{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261031-r07-martingale-0054", "pilot_number": "R0066-33704", "number": 33704, "family_id": "qf-mod31-martdeep-affine-stability", "title": { "zh-Hant": "第 33704 題：Martingale深度", "en": "Question 33704: One Fixed Affine Transformation Preserves the Same-Filtration Martingale" }, "original_question": { "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" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261014-advance-20261031-r07-martingale-0054", "batch_id": "batch-20261014-advance-20261031-r07-martingale-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "b03d1ed5d3fb4ba7dc8c489f029363b7f3ed0ab7aecc75f5b0e59070ec0cdd92", "family_id": "qf-mod31-martdeep-affine-stability", "seed": 202610317054, "semantic_template": "qf-mod31-martdeep-affine-stability/{\"initial\":-9,\"scale\":1,\"shift\":6,\"terminal\":[-10,-8,-9,-9]}" }, "fields": { "title": "One Fixed Affine Transformation Preserves the Same-Filtration Martingale", "stem": "Use the declared equiprobable one-step martingale with constant initial=-9 and complete terminal values=[-10, -8, -9, -9]. The initial information is trivial and the terminal information reveals these outcomes. Fixed scale=1, shift=6. Give (initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale?,affine_transform_preserves_same_filtration_martingale).", "answer": { "kind": "expression", "value": "(-9, [-10, -8, -9, -9], 1, 6, -3, [-4, -2, -3, -3], Yes, affine_transform_preserves_same_filtration_martingale)", "explanation": "First require the terminal mean to equal the initial value. Apply the same fixed scale and shift to both times; conditional expectation linearity preserves the martingale under the same filtration. Zero or negative scale is allowed. This does not permit time-dependent or random coefficients without further conditions. The exact result, retaining the requested order, is (-9, [-10, -8, -9, -9], 1, 6, -3, [-4, -2, -3, -3], Yes, affine_transform_preserves_same_filtration_martingale)." }, "skills": [ "One Fixed Affine Transformation Preserves the Same-Filtration Martingale" ], "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review." } }, "givens": [ { "id": "G001", "text": { "zh-Hant": "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。", "en": "Use the declared equiprobable one-step martingale with constant initial=-9 and complete terminal values=[-10, -8, -9, -9]. The initial information is trivial and the terminal information reveals these outcomes. Fixed scale=1, shift=6. Give (initial,terminal,scale,shift,transformed_initial,transformed_terminal,martingale?,affine_transform_preserves_same_filtration_martingale)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-mod31-martdeep-affine-stability, [domain, initial, operation, scale, shift, terminal]]", "after": "derived = [martdeep-affine-stability, Exact_finite_martingale_construction]", "relation": "implies", "rule_id": "R66_EXACT_source_bank_keys_local_operation_domain", "conditions": [], "explanation": { "zh-Hant": "原bank的operation是LOCAL hyphen，keys與domain各自精確匹配。欄位順序及數字/Boolean/字串角色依來源，所有有理數文字整數省略/1；不改原題與英文、MKO、AST或狀態。", "en": "THIS source uses LOCAL-hyphen operations with exact keys/domain.Keep source field order and numeric/Boolean/string roles;integer rational texts omit/1.Original questions,English,MKOs,ASTs and statuses remain unchanged." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本步原始角色、完整前提與欄序；只接受這些條件下的結論，不把單向結論還原為唯一前提，也不把有限核對稱一般形式證明。", "en": "Reverse-audit THIS step against its ORIGINAL ordered roles and complete premises.Accept the conclusion only under these conditions;do not invert a one-way implication or call a finite check a general formal proof." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "Affine ORIGINAL terminal sum := sum(-10, -8, -9, -9)", "after": "Affine ORIGINAL terminal sum = -36", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL terminal sum，不以小數近似替代。", "en": "Recompute Affine ORIGINAL terminal sum with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "-10", "-8", "-9", "-9" ], "output": "-36", "label": "Affine ORIGINAL terminal sum" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "Affine ORIGINAL initial times outcome count := mul(-9, 4)", "after": "Affine ORIGINAL initial times outcome count = -36", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL initial times outcome count，不以小數近似替代。", "en": "Recompute Affine ORIGINAL initial times outcome count with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "-9", "4" ], "output": "-36", "label": "Affine ORIGINAL initial times outcome count" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [-9, [-10, -8, -9, -9], -36, -36]", "after": "derived = [是]", "relation": "implies", "rule_id": "Martingale_AFFINE_original_mean_premise_before_transform", "conditions": [], "explanation": { "zh-Hant": "先驗完整等機率terminal的mean=initial，F0平凡、F1顯示所有outcome；非空完整表，不能只驗轉換後的mean就倒推原process。", "en": "FIRST qualify the COMPLETE nonempty equiprobable terminal mean=initial,with trivial F0 and terminal-revealing F1.A transformed mean alone cannot repair a failed original process." