{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0001","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-12,-12,-12,-12],[-11,-12,-12,-12]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [[1, 0, [0, 1], [-11, -12]]], [[0, 0, -47/4, [-12], 否]], 否)","explanation_zh":"Wave4第四層核對=([], [[1, 0, [0, 1], [-11, -12]]], [[0, 0, -47/4, [-12], 否]], 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303001,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-12,-12,-12,-12],[-11,-12,-12,-12]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-12,-12,-12,-12],[-11,-12,-12,-12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0002","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-11,-11,-11,-11],[-11,-11,-11,-11]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, -11, [-11], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, -11, [-11], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303002,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-11,-11,-11,-11],[-11,-11,-11,-11]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-11,-11,-11,-11],[-11,-11,-11,-11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0003","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-10,-10,-10,-10],[-10,-10,-10,-10]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, -10, [-10], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, -10, [-10], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303003,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-10,-10,-10,-10],[-10,-10,-10,-10]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-10,-10,-10,-10],[-10,-10,-10,-10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0004","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-9,-9,-9,-9],[-9,-9,-9,-9]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, -9, [-9], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, -9, [-9], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303004,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-9,-9,-9,-9],[-9,-9,-9,-9]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-9,-9,-9,-9],[-9,-9,-9,-9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0005","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-8,-8,-8,-8],[-8,-8,-8,-8]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, -8, [-8], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, -8, [-8], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303005,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-8,-8,-8,-8],[-8,-8,-8,-8]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-8,-8,-8,-8],[-8,-8,-8,-8]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0006","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-7,-7,-7,-7],[-6,-7,-7,-7]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [[1, 0, [0, 1], [-6, -7]]], [[0, 0, -27/4, [-7], 否]], 否)","explanation_zh":"Wave4第四層核對=([], [[1, 0, [0, 1], [-6, -7]]], [[0, 0, -27/4, [-7], 否]], 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303006,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-7,-7,-7,-7],[-6,-7,-7,-7]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-7,-7,-7,-7],[-6,-7,-7,-7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0007","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-6,-6,-6,-6],[-6,-6,-6,-6]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, -6, [-6], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, -6, [-6], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303007,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-6,-6,-6,-6],[-6,-6,-6,-6]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-6,-6,-6,-6],[-6,-6,-6,-6]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0008","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-5,-5,-5,-5],[-5,-5,-5,-5]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, -5, [-5], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, -5, [-5], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303008,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-5,-5,-5,-5],[-5,-5,-5,-5]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-5,-5,-5,-5],[-5,-5,-5,-5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0009","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-4,-4,-4,-4],[-4,-4,-4,-4]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, -4, [-4], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, -4, [-4], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303009,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-4,-4,-4,-4],[-4,-4,-4,-4]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-4,-4,-4,-4],[-4,-4,-4,-4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0010","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-3,-3,-3,-3],[-3,-3,-3,-3]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, -3, [-3], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, -3, [-3], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303010,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-3,-3,-3,-3],[-3,-3,-3,-3]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-3,-3,-3,-3],[-3,-3,-3,-3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0011","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-2,-2,-2,-2],[-1,-2,-2,-2]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [[1, 0, [0, 1], [-1, -2]]], [[0, 0, -7/4, [-2], 否]], 否)","explanation_zh":"Wave4第四層核對=([], [[1, 0, [0, 1], [-1, -2]]], [[0, 0, -7/4, [-2], 否]], 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303011,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-2,-2,-2,-2],[-1,-2,-2,-2]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-2,-2,-2,-2],[-1,-2,-2,-2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0012","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-1,-1,-1,-1],[-1,-1,-1,-1]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, -1, [-1], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, -1, [-1], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303012,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-1,-1,-1,-1],[-1,-1,-1,-1]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-1,-1,-1,-1],[-1,-1,-1,-1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0013","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[0,0,0,0],[0,0,0,0]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, 0, [0], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, 0, [0], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303013,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[0,0,0,0],[0,0,0,0]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[0,0,0,0],[0,0,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0014","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[1,1,1,1],[1,1,1,1]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, 1, [1], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, 1, [1], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303014,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[1,1,1,1],[1,1,1,1]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[1,1,1,1],[1,1,1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0015","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[2,2,2,2],[2,2,2,2]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, 2, [2], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, 2, [2], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303015,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[2,2,2,2],[2,2,2,2]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[2,2,2,2],[2,2,2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0016","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[3,3,3,3],[4,3,3,3]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [[1, 0, [0, 1], [4, 3]]], [[0, 0, 13/4, [3], 否]], 否)","explanation_zh":"Wave4第四層核對=([], [[1, 0, [0, 1], [4, 