{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0001","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":1}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [1, -1], [-1, 1], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [1, -1], [-1, 1], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317001,"parameters":{"amplitude":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0002","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":2}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [2, -2], [-2, 2], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [2, -2], [-2, 2], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317002,"parameters":{"amplitude":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0003","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":3}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [3, -3], [-3, 3], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [3, -3], [-3, 3], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317003,"parameters":{"amplitude":3,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0004","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":4}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [4, -4], [-4, 4], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [4, -4], [-4, 4], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317004,"parameters":{"amplitude":4,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0005","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":5}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [5, -5], [-5, 5], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [5, -5], [-5, 5], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317005,"parameters":{"amplitude":5,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0006","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":6}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [6, -6], [-6, 6], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [6, -6], [-6, 6], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317006,"parameters":{"amplitude":6,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0007","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":7}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [7, -7], [-7, 7], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [7, -7], [-7, 7], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317007,"parameters":{"amplitude":7,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0008","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":8}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [8, -8], [-8, 8], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [8, -8], [-8, 8], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317008,"parameters":{"amplitude":8,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0009","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":9}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [9, -9], [-9, 9], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [9, -9], [-9, 9], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317009,"parameters":{"amplitude":9,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":9}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0010","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":10}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [10, -10], [-10, 10], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [10, -10], [-10, 10], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317010,"parameters":{"amplitude":10,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":10}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0011","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":11}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [11, -11], [-11, 11], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [11, -11], [-11, 11], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317011,"parameters":{"amplitude":11,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":11}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0012","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":12}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [12, -12], [-12, 12], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [12, -12], [-12, 12], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317012,"parameters":{"amplitude":12,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":12}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0013","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":13}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [13, -13], [-13, 13], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [13, -13], [-13, 13], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317013,"parameters":{"amplitude":13,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":13}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0014","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":14}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [14, -14], [-14, 14], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [14, -14], [-14, 14], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317014,"parameters":{"amplitude":14,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":14}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0015","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":15}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [15, -15], [-15, 15], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [15, -15], [-15, 15], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317015,"parameters":{"amplitude":15,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":15}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0016","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":16}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [16, -16], [-16, 16], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [16, -16], [-16, 16], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317016,"parameters":{"amplitude":16,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":16}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0017","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":17}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [17, -17], [-17, 17], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [17, -17], [-17, 17], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317017,"parameters":{"amplitude":17,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":17}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0018","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":18}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [18, -18], [-18, 18], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [18, -18], [-18, 18], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317018,"parameters":{"amplitude":18,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":18}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0019","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":19}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [19, -19], [-19, 19], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [19, -19], [-19, 19], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317019,"parameters":{"amplitude":19,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":19}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0020","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":20}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [20, -20], [-20, 20], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [20, -20], [-20, 20], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317020,"parameters":{"amplitude":20,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":20}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0021","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":21}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [21, -21], [-21, 21], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [21, -21], [-21, 21], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317021,"parameters":{"amplitude":21,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":21}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0022","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":22}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [22, -22], [-22, 22], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [22, -22], [-22, 22], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317022,"parameters":{"amplitude":22,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":22}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0023","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":23}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [23, -23], [-23, 23], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [23, -23], [-23, 23], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317023,"parameters":{"amplitude":23,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":23}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0024","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":24}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [24, -24], [-24, 24], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [24, -24], [-24, 24], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317024,"parameters":{"amplitude":24,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":24}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0025","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-constant-expectation-counterexample；資料={\"amplitude\":25}。請依 [X0,X1,X2,expectations,martingale,reason] 欄序回答。","answer":{"kind":"expression","value":"(0, [25, -25], [-25, 25], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)","explanation_zh":"Wave4收束核對=(0, [25, -25], [-25, 25], [0, 0, 0], 否, constant_expectations_do_not_imply_conditional_martingale_steps)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-constant-expectation-counterexample","seed":202610317025,"parameters":{"amplitude":25,"domain":"Exact_finite_martingale_construction","operation":"martdeep-constant-expectation-counterexample","semantic_template":"qf-mod31-martdeep-constant-expectation-counterexample/{\"amplitude\":25}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0026","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[1,-1,2,-2],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [1, -1], 0], [1, [2, -2], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [1, -1], 0], [1, [2, -2], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317026,"parameters":{"increments":[1,-1,2,-2],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[1,-1,2,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0027","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[2,-2,3,-3],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [2, -2], 0], [1, [3, -3], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [2, -2], 0], [1, [3, -3], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317027,"parameters":{"increments":[2,-2,3,-3],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[2,-2,3,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0028","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[3,-3,4,-4],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [3, -3], 0], [1, [4, -4], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [3, -3], 0], [1, [4, -4], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317028,"parameters":{"increments":[3,-3,4,-4],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[3,-3,4,-4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0029","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[4,-4,5,-5],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [4, -4], 0], [1, [5, -5], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [4, -4], 0], [1, [5, -5], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317029,"parameters":{"increments":[4,-4,5,-5],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[4,-4,5,-5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0030","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[5,-5,6,-6],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [5, -5], 0], [1, [6, -6], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [5, -5], 0], [1, [6, -6], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317030,"parameters":{"increments":[5,-5,6,-6],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[5,-5,6,-6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0031","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[6,-6,7,-7],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [6, -6], 0], [1, [7, -7], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [6, -6], 