[6,49],[15,49],[8,49],[20,49]],"values":[11,-1,25,-11],"blocks":[0,0,1,1],"block_label":1,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":1,\"blocks\":[0,0,1,1],\"masses\":[[6,49],[15,49],[8,49],[20,49]],\"values\":[11,-1,25,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0075","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-block-integral；資料={\"masses\":[[4,49],[10,49],[10,49],[25,49]],\"values\":[12,0,26,-12],\"blocks\":[0,1,1,2],\"block_label\":0}。請依 [block_label,indices,original_integral,conditional_integral,equal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0], 48/49, 48/49, 是, positive_block)","explanation_zh":"Wave4第三層核對=(0, [0], 48/49, 48/49, 是, positive_block)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-block-integral","seed":202610294075,"parameters":{"masses":[[4,49],[10,49],[10,49],[25,49]],"values":[12,0,26,-12],"blocks":[0,1,1,2],"block_label":0,"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-block-integral","semantic_template":"qf-mod29-condexp-block-integral/{\"block_label\":0,\"blocks\":[0,1,1,2],\"masses\":[[4,49],[10,49],[10,49],[25,49]],\"values\":[12,0,26,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0076","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[36,49],[6,49],[6,49],[1,49]],\"values\":[-12,-3,2,12],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-426/49, -426/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(-426/49, -426/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294076,"parameters":{"masses":[[36,49],[6,49],[6,49],[1,49]],"values":[-12,-3,2,12],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[36,49],[6,49],[6,49],[1,49]],\"values\":[-12,-3,2,12]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0077","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[30,49],[5,49],[12,49],[2,49]],\"values\":[-11,-2,3,11],\"blocks\":[0,0,1,1]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-282/49, -282/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(-282/49, -282/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294077,"parameters":{"masses":[[30,49],[5,49],[12,49],[2,49]],"values":[-11,-2,3,11],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,0,1,1],\"masses\":[[30,49],[5,49],[12,49],[2,49]],\"values\":[-11,-2,3,11]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0078","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[24,49],[4,49],[18,49],[3,49]],\"values\":[-10,-1,4,10],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-142/49, -142/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(-142/49, -142/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294078,"parameters":{"masses":[[24,49],[4,49],[18,49],[3,49]],"values":[-10,-1,4,10],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[24,49],[4,49],[18,49],[3,49]],\"values\":[-10,-1,4,10]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0079","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[18,49],[3,49],[24,49],[4,49]],\"values\":[-9,0,5,9],\"blocks\":[0,0,1,1]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-6/49, -6/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(-6/49, -6/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294079,"parameters":{"masses":[[18,49],[3,49],[24,49],[4,49]],"values":[-9,0,5,9],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,0,1,1],\"masses\":[[18,49],[3,49],[24,49],[4,49]],\"values\":[-9,0,5,9]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0080","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[12,49],[2,49],[30,49],[5,49]],\"values\":[-8,1,6,8],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(18/7, 18/7, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(18/7, 18/7, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294080,"parameters":{"masses":[[12,49],[2,49],[30,49],[5,49]],"values":[-8,1,6,8],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[12,49],[2,49],[30,49],[5,49]],\"values\":[-8,1,6,8]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0081","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[30,49],[12,49],[5,49],[2,49]],\"values\":[-7,2,7,7],\"blocks\":[0,0,1,1]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-137/49, -137/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(-137/49, -137/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294081,"parameters":{"masses":[[30,49],[12,49],[5,49],[2,49]],"values":[-7,2,7,7],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,0,1,1],\"masses\":[[30,49],[12,49],[5,49],[2,49]],\"values\":[-7,2,7,7]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0082","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[25,49],[10,49],[10,49],[4,49]],\"values\":[-6,3,8,6],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-16/49, -16/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(-16/49, -16/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294082,"parameters":{"masses":[[25,49],[10,49],[10,49],[4,49]],"values":[-6,3,8,6],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[25,49],[10,49],[10,49],[4,49]],\"values\":[-6,3,8,6]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0083","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[20,49],[8,49],[15,49],[6,49]],\"values\":[-5,-3,9,5],\"blocks\":[0,0,1,1]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(41/49, 41/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(41/49, 