3]]], [[0, 0, 13/4, [3], 否]], 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303016,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[3,3,3,3],[4,3,3,3]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[3,3,3,3],[4,3,3,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0017","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[4,4,4,4],[4,4,4,4]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, 4, [4], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, 4, [4], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303017,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[4,4,4,4],[4,4,4,4]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[4,4,4,4],[4,4,4,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0018","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[5,5,5,5],[5,5,5,5]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, 5, [5], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, 5, [5], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303018,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[5,5,5,5],[5,5,5,5]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[5,5,5,5],[5,5,5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0019","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[6,6,6,6],[6,6,6,6]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, 6, [6], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, 6, [6], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303019,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[6,6,6,6],[6,6,6,6]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[6,6,6,6],[6,6,6,6]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0020","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[7,7,7,7],[7,7,7,7]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, 7, [7], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, 7, [7], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303020,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[7,7,7,7],[7,7,7,7]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[7,7,7,7],[7,7,7,7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0021","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[8,8,8,8],[9,8,8,8]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [[1, 0, [0, 1], [9, 8]]], [[0, 0, 33/4, [8], 否]], 否)","explanation_zh":"Wave4第四層核對=([], [[1, 0, [0, 1], [9, 8]]], [[0, 0, 33/4, [8], 否]], 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303021,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[8,8,8,8],[9,8,8,8]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[8,8,8,8],[9,8,8,8]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0022","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[9,9,9,9],[9,9,9,9]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, 9, [9], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, 9, [9], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303022,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[9,9,9,9],[9,9,9,9]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[9,9,9,9],[9,9,9,9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0023","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[10,10,10,10],[10,10,10,10]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, 10, [10], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, 10, [10], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303023,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[10,10,10,10],[10,10,10,10]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[10,10,10,10],[10,10,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0024","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[11,11,11,11],[11,11,11,11]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, 11, [11], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, 11, [11], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303024,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[11,11,11,11],[11,11,11,11]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[11,11,11,11],[11,11,11,11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0025","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-qualification；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[12,12,12,12],[12,12,12,12]]}。請依 [nesting_failures,adaptedness_failures,conditional_steps,martingale] 欄序回答。","answer":{"kind":"expression","value":"([], [], [[0, 0, 12, [12], 是]], 是)","explanation_zh":"Wave4第四層核對=([], [], [[0, 0, 12, [12], 是]], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-qualification","seed":202610303025,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[12,12,12,12],[12,12,12,12]],"domain":"Exact_finite_partition_martingale","operation":"martingale-qualification","semantic_template":"qf-mod30-martingale-qualification/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[12,12,12,12],[12,12,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0026","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-12,-12,-12,-12],[-12,-12,-12,-12]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303026,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-12,-12,-12,-12],[-12,-12,-12,-12]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-12,-12,-12,-12],[-12,-12,-12,-12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0027","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-11,-11,-11,-11],[-11,-11,-11,-11]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303027,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-11,-11,-11,-11],[-11,-11,-11,-11]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-11,-11,-11,-11],[-11,-11,-11,-11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0028","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-10,-10,-10,-10],[-10,-10,-10,-10]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303028,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-10,-10,-10,-10],[-10,-10,-10,-10]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-10,-10,-10,-10],[-10,-10,-10,-10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0029","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-9,-9,-9,-9],[-9,-9,-9,-9]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303029,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-9,-9,-9,-9],[-9,-9,-9,-9]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-9,-9,-9,-9],[-9,-9,-9,-9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0030","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-8,-8,-8,-8],[-8,-8,-8,-8]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303030,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-8,-8,-8,-8],[-8,-8,-8,-8]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-8,-8,-8,-8],[-8,-8,-8,-8]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0031","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-7,-7,-7,-7],[-7,-7,-7,-7]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303031,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-7,-7,-7,-7],[-7,-7,-7,-7]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-7,-7,-7,-7],[-7,-7,-7,-7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0032","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-6,-6,-6,-6],[-6,-6,-6,-6]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303032,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-6,-6,-6,-6],[-6,-6,-6,-6]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-6,-6,-6,-6],[-6,-6,-6,-6]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0033","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-5,-5,-5,-5],[-5,-5,-5,-5]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303033,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-5,-5,-5,-5],[-5,-5,-5,-5]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-5,-5,-5,-5],[-5,-5,-5,-5