0], [1, [7, -7], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317031,"parameters":{"increments":[6,-6,7,-7],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[6,-6,7,-7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0032","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[7,-7,8,-8],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [7, -7], 0], [1, [8, -8], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [7, -7], 0], [1, [8, -8], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317032,"parameters":{"increments":[7,-7,8,-8],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[7,-7,8,-8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0033","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[8,-8,9,-9],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [8, -8], 0], [1, [9, -9], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [8, -8], 0], [1, [9, -9], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317033,"parameters":{"increments":[8,-8,9,-9],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[8,-8,9,-9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0034","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[9,-9,10,-10],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [9, -9], 0], [1, [10, -10], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [9, -9], 0], [1, [10, -10], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317034,"parameters":{"increments":[9,-9,10,-10],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[9,-9,10,-10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0035","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[10,-10,11,-11],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [10, -10], 0], [1, [11, -11], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [10, -10], 0], [1, [11, -11], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317035,"parameters":{"increments":[10,-10,11,-11],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[10,-10,11,-11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0036","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[11,-11,12,-12],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [11, -11], 0], [1, [12, -12], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [11, -11], 0], [1, [12, -12], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317036,"parameters":{"increments":[11,-11,12,-12],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[11,-11,12,-12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0037","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[12,-12,13,-13],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [12, -12], 0], [1, [13, -13], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [12, -12], 0], [1, [13, -13], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317037,"parameters":{"increments":[12,-12,13,-13],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[12,-12,13,-13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0038","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[13,-13,14,-14],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [13, -13], 0], [1, [14, -14], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [13, -13], 0], [1, [14, -14], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317038,"parameters":{"increments":[13,-13,14,-14],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[13,-13,14,-14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0039","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[14,-14,15,-15],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [14, -14], 0], [1, [15, -15], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [14, -14], 0], [1, [15, -15], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317039,"parameters":{"increments":[14,-14,15,-15],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[14,-14,15,-15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0040","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[15,-15,16,-16],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [15, -15], 0], [1, [16, -16], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [15, -15], 0], [1, [16, -16], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317040,"parameters":{"increments":[15,-15,16,-16],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[15,-15,16,-16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0041","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[16,-16,17,-17],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [16, -16], 0], [1, [17, -17], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [16, -16], 0], [1, [17, -17], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317041,"parameters":{"increments":[16,-16,17,-17],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[16,-16,17,-17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0042","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[17,-17,18,-18],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [17, -17], 0], [1, [18, -18], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [17, -17], 0], [1, [18, -18], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317042,"parameters":{"increments":[17,-17,18,-18],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[17,-17,18,-18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0043","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[18,-18,19,-19],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [18, -18], 0], [1, [19, -19], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [18, -18], 0], [1, [19, -19], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317043,"parameters":{"increments":[18,-18,19,-19],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[18,-18,19,-19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0044","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[19,-19,20,-20],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [19, -19], 0], [1, [20, -20], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [19, -19], 0], [1, [20, -20], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317044,"parameters":{"increments":[19,-19,20,-20],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[19,-19,20,-20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0045","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[20,-20,21,-21],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [20, -20], 