41/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294083,"parameters":{"masses":[[20,49],[8,49],[15,49],[6,49]],"values":[-5,-3,9,5],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,0,1,1],\"masses\":[[20,49],[8,49],[15,49],[6,49]],\"values\":[-5,-3,9,5]}"}},"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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0084","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[15,49],[6,49],[20,49],[8,49]],\"values\":[-4,-2,10,4],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(160/49, 160/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(160/49, 160/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294084,"parameters":{"masses":[[15,49],[6,49],[20,49],[8,49]],"values":[-4,-2,10,4],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[15,49],[6,49],[20,49],[8,49]],\"values\":[-4,-2,10,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0085","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[10,49],[4,49],[25,49],[10,49]],\"values\":[-3,-1,11,3],\"blocks\":[0,0,1,1]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(271/49, 271/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(271/49, 271/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294085,"parameters":{"masses":[[10,49],[4,49],[25,49],[10,49]],"values":[-3,-1,11,3],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,0,1,1],\"masses\":[[10,49],[4,49],[25,49],[10,49]],\"values\":[-3,-1,11,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0086","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[24,49],[18,49],[4,49],[3,49]],\"values\":[-2,0,12,2],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(6/49, 6/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(6/49, 6/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294086,"parameters":{"masses":[[24,49],[18,49],[4,49],[3,49]],"values":[-2,0,12,2],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[24,49],[18,49],[4,49],[3,49]],\"values\":[-2,0,12,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0087","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[20,49],[15,49],[8,49],[6,49]],\"values\":[-1,1,13,1],\"blocks\":[0,0,1,1]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(15/7, 15/7, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(15/7, 15/7, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294087,"parameters":{"masses":[[20,49],[15,49],[8,49],[6,49]],"values":[-1,1,13,1],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,0,1,1],\"masses\":[[20,49],[15,49],[8,49],[6,49]],\"values\":[-1,1,13,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0088","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[16,49],[12,49],[12,49],[9,49]],\"values\":[0,2,14,0],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(192/49, 192/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(192/49, 192/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294088,"parameters":{"masses":[[16,49],[12,49],[12,49],[9,49]],"values":[0,2,14,0],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[16,49],[12,49],[12,49],[9,49]],\"values\":[0,2,14,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0089","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[12,49],[9,49],[16,49],[12,49]],\"values\":[1,3,15,-1],\"blocks\":[0,0,1,1]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(267/49, 267/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(267/49, 267/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294089,"parameters":{"masses":[[12,49],[9,49],[16,49],[12,49]],"values":[1,3,15,-1],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,0,1,1],\"masses\":[[12,49],[9,49],[16,49],[12,49]],\"values\":[1,3,15,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0090","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[8,49],[6,49],[20,49],[15,49]],\"values\":[2,-3,16,-2],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(288/49, 288/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(288/49, 288/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294090,"parameters":{"masses":[[8,49],[6,49],[20,49],[15,49]],"values":[2,-3,16,-2],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[8,49],[6,49],[20,49],[15,49]],\"values\":[2,-3,16,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0091","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[18,49],[24,49],[3,49],[4,49]],\"values\":[3,-2,17,-3],\"blocks\":[0,0,1,1]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(45/49, 45/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(45/49, 45/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294091,"parameters":{"masses":[[18,49],[24,49],[3,49],[4,49]],"values":[3,-2,17,-3],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,0,1,1],\"masses\":[[18,49],[24,49],[3,49],[4,49]],\"values\":[3,-2,17,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0092","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[15,49],[20,49],[6,49],[8,49]],\"values\":[4,-1,18,-4],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(116/49, 116/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(116/49, 