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0034","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-4,-4,-4,-4],[-4,-4,-4,-4]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303034,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-4,-4,-4,-4],[-4,-4,-4,-4]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-4,-4,-4,-4],[-4,-4,-4,-4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0035","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-3,-3,-3,-3],[-3,-3,-3,-3]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303035,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-3,-3,-3,-3],[-3,-3,-3,-3]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-3,-3,-3,-3],[-3,-3,-3,-3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0036","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-2,-2,-2,-2],[-2,-2,-2,-2]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303036,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-2,-2,-2,-2],[-2,-2,-2,-2]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-2,-2,-2,-2],[-2,-2,-2,-2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0037","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-1,-1,-1,-1],[-1,-1,-1,-1]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303037,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-1,-1,-1,-1],[-1,-1,-1,-1]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-1,-1,-1,-1],[-1,-1,-1,-1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0038","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[0,0,0,0],[0,0,0,0]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303038,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[0,0,0,0],[0,0,0,0]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[0,0,0,0],[0,0,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0039","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[1,1,1,1],[1,1,1,1]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303039,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[1,1,1,1],[1,1,1,1]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[1,1,1,1],[1,1,1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0040","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[2,2,2,2],[2,2,2,2]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303040,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[2,2,2,2],[2,2,2,2]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[2,2,2,2],[2,2,2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0041","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[3,3,3,3],[3,3,3,3]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303041,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[3,3,3,3],[3,3,3,3]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[3,3,3,3],[3,3,3,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0042","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[4,4,4,4],[4,4,4,4]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303042,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[4,4,4,4],[4,4,4,4]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[4,4,4,4],[4,4,4,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0043","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[5,5,5,5],[5,5,5,5]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303043,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[5,5,5,5],[5,5,5,5]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[5,5,5,5],[5,5,5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0044","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[6,6,6,6],[6,6,6,6]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303044,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[6,6,6,6],[6,6,6,6]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[6,6,6,6],[6,6,6,6]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0045","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[7,7,7,7],[7,7,7,7]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303045,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[7,7,7,7],[7,7,7,7]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[7,7,7,7],[7,7,7,7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0046","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[8,8,8,8],[8,8,8,8]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303046,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[8,8,8,8],[8,8,8,8]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[8,8,8,8],[8,8,8,8]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0047","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[9,9,9,9],[9,9,9,9]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303047,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[9,9,9,9],[9,9,9,9]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[9,9,9,9],[9,9,9,9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0048","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[10,10,10,10],[10,10,10,10]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303048,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[10,10,10,10],[10,10,10,10]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[10,10,10,10],[10,10,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0049","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[11,11,11,11],[11,11,11,11]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303049,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[11,11,11,11],[11,11,11,11]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[11,11,11,11],[11,11,11,11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0050","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-adaptedness；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[12,12,12,12],[12,12,12,12]]}。請依 [nesting_failures,adaptedness_failures,adapted] 欄序回答。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"Wave4第四層核對=([], [], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-adaptedness","seed":202610303050,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[12,12,12,12],[12,12,12,12]],"domain":"Exact_finite_partition_martingale","operation":"martingale-adaptedness","semantic_template":"qf-mod30-martingale-adaptedness/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[12,12,12,12],[12,12,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0051","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-12,-12,-12,-12],[-12,-12,-12,-12]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, -12, [-12], 是)","explanation_zh":"Wave4第四層核對=(0, 0, -12, [-12], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303051,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-12,-12,-12,-12],[-12,-12,-12,-12]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-12,-12,-12,-12],[-12,-12,-12,-12]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0052","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-11,-11,-11,-11],[-11,-11,-11,-11]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, -11, [-11], 是)","explanation_zh":"Wave4第四層核對=(0, 0, -11, [-11], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303052,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-11,-11,-11,-11],[-11,-11,-11,-11]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-11,-11,-11,-11],[-11,-11,-11,-11]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0053","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-10,-10,-10,-10],[-10,-10,-10,-10]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, -10, [-10], 是)","explanation_zh":"Wave4第四層核對=(0, 0, -10, [-10], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303053,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-10,-10,-10,-10],[-10,-10,-10,-10]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-10,-10,-10,-10],[-10,-10,-10,-10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0054","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-9,-9,-9,-9],[-9,-9,-9,-9]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, -9, [-9], 