0], [1, [21, -21], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [20, -20], 0], [1, [21, -21], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317045,"parameters":{"increments":[20,-20,21,-21],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[20,-20,21,-21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0046","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[21,-21,22,-22],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [21, -21], 0], [1, [22, -22], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [21, -21], 0], [1, [22, -22], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317046,"parameters":{"increments":[21,-21,22,-22],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[21,-21,22,-22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0047","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[22,-22,23,-23],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [22, -22], 0], [1, [23, -23], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [22, -22], 0], [1, [23, -23], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317047,"parameters":{"increments":[22,-22,23,-23],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[22,-22,23,-23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0048","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[23,-23,24,-24],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [23, -23], 0], [1, [24, -24], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [23, -23], 0], [1, [24, -24], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317048,"parameters":{"increments":[23,-23,24,-24],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[23,-23,24,-24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0049","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[24,-24,25,-25],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [24, -24], 0], [1, [25, -25], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [24, -24], 0], [1, [25, -25], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317049,"parameters":{"increments":[24,-24,25,-25],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[24,-24,25,-25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0050","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-difference-mean；資料={\"increments\":[25,-25,26,-26],\"blocks\":[0,0,1,1]}。請依 [conditional_rows,all_zero,classification] 欄序回答。","answer":{"kind":"expression","value":"([[0, [25, -25], 0], [1, [26, -26], 0]], 是, conditional_mean_zero_difference)","explanation_zh":"Wave4收束核對=([[0, [25, -25], 0], [1, [26, -26], 0]], 是, conditional_mean_zero_difference)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-difference-mean","seed":202610317050,"parameters":{"increments":[25,-25,26,-26],"blocks":[0,0,1,1],"domain":"Exact_finite_martingale_construction","operation":"martdeep-difference-mean","semantic_template":"qf-mod31-martdeep-difference-mean/{\"blocks\":[0,0,1,1],\"increments\":[25,-25,26,-26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0051","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":-12,\"terminal\":[-13,-11,-12,-12],\"scale\":-2,\"shift\":3}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-12, [-13, -11, -12, -12], -2, 3, 27, [29, 25, 27, 27], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(-12, [-13, -11, -12, -12], -2, 3, 27, [29, 25, 27, 27], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317051,"parameters":{"initial":-12,"terminal":[-13,-11,-12,-12],"scale":-2,"shift":3,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":-12,\"scale\":-2,\"shift\":3,\"terminal\":[-13,-11,-12,-12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0052","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":-11,\"terminal\":[-12,-10,-11,-11],\"scale\":-1,\"shift\":4}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-11, [-12, -10, -11, -11], -1, 4, 15, [16, 14, 15, 15], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(-11, [-12, -10, -11, -11], -1, 4, 15, [16, 14, 15, 15], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317052,"parameters":{"initial":-11,"terminal":[-12,-10,-11,-11],"scale":-1,"shift":4,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":-11,\"scale\":-1,\"shift\":4,\"terminal\":[-12,-10,-11,-11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0053","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":-10,\"terminal\":[-11,-9,-10,-10],\"scale\":0,\"shift\":5}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-10, [-11, -9, -10, -10], 0, 5, 5, [5, 5, 5, 5], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(-10, [-11, -9, -10, -10], 0, 5, 5, [5, 5, 5, 5], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317053,"parameters":{"initial":-10,"terminal":[-11,-9,-10,-10],"scale":0,"shift":5,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":-10,\"scale\":0,\"shift\":5,\"terminal\":[-11,-9,-10,-10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0054","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":-9,\"terminal\":[-10,-8,-9,-9],\"scale\":1,\"shift\":6}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-9, [-10, -8, -9, -9], 1, 6, -3, [-4, -2, -3, -3], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(-9, [-10, -8, -9, -9], 1, 6, -3, [-4, -2, -3, -3], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317054,"parameters":{"initial":-9,"terminal":[-10,-8,-9,-9],"scale":1,"shift":6,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":-9,\"scale\":1,\"shift\":6,\"terminal\":[-10,-8,-9,-9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0055","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":-8,\"terminal\":[-9,-7,-8,-8],\"scale\":2,\"shift\":7}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-8, [-9, -7, -8, -8], 2, 7, -9, [-11, -7, -9, -9], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(-8, [-9, -7, -8, -8], 2, 7, -9, [-11, -7, -9, -9], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317055,"parameters":{"initial":-8,"terminal":[-9,-7,-8,-8],"scale":2,"shift":7,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":-8,\"scale\":2,\"shift\":7,\"terminal\":[-9,-7,-8,-8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0056","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":-7,\"terminal\":[-8,-6,-7,-7],\"scale\":-2,\"shift\":8}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-7, [-8, -6, -7, -7], -2, 