{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261031-r07-martingale-0076", "pilot_number": "R0066-33776", "number": 33776, "family_id": "qf-mod31-martdeep-fair-partial-sum", "title": { "zh-Hant": "第 33776 題：Martingale深度", "en": "Question 33776: A Declared Fair Independent-Increment Model Supplies a Specific Martingale" }, "original_question": { "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" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261014-advance-20261031-r07-martingale-0076", "batch_id": "batch-20261014-advance-20261031-r07-martingale-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "468e2ded99910ed491664c71a6a0b0a1f1e1bfc6bb41ebf785756df64db901ed", "family_id": "qf-mod31-martdeep-fair-partial-sum", "seed": 202610317076, "semantic_template": "qf-mod31-martdeep-fair-partial-sum/{\"scale\":1,\"steps\":1}" }, "fields": { "title": "A Declared Fair Independent-Increment Model Supplies a Specific Martingale", "stem": "Use steps=1 independent equiprobable signs, each increment ±scale with scale=1>0, on the full finite sign-product space with its natural revealed-sign filtration. Give (steps,scale,support,multiplicities,total_paths,martingale?,independent_fair_signed_increments_have_conditional_mean_zero). List support by increasing number of positive signs; retain total_paths as exact 2^steps text.", "answer": { "kind": "expression", "value": "(1, 1, [-1, 1], [1, 1], 2^1, Yes, independent_fair_signed_increments_have_conditional_mean_zero)", "explanation": "The terminal value with k positive signs is scale*(2*k−steps), with binomial multiplicity choose(steps,k). Every next increment has conditional mean zero in this explicitly independent fair model. These premises do not follow from an arbitrary martingale, nor do stopping, convergence or Markov theorems follow from this finite calculation. The exact result, retaining the requested order, is (1, 1, [-1, 1], [1, 1], 2^1, Yes, independent_fair_signed_increments_have_conditional_mean_zero)." }, "skills": [ "A Declared Fair Independent-Increment Model Supplies a Specific 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-fair-partial-sum；資料={\"steps\":1,\"scale\":1}。請依 [steps,scale,support,multiplicities,total_paths,martingale,certificate] 欄序回答。", "en": "Use steps=1 independent equiprobable signs, each increment ±scale with scale=1>0, on the full finite sign-product space with its natural revealed-sign filtration. Give (steps,scale,support,multiplicities,total_paths,martingale?,independent_fair_signed_increments_have_conditional_mean_zero). List support by increasing number of positive signs; retain total_paths as exact 2^steps text." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-mod31-martdeep-fair-partial-sum, [domain, operation, scale, steps]]", "after": "derived = [martdeep-fair-partial-sum, 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": "Fair ORIGINAL two positive signs k=0 := mul(2, 0)", "after": "Fair ORIGINAL two positive signs k=0 = 0", "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 Fair ORIGINAL two positive signs k=0，不以小數近似替代。", "en": "Recompute Fair ORIGINAL two positive signs k=0 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "2", "0" ], "output": "0", "label": "Fair ORIGINAL two positive signs k=0" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "Fair ORIGINAL positive minus negative count k=0 := sub(0, 1)", "after": "Fair ORIGINAL positive minus negative count k=0 = -1", "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 Fair ORIGINAL positive minus negative count k=0，不以小數近似替代。", "en": "Recompute Fair ORIGINAL positive minus negative count k=0 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "0", "1" ], "output": "-1", "label": "Fair ORIGINAL positive minus negative count k=0" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "Fair ORIGINAL scale times signed count k=0 := mul(1, -1)", "after": "Fair ORIGINAL scale times signed count k=0 = -1", "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 Fair ORIGINAL scale times signed count k=0，不以小數近似替代。", "en": "Recompute Fair ORIGINAL scale times signed count k=0 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "-1" ], "output": "-1", "label": "Fair ORIGINAL scale times signed count k=0" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "source roles = [1, 1, 0]", "after": "derived = [-1, 1]", "relation": "implies", "rule_id": "Martingale_FAIR_EACH_complete_terminal_support_binomial_count", "conditions": [], "explanation": { "zh-Hant": "k個正sign、n−k個負sign給scale*(2k−n)，選正sign位置有choose(n,k)條；逐k=0..n保留全部terminal support與multiplicity。", "en": "k positive and n−k negative signs give scale*(2k−n),with choose(n,k)choices of positive positions.Retain EVERY k=0..n support value and multiplicity." }, "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": "S006", "uses": [ "G001", "S005" ], "before": "Fair ORIGINAL binomial previous times remaining k=1 := mul(1, 1)", "after": "Fair ORIGINAL binomial previous times remaining k=1 = 1", "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 Fair ORIGINAL binomial previous times remaining k=1，不以小數近似替代。", "en": "Recompute Fair ORIGINAL binomial previous times