是)","explanation_zh":"Wave4第四層核對=(0, 0, -9, [-9], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303054,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-9,-9,-9,-9],[-9,-9,-9,-9]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-9,-9,-9,-9],[-9,-9,-9,-9]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0055","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-8,-8,-8,-8],[-8,-8,-8,-8]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, -8, [-8], 是)","explanation_zh":"Wave4第四層核對=(0, 0, -8, [-8], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303055,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-8,-8,-8,-8],[-8,-8,-8,-8]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-8,-8,-8,-8],[-8,-8,-8,-8]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0056","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-7,-7,-7,-7],[-7,-7,-7,-7]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, -7, [-7], 是)","explanation_zh":"Wave4第四層核對=(0, 0, -7, [-7], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303056,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-7,-7,-7,-7],[-7,-7,-7,-7]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-7,-7,-7,-7],[-7,-7,-7,-7]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0057","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-6,-6,-6,-6],[-6,-6,-6,-6]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, -6, [-6], 是)","explanation_zh":"Wave4第四層核對=(0, 0, -6, [-6], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303057,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-6,-6,-6,-6],[-6,-6,-6,-6]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-6,-6,-6,-6],[-6,-6,-6,-6]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0058","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-5,-5,-5,-5],[-5,-5,-5,-5]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, -5, [-5], 是)","explanation_zh":"Wave4第四層核對=(0, 0, -5, [-5], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303058,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-5,-5,-5,-5],[-5,-5,-5,-5]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-5,-5,-5,-5],[-5,-5,-5,-5]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0059","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-4,-4,-4,-4],[-4,-4,-4,-4]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, -4, [-4], 是)","explanation_zh":"Wave4第四層核對=(0, 0, -4, [-4], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303059,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-4,-4,-4,-4],[-4,-4,-4,-4]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-4,-4,-4,-4],[-4,-4,-4,-4]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0060","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-3,-3,-3,-3],[-3,-3,-3,-3]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, -3, [-3], 是)","explanation_zh":"Wave4第四層核對=(0, 0, -3, [-3], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303060,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-3,-3,-3,-3],[-3,-3,-3,-3]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-3,-3,-3,-3],[-3,-3,-3,-3]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0061","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-2,-2,-2,-2],[-2,-2,-2,-2]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, -2, [-2], 是)","explanation_zh":"Wave4第四層核對=(0, 0, -2, [-2], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303061,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-2,-2,-2,-2],[-2,-2,-2,-2]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-2,-2,-2,-2],[-2,-2,-2,-2]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0062","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-1,-1,-1,-1],[-1,-1,-1,-1]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, -1, [-1], 是)","explanation_zh":"Wave4第四層核對=(0, 0, -1, [-1], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303062,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-1,-1,-1,-1],[-1,-1,-1,-1]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-1,-1,-1,-1],[-1,-1,-1,-1]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0063","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[0,0,0,0],[0,0,0,0]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 0, [0], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 0, [0], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303063,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[0,0,0,0],[0,0,0,0]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[0,0,0,0],[0,0,0,0]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0064","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[1,1,1,1],[1,1,1,1]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 1, [1], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 1, [1], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303064,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[1,1,1,1],[1,1,1,1]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[1,1,1,1],[1,1,1,1]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0065","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[2,2,2,2],[2,2,2,2]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 2, [2], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 2, [2], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303065,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[2,2,2,2],[2,2,2,2]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[2,2,2,2],[2,2,2,2]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0066","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[3,3,3,3],[3,3,3,3]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 3, [3], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 3, [3], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303066,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[3,3,3,3],[3,3,3,3]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[3,3,3,3],[3,3,3,3]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0067","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[4,4,4,4],[4,4,4,4]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 4, [4], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 4, [4], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303067,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[4,4,4,4],[4,4,4,4]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[4,4,4,4],[4,4,4,4]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0068","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[5,5,5,5],[5,5,5,5]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 5, [5], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 5, [5], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303068,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[5,5,5,5],[5,5,5,5]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[5,5,5,5],[5,5,5,5]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0069","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[6,6,6,6],[6,6,6,6]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 6, [6], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 6, [6], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303069,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[6,6,6,6],[6,6,6,6]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[6,6,6,6],[6,6,6,6]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0070","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[7,7,7,7],[7,7,7,7]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 7, [7], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 