8, 22, [24, 20, 22, 22], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(-7, [-8, -6, -7, -7], -2, 8, 22, [24, 20, 22, 22], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317056,"parameters":{"initial":-7,"terminal":[-8,-6,-7,-7],"scale":-2,"shift":8,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":-7,\"scale\":-2,\"shift\":8,\"terminal\":[-8,-6,-7,-7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0057","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":-6,\"terminal\":[-7,-5,-6,-6],\"scale\":-1,\"shift\":9}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-6, [-7, -5, -6, -6], -1, 9, 15, [16, 14, 15, 15], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(-6, [-7, -5, -6, -6], -1, 9, 15, [16, 14, 15, 15], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317057,"parameters":{"initial":-6,"terminal":[-7,-5,-6,-6],"scale":-1,"shift":9,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":-6,\"scale\":-1,\"shift\":9,\"terminal\":[-7,-5,-6,-6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0058","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":-5,\"terminal\":[-6,-4,-5,-5],\"scale\":0,\"shift\":10}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-5, [-6, -4, -5, -5], 0, 10, 10, [10, 10, 10, 10], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(-5, [-6, -4, -5, -5], 0, 10, 10, [10, 10, 10, 10], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317058,"parameters":{"initial":-5,"terminal":[-6,-4,-5,-5],"scale":0,"shift":10,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":-5,\"scale\":0,\"shift\":10,\"terminal\":[-6,-4,-5,-5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0059","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":-4,\"terminal\":[-5,-3,-4,-4],\"scale\":1,\"shift\":11}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-4, [-5, -3, -4, -4], 1, 11, 7, [6, 8, 7, 7], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(-4, [-5, -3, -4, -4], 1, 11, 7, [6, 8, 7, 7], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317059,"parameters":{"initial":-4,"terminal":[-5,-3,-4,-4],"scale":1,"shift":11,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":-4,\"scale\":1,\"shift\":11,\"terminal\":[-5,-3,-4,-4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0060","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":-3,\"terminal\":[-4,-2,-3,-3],\"scale\":2,\"shift\":12}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-3, [-4, -2, -3, -3], 2, 12, 6, [4, 8, 6, 6], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(-3, [-4, -2, -3, -3], 2, 12, 6, [4, 8, 6, 6], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317060,"parameters":{"initial":-3,"terminal":[-4,-2,-3,-3],"scale":2,"shift":12,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":-3,\"scale\":2,\"shift\":12,\"terminal\":[-4,-2,-3,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0061","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":-2,\"terminal\":[-3,-1,-2,-2],\"scale\":-2,\"shift\":13}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-2, [-3, -1, -2, -2], -2, 13, 17, [19, 15, 17, 17], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(-2, [-3, -1, -2, -2], -2, 13, 17, [19, 15, 17, 17], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317061,"parameters":{"initial":-2,"terminal":[-3,-1,-2,-2],"scale":-2,"shift":13,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":-2,\"scale\":-2,\"shift\":13,\"terminal\":[-3,-1,-2,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0062","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":-1,\"terminal\":[-2,0,-1,-1],\"scale\":-1,\"shift\":14}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(-1, [-2, 0, -1, -1], -1, 14, 15, [16, 14, 15, 15], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(-1, [-2, 0, -1, -1], -1, 14, 15, [16, 14, 15, 15], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317062,"parameters":{"initial":-1,"terminal":[-2,0,-1,-1],"scale":-1,"shift":14,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":-1,\"scale\":-1,\"shift\":14,\"terminal\":[-2,0,-1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0063","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":0,\"terminal\":[-1,1,0,0],\"scale\":0,\"shift\":15}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(0, [-1, 1, 0, 0], 0, 15, 15, [15, 15, 15, 15], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(0, [-1, 1, 0, 0], 0, 15, 15, [15, 15, 15, 15], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317063,"parameters":{"initial":0,"terminal":[-1,1,0,0],"scale":0,"shift":15,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":0,\"scale\":0,\"shift\":15,\"terminal\":[-1,1,0,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0064","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":1,\"terminal\":[0,2,1,1],\"scale\":1,\"shift\":16}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, [0, 2, 1, 1], 1, 16, 17, [16, 18, 17, 17], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(1, [0, 2, 1, 1], 1, 16, 17, [16, 18, 17, 17], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317064,"parameters":{"initial":1,"terminal":[0,2,1,1],"scale":1,"shift":16,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":1,\"scale\":1,\"shift\":16,\"terminal\":[0,2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0065","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":2,\"terminal\":[1,3,2,2],\"scale\":2,\"shift\":17}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, [1, 3, 2, 2], 2, 17, 21, [19, 23, 21, 21], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(2, [1, 3, 2, 2], 2, 17, 21, [19, 23, 21, 21], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317065,"parameters":{"initial":2,"terminal":[1,3,2,2],"scale":2,"shift":17,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":2,\"scale\":2,\"shift\":17,\"terminal\":[1,3,2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0066","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":3,\"terminal\":[2,4,3,3],\"scale\":-2,\"shift\":18}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, [2, 4, 3, 3], -2, 18, 12, [14, 10, 12, 12], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(3, [2, 4, 3, 3], -2, 18, 12, [14, 10, 12, 12], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317066,"parameters":{"initial":3,"terminal":[2,4,3,3],"scale":-2,"shift":18,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":3,\"scale\":-2,\"shift\":18,\"terminal\":[2,4,3,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0067","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":4,\"terminal\":[3,5,4,4],\"scale\":-1,\"shift\":19}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, [3, 5, 4, 4], -1, 19, 15, [16, 14, 15, 15], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(4, [3, 5, 4, 4], -1, 19, 15, [16, 14, 15, 15], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317067,"parameters":{"initial":4,"terminal":[3,5,4,4],"scale":-1,"shift":19,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":4,\"scale\":-1,\"shift\":19,\"terminal\":[3,5,4,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0068","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":5,\"terminal\":[4,6,5,5],\"scale\":0,\"shift\":20}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, [4, 6, 5, 5], 0, 20, 20, [20, 20, 20, 20], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(5, [4, 6, 5, 5], 0, 20, 20, [20, 20, 20, 20], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317068,"parameters":{"initial":5,"terminal":[4,6,5,5],"scale":0,"shift":20,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":5,\"scale\":0,\"shift\":20,\"terminal\":[4,6,5,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0069","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":6,\"terminal\":[5,7,6,6],\"scale\":1,\"shift\":21}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(6, [5, 7, 6, 6], 1, 21, 27, [26, 28, 27, 27], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(6, [5, 7, 6, 6], 1, 21, 27, [26, 28, 27, 27], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317069,"parameters":{"initial":6,"terminal":[5,7,6,6],"scale":1,"shift":21,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":6,\"scale\":1,\"shift\":21,\"terminal\":[5,7,6,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0070","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":7,\"terminal\":[6,8,7,7],\"scale\":2,\"shift\":22}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(7, [6, 8, 7, 7], 2, 22, 36, [34, 38, 36, 36], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(7, [6, 8, 7, 7], 2, 22, 36, [34, 38, 36, 36], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317070,"parameters":{"initial":7,"terminal":[6,8,7,7],"scale":2,"shift":22,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":7,\"scale\":2,\"shift\":22,\"terminal\":[6,8,7,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0071","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":8,\"terminal\":[7,9,8,8],\"scale\":-2,\"shift\":23}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(8, [7, 9, 8, 8], -2, 23, 7, [9, 5, 7, 7], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(8, [7, 9, 8, 8], -2, 23, 7, [9, 5, 7, 7], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317071,"parameters":{"initial":8,"terminal":[7,9,8,8],"scale":-2,"shift":23,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":8,\"scale\":-2,\"shift\":23,\"terminal\":[7,9,8,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0072","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":9,\"terminal\":[8,10,9,9],\"scale\":-1,\"shift\":24}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(9, [8, 10, 9, 9], -1, 24, 15, [16, 14, 15, 15], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(9, [8, 10, 9, 9], -1, 24, 15, [16, 14, 15, 15], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317072,"parameters":{"initial":9,"terminal":[8,10,9,9],"scale":-1,"shift":24,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":9,\"scale\":-1,\"shift\":24,\"terminal\":[8,10,9,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0073","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":10,\"terminal\":[9,11,10,10],\"scale\":0,\"shift\":25}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(10, [9, 11, 10, 10], 0, 25, 25, [25, 25, 25, 25], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(10, [9, 11, 10, 10], 0, 25, 25, [25, 25, 25, 25], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317073,"parameters":{"initial":10,"terminal":[9,11,10,10],"scale":0,"shift":25,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":10,\"scale\":0,\"shift\":25,\"terminal\":[9,11,10,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0074","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":11,\"terminal\":[10,12,11,11],\"scale\":1,\"shift\":26}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(11, [10, 12, 11, 11], 1, 26, 37, [36, 38, 37, 37], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(11, [10, 12, 11, 11], 1, 26, 37, [36, 38, 37, 37], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317074,"parameters":{"initial":11,"terminal":[10,12,11,11],"scale":1,"shift":26,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":11,\"scale\":1,\"shift\":26,\"terminal\":[10,12,11,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0075","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-affine-stability；資料={\"initial\":12,\"terminal\":[11,13,12,12],\"scale\":2,\"shift\":27}。請依 [initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(12, [11, 13, 12, 12], 2, 27, 51, [49, 53, 51, 51], 是, affine_transform_preserves_same_filtration_martingale)","explanation_zh":"Wave4收束核對=(12, [11, 13, 12, 12], 2, 27, 51, [49, 53, 51, 51], 是, affine_transform_preserves_same_filtration_martingale)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-affine-stability","seed":202610317075,"parameters":{"initial":12,"terminal":[11,13,12,12],"scale":2,"shift":27,"domain":"Exact_finite_martingale_construction","operation":"martdeep-affine-stability","semantic_template":"qf-mod31-martdeep-affine-stability/{\"initial\":12,\"scale\":2,\"shift\":27,\"terminal\":[11,13,12,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0076","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":1,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, [-1, 1], [1, 1], 2^1, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(1, 1, [-1, 1], [1, 1], 2^1, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317076,"parameters":{"steps":1,"scale":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0077","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":2,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, 