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本步原始角色、完整前提與欄序；只接受這些條件下的結論，不把單向結論還原為唯一前提，也不把有限核對稱一般形式證明。", "en": "Reverse-audit THIS step against its ORIGINAL ordered roles and complete premises.Accept the conclusion only under these conditions;do not invert a one-way implication or call a finite check a general formal proof." } }, "arithmetic": null }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "Affine ORIGINAL scale times initial := mul(1, -9)", "after": "Affine ORIGINAL scale times initial = -9", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL scale times initial，不以小數近似替代。", "en": "Recompute Affine ORIGINAL scale times initial with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "-9" ], "output": "-9", "label": "Affine ORIGINAL scale times initial" } }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "Affine ORIGINAL scaled initial plus fixed shift := sum(-9, 6)", "after": "Affine ORIGINAL scaled initial plus fixed shift = -3", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL scaled initial plus fixed shift，不以小數近似替代。", "en": "Recompute Affine ORIGINAL scaled initial plus fixed shift with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "-9", "6" ], "output": "-3", "label": "Affine ORIGINAL scaled initial plus fixed shift" } }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "Affine ORIGINAL terminal product0 := mul(1, -10)", "after": "Affine ORIGINAL terminal product0 = -10", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL terminal product0，不以小數近似替代。", "en": "Recompute Affine ORIGINAL terminal product0 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "-10" ], "output": "-10", "label": "Affine ORIGINAL terminal product0" } }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "Affine ORIGINAL transformed terminal0 := sum(-10, 6)", "after": "Affine ORIGINAL transformed terminal0 = -4", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL transformed terminal0，不以小數近似替代。", "en": "Recompute Affine ORIGINAL transformed terminal0 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "-10", "6" ], "output": "-4", "label": "Affine ORIGINAL transformed terminal0" } }, { "id": "S009", "uses": [ "G001", "S008" ], "before": "Affine ORIGINAL terminal product1 := mul(1, -8)", "after": "Affine ORIGINAL terminal product1 = -8", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL terminal product1，不以小數近似替代。", "en": "Recompute Affine ORIGINAL terminal product1 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "-8" ], "output": "-8", "label": "Affine ORIGINAL terminal product1" } }, { "id": "S010", "uses": [ "G001", "S009" ], "before": "Affine ORIGINAL transformed terminal1 := sum(-8, 6)", "after": "Affine ORIGINAL transformed terminal1 = -2", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL transformed terminal1，不以小數近似替代。", "en": "Recompute Affine ORIGINAL transformed terminal1 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "-8", "6" ], "output": "-2", "label": "Affine ORIGINAL transformed terminal1" } }, { "id": "S011", "uses": [ "G001", "S010" ], "before": "Affine ORIGINAL terminal product2 := mul(1, -9)", "after": "Affine ORIGINAL terminal product2 = -9", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL terminal product2，不以小數近似替代。", "en": "Recompute Affine ORIGINAL terminal product2 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "-9" ], "output": "-9", "label": "Affine ORIGINAL terminal product2" } }, { "id": "S012", "uses": [ "G001", "S011" ], "before": "Affine ORIGINAL transformed terminal2 := sum(-9, 6)", "after": "Affine ORIGINAL transformed terminal2 = -3", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL transformed terminal2，不以小數近似替代。", "en": "Recompute Affine ORIGINAL transformed terminal2 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "-9", "6" ], "output": "-3", "label": "Affine ORIGINAL transformed terminal2" } }, { "id": "S013", "uses": [ "G001", "S012" ], "before": "Affine ORIGINAL terminal product3 := mul(1, -9)", "after": "Affine ORIGINAL terminal product3 = -9", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL terminal product3，不以小數近似替代。", "en": "Recompute Affine ORIGINAL terminal product3 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "-9" ], "output": "-9", "label": "Affine ORIGINAL terminal product3" } }, { "id": "S014", "uses": [ "G001", "S013" ], "before": "Affine ORIGINAL transformed terminal3 := sum(-9, 6)", "after": "Affine ORIGINAL transformed terminal3 = -3", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL transformed terminal3，不以小數近似替代。", "en": "Recompute Affine ORIGINAL transformed terminal3 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "-9", "6" ], "output": "-3", "label": "Affine ORIGINAL transformed terminal3" } }, { "id": "S015", "uses": [ "G001", "S014" ], "before": "Affine ORIGINAL transformed sum := sum(-4, -2, -3, -3)", "after": "Affine ORIGINAL transformed sum = -12", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL transformed sum，不以小數近似替代。", "en": "Recompute Affine ORIGINAL transformed sum