7, [7], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303070,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[7,7,7,7],[7,7,7,7]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[7,7,7,7],[7,7,7,7]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0071","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[8,8,8,8],[8,8,8,8]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 8, [8], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 8, [8], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303071,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[8,8,8,8],[8,8,8,8]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[8,8,8,8],[8,8,8,8]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0072","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[9,9,9,9],[9,9,9,9]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 9, [9], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 9, [9], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303072,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[9,9,9,9],[9,9,9,9]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[9,9,9,9],[9,9,9,9]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0073","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[10,10,10,10],[10,10,10,10]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 10, [10], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 10, [10], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303073,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[10,10,10,10],[10,10,10,10]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[10,10,10,10],[10,10,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0074","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[11,11,11,11],[11,11,11,11]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 11, [11], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 11, [11], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303074,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[11,11,11,11],[11,11,11,11]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[11,11,11,11],[11,11,11,11]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0075","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-conditional-step；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[12,12,12,12],[12,12,12,12]],\"time\":0,\"block_label\":0}。請依 [time,block_label,conditional_mean,current_values,pass] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 12, [12], 是)","explanation_zh":"Wave4第四層核對=(0, 0, 12, [12], 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-conditional-step","seed":202610303075,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[12,12,12,12],[12,12,12,12]],"time":0,"block_label":0,"domain":"Exact_finite_partition_martingale","operation":"martingale-conditional-step","semantic_template":"qf-mod30-martingale-conditional-step/{\"block_label\":0,\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[12,12,12,12],[12,12,12,12]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0076","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-12,-12,-12,-12],[-12,-12,-12,-12]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([-12, -12], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([-12, -12], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303076,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-12,-12,-12,-12],[-12,-12,-12,-12]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-12,-12,-12,-12],[-12,-12,-12,-12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0077","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-11,-11,-11,-11],[-11,-11,-11,-11]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([-11, -11], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([-11, -11], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303077,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-11,-11,-11,-11],[-11,-11,-11,-11]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-11,-11,-11,-11],[-11,-11,-11,-11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0078","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-10,-10,-10,-10],[-10,-10,-10,-10]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([-10, -10], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([-10, -10], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303078,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-10,-10,-10,-10],[-10,-10,-10,-10]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-10,-10,-10,-10],[-10,-10,-10,-10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0079","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-9,-9,-9,-9],[-9,-9,-9,-9]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([-9, -9], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([-9, -9], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303079,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-9,-9,-9,-9],[-9,-9,-9,-9]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-9,-9,-9,-9],[-9,-9,-9,-9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0080","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-8,-8,-8,-8],[-8,-8,-8,-8]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([-8, -8], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([-8, -8], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303080,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-8,-8,-8,-8],[-8,-8,-8,-8]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-8,-8,-8,-8],[-8,-8,-8,-8]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0081","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-7,-7,-7,-7],[-7,-7,-7,-7]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([-7, -7], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([-7, -7], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303081,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-7,-7,-7,-7],[-7,-7,-7,-7]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-7,-7,-7,-7],[-7,-7,-7,-7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0082","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-6,-6,-6,-6],[-6,-6,-6,-6]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([-6, -6], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([-6, -6], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303082,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-6,-6,-6,-6],[-6,-6,-6,-6]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-6,-6,-6,-6],[-6,-6,-6,-6]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0083","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-5,-5,-5,-5],[-5,-5,-5,-5]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([-5, -5], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([-5, -5], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303083,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-5,-5,-5,-5],[-5,-5,-5,-5]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-5,-5,-5,-5],[-5,-5,-5,-5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0084","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-4,-4,-4,-4],[-4,-4,-4,-4]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([-4, -4], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([-4, -4], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303084,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-4,-4,-4,-4],[-4,-4,-4,-4]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-4,-4,-4,-4],[-4,-4,-4,-4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0085","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-3,-3,-3,-3],[-3,-3,-3,-3]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([-3, -3], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([-3, -3], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303085,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-3,-3,-3,-3],[-3,-3,-3,-3]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-3,-3,-3,-3],[-3,-3,-3,-3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0086","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-2,-2,-2,-2],[-2,-2,-2,-2]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([-2, -2], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([-2, -2], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303086,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-2,-2,-2,-2],[-2,-2,-2,-2]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-2,-2,-2,-2],[-2,-2,-2,-2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0087","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-1,-1,-1,-1],[-1,-1,-1,-1]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([-1, -1], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([-1, -1], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303087,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[-1,-1,-1,-1],[-1,-1,-1,-1]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[-1,-1,-1,-1],[-1,-1,-1,-1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0088","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[0,0,0,0],[0,0,0,0]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 0], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([0, 0], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303088,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[0,0,0,0],[0,0,0,0]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[0,0,0,0],[0,0,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0089","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[1,1,1,1],[1,1,1,1]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 1], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([1, 1], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303089,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[1,1,1,1],[1,1,1,1]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[1,1,1,1],[1,1,1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0090","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[2,2,2,2],[2,2,2,2]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([2, 2], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([2, 2], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303090,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[2,2,2,2],[2,2,2,2]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[2,2,2,2],[2,2,2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0091","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[3,3,3,3],[3,3,3,3]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 3], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([3, 3], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303091,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[3,3,3,3],[3,3,3,3]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[3,3,3,3],[3,3,3,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0092","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[4,4,4,4],[4,4,4,4]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([4, 4], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([4, 4], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303092,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[4,4,4,4],[4,4,4,4]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[4,4,4,4],[4,4,4,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0093","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[5,5,5,5],[5,5,5,5]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([5, 5], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([5, 5], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303093,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[5,5,5,5],[5,5,5,5]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[5,5,5,5],[5,5,5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0094","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[6,6,6,6],[6,6,6,6]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([6, 6], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([6, 6], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303094,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[6,6,6,6],[6,6,6,6]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[6,6,6,6],[6,6,6,6]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0095","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[7,7,7,7],[7,7,7,7]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([7, 7], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([7, 7], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303095,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[7,7,7,7],[7,7,7,7]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[7,7,7,7],[7,7,7,7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0096","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[8,8,8,8],[8,8,8,8]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([8, 8], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([8, 8], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303096,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[8,8,8,8],[8,8,8,8]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[8,8,8,8],[8,8,8,8]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0097","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[9,9,9,9],[9,9,9,9]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([9, 9], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([9, 9], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303097,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[9,9,9,9],[9,9,9,9]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[9,9,9,9],[9,9,9,9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0098","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[10,10,10,10],[10,10,10,10]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([10, 10], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([10, 10], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303098,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[10,10,10,10],[10,10,10,10]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[10,10,10,10],[10,10,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0099","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[11,11,11,11],[11,11,11,11]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([11, 11], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([11, 11], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303099,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[11,11,11,11],[11,11,11,11]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[11,11,11,11],[11,11,11,11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r03-martingale-0100","batch_id":"batch-20261014-advance-20261030-r03-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"有限Martingale","stem_zh":"同一有限probability space filtration與process。操作=martingale-expectation-invariant；資料={\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[12,12,12,12],[12,12,12,12]]}。請依 [expectations,invariant,boundary] 欄序回答。","answer":{"kind":"expression","value":"([12, 12], 是, expectation_invariance_is_consequence_not_definition)","explanation_zh":"Wave4第四層核對=([12, 12], 是, expectation_invariance_is_consequence_not_definition)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；逐時核adapted integrable及conditional expectation等式；零質量block只a.s.且不推出Markov stopping或convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限Martingale"]},"variant":{"family_id":"qf-mod30-martingale-expectation-invariant","seed":202610303100,"parameters":{"masses":[[1,4],[1,4],[1,4],[1,4]],"partitions":[[0,0,0,0],[0,0,1,1]],"process_values":[[12,12,12,12],[12,12,12,12]],"domain":"Exact_finite_partition_martingale","operation":"martingale-expectation-invariant","semantic_template":"qf-mod30-martingale-expectation-invariant/{\"masses\":[[1,4],[1,4],[1,4],[1,4]],\"partitions\":[[0,0,0,0],[0,0,1,1]],\"process_values\":[[12,12,12,12],[12,12,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}