remaining k=1 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "1" ], "output": "1", "label": "Fair ORIGINAL binomial previous times remaining k=1" } }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "Fair ORIGINAL binomial recurrence division k=1 := div(1, 1)", "after": "Fair ORIGINAL binomial recurrence division k=1 = 1", "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 Fair ORIGINAL binomial recurrence division k=1，不以小數近似替代。", "en": "Recompute Fair ORIGINAL binomial recurrence division k=1 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "div", "inputs": [ "1", "1" ], "output": "1", "label": "Fair ORIGINAL binomial recurrence division k=1" } }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "Fair ORIGINAL two positive signs k=1 := mul(2, 1)", "after": "Fair ORIGINAL two positive signs k=1 = 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 Fair ORIGINAL two positive signs k=1，不以小數近似替代。", "en": "Recompute Fair ORIGINAL two positive signs k=1 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "2", "1" ], "output": "2", "label": "Fair ORIGINAL two positive signs k=1" } }, { "id": "S009", "uses": [ "G001", "S008" ], "before": "Fair ORIGINAL positive minus negative count k=1 := sub(2, 1)", "after": "Fair ORIGINAL positive minus negative count k=1 = 1", "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 Fair ORIGINAL positive minus negative count k=1，不以小數近似替代。", "en": "Recompute Fair ORIGINAL positive minus negative count k=1 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "2", "1" ], "output": "1", "label": "Fair ORIGINAL positive minus negative count k=1" } }, { "id": "S010", "uses": [ "G001", "S009" ], "before": "Fair ORIGINAL scale times signed count k=1 := mul(1, 1)", "after": "Fair ORIGINAL scale times signed count k=1 = 1", "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 Fair ORIGINAL scale times signed count k=1，不以小數近似替代。", "en": "Recompute Fair ORIGINAL scale times signed count k=1 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "1" ], "output": "1", "label": "Fair ORIGINAL scale times signed count k=1" } }, { "id": "S011", "uses": [ "G001", "S010" ], "before": "source roles = [1, 1, 1]", "after": "derived = [1, 1]", "relation": "implies", "rule_id": "Martingale_FAIR_EACH_complete_terminal_support_binomial_count", "conditions": [], "explanation": { "zh-Hant": "k個正sign、n−k個負sign給scale*(2k−n)，選正sign位置有choose(n,k)條；逐k=0..n保留全部terminal support與multiplicity。", "en": "k positive and n−k negative signs give scale*(2k−n),with choose(n,k)choices of positive positions.Retain EVERY k=0..n support value and multiplicity." }, "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": "S012", "uses": [ "G001", "S011" ], "before": "Fair ORIGINAL all binomial multiplicities := sum(1, 1)", "after": "Fair ORIGINAL all binomial multiplicities = 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 Fair ORIGINAL all binomial multiplicities，不以小數近似替代。", "en": "Recompute Fair ORIGINAL all binomial multiplicities with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1", "1" ], "output": "2", "label": "Fair ORIGINAL all binomial multiplicities" } }, { "id": "S013", "uses": [ "G001", "S012" ], "before": "source roles = [1, 1, 2]", "after": "derived = [[time=0, prefixes=1, next_signs=+s,-s equiprobable, conditional_increment_mean=0]]", "relation": "implies", "rule_id": "Martingale_FAIR_PRODUCT_space_natural_filtration_EVERY_prefix", "conditions": [], "explanation": { "zh-Hant": "前提為完整2^n等機率獨立sign product space與逐sign揭露filtration；每個prefix下一sign的正負延伸等多，條件增量mean=(s−s)/2=0，partial sum adapted/可積，故本有限process為martingale。不把獨立增量說成任意martingale必備，也不套stopping/收斂定理。", "en": "The PREMISE is the FULL equiprobable independent sign-product space and its revealed-sign filtration.At EVERY prefix,the next±sign extensions have equal count,so conditional increment mean=(s−s)/2=0.The adapted finite integrable partial sums form THIS martingale.This does not make independent increments necessary for arbitrary martingales or supply stopping/convergence theorems." }, "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": [ 1, 1, [ -1, 1 ], [ 1, 1 ], "2^1", true, "independent_fair_signed_increments_have_conditional_mean_zero" ] }, "conclusion": { "canonical_value": "(1, 1, [-1, 1], [1, 1], 2^1, 是, independent_fair_signed_increments_have_conditional_mean_zero)", "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": 76, "original_line_sha256": "e0bf2c5cd30a2ff7bf5834f81fc0f0d06961a2fda530968ddd1555d810456ee0", "question_compact_sha256": "468e2ded99910ed491664c71a6a0b0a1f1e1bfc6bb41ebf785756df64db901ed", "english_row_compact_sha256": "9f2315be916d6299a4ffe293744b77eb5615ad3b601e02ea6d7c731e80cf3d3d", "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": "7ccf8d7a6fdf5a660756cc0f41849131aadb37ab0d5601d10bf4643af2c4bdb9", "original_candidate_line_sha256": "7ccf8d7a6fdf5a660756cc0f41849131aadb37ab0d5601d10bf4643af2c4bdb9" }, "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": 13, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "4f481a53e010e6cf3db124cab76bf653b3a9488b8377185cf9ef6782c6961a9e", "arithmetic_steps": 9 }, "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." } }