1, [-2, 0, 2], [1, 2, 1], 2^2, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(2, 1, [-2, 0, 2], [1, 2, 1], 2^2, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317077,"parameters":{"steps":2,"scale":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0078","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":3,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, [-3, -1, 1, 3], [1, 3, 3, 1], 2^3, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(3, 1, [-3, -1, 1, 3], [1, 3, 3, 1], 2^3, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317078,"parameters":{"steps":3,"scale":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0079","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":4,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, 1, [-4, -2, 0, 2, 4], [1, 4, 6, 4, 1], 2^4, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(4, 1, [-4, -2, 0, 2, 4], [1, 4, 6, 4, 1], 2^4, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317079,"parameters":{"steps":4,"scale":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0080","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":5,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 1, [-5, -3, -1, 1, 3, 5], [1, 5, 10, 10, 5, 1], 2^5, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(5, 1, [-5, -3, -1, 1, 3, 5], [1, 5, 10, 10, 5, 1], 2^5, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317080,"parameters":{"steps":5,"scale":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0081","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":6,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(6, 1, [-6, -4, -2, 0, 2, 4, 6], [1, 6, 15, 20, 15, 6, 1], 2^6, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(6, 1, [-6, -4, -2, 0, 2, 4, 6], [1, 6, 15, 20, 15, 6, 1], 2^6, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317081,"parameters":{"steps":6,"scale":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0082","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":7,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(7, 1, [-7, -5, -3, -1, 1, 3, 5, 7], [1, 7, 21, 35, 35, 21, 7, 1], 2^7, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(7, 1, [-7, -5, -3, -1, 1, 3, 5, 7], [1, 7, 21, 35, 35, 21, 7, 1], 2^7, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317082,"parameters":{"steps":7,"scale":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0083","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":8,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(8, 1, [-8, -6, -4, -2, 0, 2, 4, 6, 8], [1, 8, 28, 56, 70, 56, 28, 8, 1], 2^8, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(8, 1, [-8, -6, -4, -2, 0, 2, 4, 6, 8], [1, 8, 28, 56, 70, 56, 28, 8, 1], 2^8, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317083,"parameters":{"steps":8,"scale":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0084","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":9,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(9, 1, [-9, -7, -5, -3, -1, 1, 3, 5, 7, 9], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], 2^9, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(9, 1, [-9, -7, -5, -3, -1, 1, 3, 5, 7, 9], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], 2^9, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317084,"parameters":{"steps":9,"scale":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":9}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0085","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":10,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(10, 1, [-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], 2^10, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(10, 1, [-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], 2^10, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317085,"parameters":{"steps":10,"scale":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":10}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0086","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":11,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(11, 1, [-11, -9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], 2^11, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(11, 1, [-11, -9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], 2^11, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317086,"parameters":{"steps":11,"scale":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":11}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0087","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":12,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(12, 1, [-12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], 2^12, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(12, 1, [-12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], 2^12, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317087,"parameters":{"steps":12,"scale":1,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":12}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0088","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":1,\"scale\":2}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, [-2, 2], [1, 1], 2^1, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(1, 2, [-2, 2], [1, 1], 2^1, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317088,"parameters":{"steps":1,"scale":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":2,\"steps\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0089","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":2,\"scale\":2}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [-4, 0, 4], [1, 2, 1], 2^2, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(2, 2, [-4, 0, 4], [1, 2, 1], 2^2, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317089,"parameters":{"steps":2,"scale":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":2,\"steps\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0090","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":3,\"scale\":2}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, [-6, -2, 2, 6], [1, 3, 3, 1], 2^3, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(3, 2, [-6, -2, 2, 6], [1, 3, 3, 1], 