116/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294092,"parameters":{"masses":[[15,49],[20,49],[6,49],[8,49]],"values":[4,-1,18,-4],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[15,49],[20,49],[6,49],[8,49]],\"values\":[4,-1,18,-4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0093","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[12,49],[16,49],[9,49],[12,49]],\"values\":[5,0,19,-5],\"blocks\":[0,0,1,1]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(171/49, 171/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(171/49, 171/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294093,"parameters":{"masses":[[12,49],[16,49],[9,49],[12,49]],"values":[5,0,19,-5],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,0,1,1],\"masses\":[[12,49],[16,49],[9,49],[12,49]],\"values\":[5,0,19,-5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0094","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[9,49],[12,49],[12,49],[16,49]],\"values\":[6,1,20,-6],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(30/7, 30/7, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(30/7, 30/7, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294094,"parameters":{"masses":[[9,49],[12,49],[12,49],[16,49]],"values":[6,1,20,-6],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[9,49],[12,49],[12,49],[16,49]],\"values\":[6,1,20,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0095","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[6,49],[8,49],[15,49],[20,49]],\"values\":[7,2,21,-7],\"blocks\":[0,0,1,1]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(233/49, 233/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(233/49, 233/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294095,"parameters":{"masses":[[6,49],[8,49],[15,49],[20,49]],"values":[7,2,21,-7],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,0,1,1],\"masses\":[[6,49],[8,49],[15,49],[20,49]],\"values\":[7,2,21,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0096","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[12,49],[30,49],[2,49],[5,49]],\"values\":[8,3,22,-8],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(190/49, 190/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(190/49, 190/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294096,"parameters":{"masses":[[12,49],[30,49],[2,49],[5,49]],"values":[8,3,22,-8],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[12,49],[30,49],[2,49],[5,49]],\"values\":[8,3,22,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0097","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[10,49],[25,49],[4,49],[10,49]],\"values\":[9,-3,23,-9],\"blocks\":[0,0,1,1]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(17/49, 17/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(17/49, 17/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294097,"parameters":{"masses":[[10,49],[25,49],[4,49],[10,49]],"values":[9,-3,23,-9],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,0,1,1],\"masses\":[[10,49],[25,49],[4,49],[10,49]],\"values\":[9,-3,23,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0098","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[8,49],[20,49],[6,49],[15,49]],\"values\":[10,-2,24,-10],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(34/49, 34/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(34/49, 34/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294098,"parameters":{"masses":[[8,49],[20,49],[6,49],[15,49]],"values":[10,-2,24,-10],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[8,49],[20,49],[6,49],[15,49]],\"values\":[10,-2,24,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0099","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[6,49],[15,49],[8,49],[20,49]],\"values\":[11,-1,25,-11],\"blocks\":[0,0,1,1]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(31/49, 31/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(31/49, 31/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294099,"parameters":{"masses":[[6,49],[15,49],[8,49],[20,49]],"values":[11,-1,25,-11],"blocks":[0,0,1,1],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,0,1,1],\"masses\":[[6,49],[15,49],[8,49],[20,49]],\"values\":[11,-1,25,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r04-conditional-expectation-0100","batch_id":"batch-20261014-advance-20261029-r04-conditional-expectation-foundations","language":"zh-Hant","source_mko_ids":["mko-conditional-expectation"],"title_zh":"有限條件期望","stem_zh":"X機率law與conditioning partition綁同一有限空間。操作=condexp-total-expectation；資料={\"masses\":[[4,49],[10,49],[10,49],[25,49]],\"values\":[12,0,26,-12],\"blocks\":[0,1,1,2]}。請依 [E_X,E_conditional,equal,certificate] 欄序回答。","answer":{"kind":"expression","value":"(8/49, 8/49, 是, tower_to_trivial_sigma_algebra)","explanation_zh":"Wave4第三層核對=(8/49, 8/49, 是, tower_to_trivial_sigma_algebra)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；結果block可測並保持每個正質量block積分；零質量block只a.s.決定且不得除以零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限條件期望"]},"variant":{"family_id":"qf-mod29-condexp-total-expectation","seed":202610294100,"parameters":{"masses":[[4,49],[10,49],[10,49],[25,49]],"values":[12,0,26,-12],"blocks":[0,1,1,2],"domain":"Exact_finite_partition_conditional_expectation","operation":"condexp-total-expectation","semantic_template":"qf-mod29-condexp-total-expectation/{\"blocks\":[0,1,1,2],\"masses\":[[4,49],[10,49],[10,49],[25,49]],\"values\":[12,0,26,-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、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}