with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "-4", "-2", "-3", "-3" ], "output": "-12", "label": "Affine ORIGINAL transformed sum" } }, { "id": "S016", "uses": [ "G001", "S015" ], "before": "Affine ORIGINAL transformed initial times count := mul(-3, 4)", "after": "Affine ORIGINAL transformed initial times count = -12", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本步原操作數與次序精確運算；來源有理數的pre-reduction界另行保留，不用浮點或偷偷跨bank放寬。", "en": "Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Affine ORIGINAL transformed initial times count，不以小數近似替代。", "en": "Recompute Affine ORIGINAL transformed initial times count with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "-3", "4" ], "output": "-12", "label": "Affine ORIGINAL transformed initial times count" } }, { "id": "S017", "uses": [ "G001", "S016" ], "before": "source roles = [1, 6, -9, [-10, -8, -9, -9]]", "after": "derived = [-3, [-4, -2, -3, -3], 是]", "relation": "implies", "rule_id": "Martingale_FIXED_same_filtration_affine_linearity", "conditions": [], "explanation": { "zh-Hant": "同一固定scale與shift作用於兩個時間，在同一filtration由conditional expectation線性保持martingale；scale=0或負合法，不允許偷換時變/隨機係數。衍生整數不重套raw100萬界。", "en": "Apply the SAME fixed scale/shift at both times.Under the SAME filtration,conditional-expectation linearity preserves the martingale.Zero or negative scale is allowed;time-dependent/random coefficients are not supplied.Derived integers are not recapped at the RAW million bound." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本步原始角色、完整前提與欄序；只接受這些條件下的結論，不把單向結論還原為唯一前提，也不把有限核對稱一般形式證明。", "en": "Reverse-audit THIS step against its ORIGINAL ordered roles and complete premises.Accept the conclusion only under these conditions;do not invert a one-way implication or call a finite check a general formal proof." } }, "arithmetic": null } ], "math_model": { "result": [ -9, [ -10, -8, -9, -9 ], 1, 6, -3, [ -4, -2, -3, -3 ], true, "affine_transform_preserves_same_filtration_martingale" ] }, "conclusion": { "canonical_value": "(-9, [-10, -8, -9, -9], 1, 6, -3, [-4, -2, -3, -3], 是, affine_transform_preserves_same_filtration_martingale)", "explanation": { "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。", "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged." } }, "definition_note": { "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。", "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate." }, "source": { "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db", "question_binding": { "batch_id": "batch-20261014-advance-20261031-r07-martingale-foundations", "batch_path": "public/data/questions/batches/batch-20261014-advance-20261031-r07-martingale-foundations/questions.jsonl", "batch_sha256": "ee82a8e65508794c0f2899807a2e0f55a4c717acd7a4691a97b1de21d4c4a698", "original_line": 54, "original_line_sha256": "f4791600901424cd22357ab813b87f6013c028a42228dc62e6346b94043c1bad", "question_compact_sha256": "b03d1ed5d3fb4ba7dc8c489f029363b7f3ed0ab7aecc75f5b0e59070ec0cdd92", "english_row_compact_sha256": "cabd64af490830b2ad08c3b5440138d6ec7435ac081dfd8e67a42ad9a37cacf7", "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261031-r07-martingale-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261031-r07-martingale-foundations.en.jsonl" }, "mko_bindings": { "mko-martingale": { "sha256": "25744aeb70a10daa6dcabb09f5b71bc0ee3e9f2c266412b727873f5e2abddf7b", "english_sha256": "baf1b76a7fdf33a34d203015ec0ab002e6398566cc74b3d6decc7de93b52132e", "original_path": "public/data/mko/martingale.json", "english_path": "public/data/i18n/editions/mko-martingale.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "df58fcce25614251047f7c41d31ff93b5bfec19cd9bbcaa5fbb42a4daceb0310", "original_candidate_sha256": "375095c97f6db0974d27c6bc61bbfdd479a217d3f52d6e1ce92ca1b97590146b", "original_candidate_line_sha256": "375095c97f6db0974d27c6bc61bbfdd479a217d3f52d6e1ce92ca1b97590146b" }, "historical_source_state": { "review_state": { "derivation": "candidate_authored_and_locally_checked", "source_question_state": "candidate", "independent_AI_or_human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN" }, "scope_note": { "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。", "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged." }, "label": "Frozen producer metadata; current per-question review is separate below." }, "revision": { "id": "review-20261026-012-p67", "review_date": "2026-10-26", "owner_authorized_reader_publication": true, "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.", "review_receipts": { "semantic_review_sha256": "99b4f114b2ec93164b6aa5681e0107033a240e7a3f0a8988633ba65320ede267", "question_first_witness_sha256": "d9bd3a1940da8a73f790ee3fe460c9a8523791bdbe72c8e0304e3740b66710cc" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 17, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "28237d5b396bf8159c382f4b7266bece656971bc8591028ada90a1b3c4603840", "arithmetic_steps": 14 }, "uses_answer_as_premise": false, "human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN", "Canonical_truth_promotion": false, "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged." } }