2^3, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317090,"parameters":{"steps":3,"scale":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":2,\"steps\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0091","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":4,\"scale\":2}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, 2, [-8, -4, 0, 4, 8], [1, 4, 6, 4, 1], 2^4, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(4, 2, [-8, -4, 0, 4, 8], [1, 4, 6, 4, 1], 2^4, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317091,"parameters":{"steps":4,"scale":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":2,\"steps\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0092","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":5,\"scale\":2}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, [-10, -6, -2, 2, 6, 10], [1, 5, 10, 10, 5, 1], 2^5, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(5, 2, [-10, -6, -2, 2, 6, 10], [1, 5, 10, 10, 5, 1], 2^5, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317092,"parameters":{"steps":5,"scale":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":2,\"steps\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0093","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":6,\"scale\":2}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(6, 2, [-12, -8, -4, 0, 4, 8, 12], [1, 6, 15, 20, 15, 6, 1], 2^6, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(6, 2, [-12, -8, -4, 0, 4, 8, 12], [1, 6, 15, 20, 15, 6, 1], 2^6, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317093,"parameters":{"steps":6,"scale":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":2,\"steps\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0094","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":7,\"scale\":2}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(7, 2, [-14, -10, -6, -2, 2, 6, 10, 14], [1, 7, 21, 35, 35, 21, 7, 1], 2^7, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(7, 2, [-14, -10, -6, -2, 2, 6, 10, 14], [1, 7, 21, 35, 35, 21, 7, 1], 2^7, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317094,"parameters":{"steps":7,"scale":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":2,\"steps\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0095","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":8,\"scale\":2}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(8, 2, [-16, -12, -8, -4, 0, 4, 8, 12, 16], [1, 8, 28, 56, 70, 56, 28, 8, 1], 2^8, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(8, 2, [-16, -12, -8, -4, 0, 4, 8, 12, 16], [1, 8, 28, 56, 70, 56, 28, 8, 1], 2^8, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317095,"parameters":{"steps":8,"scale":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":2,\"steps\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0096","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":9,\"scale\":2}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(9, 2, [-18, -14, -10, -6, -2, 2, 6, 10, 14, 18], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], 2^9, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(9, 2, [-18, -14, -10, -6, -2, 2, 6, 10, 14, 18], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], 2^9, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317096,"parameters":{"steps":9,"scale":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":2,\"steps\":9}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0097","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":10,\"scale\":2}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(10, 2, [-20, -16, -12, -8, -4, 0, 4, 8, 12, 16, 20], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], 2^10, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(10, 2, [-20, -16, -12, -8, -4, 0, 4, 8, 12, 16, 20], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], 2^10, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317097,"parameters":{"steps":10,"scale":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":2,\"steps\":10}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0098","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":11,\"scale\":2}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(11, 2, [-22, -18, -14, -10, -6, -2, 2, 6, 10, 14, 18, 22], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], 2^11, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(11, 2, [-22, -18, -14, -10, -6, -2, 2, 6, 10, 14, 18, 22], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], 2^11, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317098,"parameters":{"steps":11,"scale":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":2,\"steps\":11}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0099","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":12,\"scale\":2}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(12, 2, [-24, -20, -16, -12, -8, -4, 0, 4, 8, 12, 16, 20, 24], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], 2^12, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(12, 2, [-24, -20, -16, -12, -8, -4, 0, 4, 8, 12, 16, 20, 24], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], 2^12, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317099,"parameters":{"steps":12,"scale":2,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":2,\"steps\":12}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r07-martingale-0100","batch_id":"batch-20261014-advance-20261031-r07-martingale-foundations","language":"zh-Hant","source_mko_ids":["mko-martingale"],"title_zh":"Martingale深度","stem_zh":"同一有限機率空間與filtration的精確模型。操作=martdeep-fair-partial-sum；資料={\"steps\":1,\"scale\":3}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, [-3, 3], [1, 1], 2^1, 是, independent_fair_signed_increments_have_conditional_mean_zero)","explanation_zh":"Wave4收束核對=(1, 3, [-3, 3], [1, 1], 2^1, 是, independent_fair_signed_increments_have_conditional_mean_zero)；依完整明示資料重算；常期望不足；差分須逐資訊block條件均值為零；不引入optional stopping、收斂、Markov或獨立增量聲明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Martingale深度"]},"variant":{"family_id":"qf-mod31-martdeep-fair-partial-sum","seed":202610317100,"parameters":{"steps":1,"scale":3,"domain":"Exact_finite_martingale_construction","operation":"martdeep-fair-partial-sum","semantic_template":"qf-mod31-martdeep-fair-partial-sum/{\"scale\":3,\"steps\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}