{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261106-r03-estimator-bias-0098", "pilot_number": "R0037-19373", "number": 19373, "family_id": "qf-mod37-bias-observed-boundary", "title": { "zh-Hant": "第 19373 題：估計量偏誤", "en": "Question 19373: One Realized Estimate Does Not Establish Bias or Other Properties" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261014-advance-20261106-r03-estimator-bias-0098", "batch_id": "batch-20261014-advance-20261106-r03-estimator-bias-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-estimator-bias" ], "title_zh": "估計量偏誤", "stem_zh": "共同有限樣本空間、逐theta sampling law與同一total estimator。操作=bias-observed-boundary；資料={\"theta_values\":[[1,2],[23,25]],\"laws\":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],\"statistic\":[0,1,24,25],\"parameter\":0,\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "answer": { "kind": "expression", "value": "(0, 2, 24, 177/8, 否, observed_estimate_not_bias_and_unbiased_not_zero_variance_consistency_sufficiency_or_minimum_MSE)", "explanation_zh": "Wave5封閉層核對=(0, 2, 24, 177/8, 否, observed_estimate_not_bias_and_unbiased_not_zero_variance_consistency_sufficiency_or_minimum_MSE)；依完整明示資料獨立重算；Bias_theta(T)=E_theta[T]-theta且期望來自同一theta抽樣分布；unbiased要求每個theta；單一estimate不足且不推出零變異一致充分或最小MSE。" }, "difficulty": { "band": "undergraduate_core", "level": 3, "skills": [ "估計量偏誤" ] }, "variant": { "family_id": "qf-mod37-bias-observed-boundary", "seed": 202611063098, "parameters": { "theta_values": [ [ 1, 2 ], [ 23, 25 ] ], "laws": [ [ [ 1, 32 ], [ 2, 32 ], [ 3, 32 ], [ 26, 32 ] ], [ [ 2, 36 ], [ 3, 36 ], [ 4, 36 ], [ 27, 36 ] ] ], "statistic": [ 0, 1, 24, 25 ], "parameter": 0, "outcome": 2, "domain": "Finite_parametric_estimator_bias", "operation": "bias-observed-boundary", "semantic_template": "qf-mod37-bias-observed-boundary/{\"laws\":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],\"outcome\":2,\"parameter\":0,\"statistic\":[0,1,24,25],\"theta_values\":[[1,2],[23,25]]}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_finite_or_symbolic_model", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "候選須主端重算；不構成人工審定、greedy最優性、maximal等於maximum、單一theta無偏、variance推MSE、Fermat converse、有限搜尋完整Diophantine解、唯一quotient代表元、Lean或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-20261106-r03-estimator-bias-0098", "batch_id": "batch-20261014-advance-20261106-r03-estimator-bias-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "0184de19ca2cead94946aabd389da85c52ab7ea318645c734b2cbbe9e9f970c2", "family_id": "qf-mod37-bias-observed-boundary", "seed": 202611063098, "semantic_template": "qf-mod37-bias-observed-boundary/{\"laws\":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],\"outcome\":2,\"parameter\":0,\"statistic\":[0,1,24,25],\"theta_values\":[[1,2],[23,25]]}" }, "fields": { "title": "One Realized Estimate Does Not Establish Bias or Other Properties", "stem": "Use indexed parameter slots Fin(2)={0,…,1}, complete exact rational law rows=[[1/32, 2/32, 3/32, 26/32], [2/36, 3/36, 4/36, 27/36]], and one parameter-independent total statistic T=[0, 1, 24, 25] in common outcome order. Every row is nonnegative and sums to1. The aligned parameter values are theta_values=[1/2, 23/25], and the target is g(theta)=theta. Keep all expectations and moments under the same selected law; zero-mass outcomes remain in the table but do not enlarge its positive-mass support. Selected parameter index=0, supplied outcome=2. Give (parameter_index, outcome, estimate, bias, observed_value_suffices_for_property_claims, boundary).", "answer": { "kind": "expression", "value": "(0, 2, 24, 177/8, No, observed_estimate_not_bias_and_unbiased_not_zero_variance_consistency_sufficiency_or_minimum_MSE)", "explanation": "Read T at that outcome and retain the separate exact bias under the selected law. No withholds other statistical-property claims from one observation; it does not assert that the estimate and bias have unequal numerical values. Unbiasedness alone does not supply zero variance, consistency, sufficiency or minimum MSE. The exact result, retaining the requested order, is (0, 2, 24, 177/8, No, observed_estimate_not_bias_and_unbiased_not_zero_variance_consistency_sufficiency_or_minimum_MSE)." }, "skills": [ "One Realized Estimate Does Not Establish Bias or Other Properties" ], "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": "共同有限樣本空間、逐theta sampling law與同一total estimator。操作=bias-observed-boundary；資料={\"theta_values\":[[1,2],[23,25]],\"laws\":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],\"statistic\":[0,1,24,25],\"parameter\":0,\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "en": "Use indexed parameter slots Fin(2)={0,…,1}, complete exact rational law rows=[[1/32, 2/32, 3/32, 26/32], [2/36, 3/36, 4/36, 27/36]], and one parameter-independent total statistic T=[0, 1, 24, 25] in common outcome order. Every row is nonnegative and sums to1. The aligned parameter values are theta_values=[1/2, 23/25], and the target is g(theta)=theta. Keep all expectations and moments under the same selected law; zero-mass outcomes remain in the table but do not enlarge its positive-mass support. Selected parameter index=0, supplied outcome=2. Give (parameter_index, outcome, estimate, bias, observed_value_suffices_for_property_claims, boundary)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source operation=bias-observed-boundary;original snapshot and mathematics retained", "after": "explicit ordered source output fields=[parameter_index, outcome, estimate, bias, observed_value_suffices_for_property_claims, boundary]", "relation": "implies", "rule_id": "source_ordered_interface_explicit_without_javascript", "conditions": [], "explanation": { "zh-Hant": "原題快照保留歷史介面標記；本頁直接列原始欄位順序，不需JavaScript或查外部表。欄位名字本身不自動是數學證據，No依各題的聲稱範圍解讀。", "en": "Retain the historical interface marker in the original snapshot while listing ordered source fields here,without JavaScript or external lookup.Field names are not mathematical evidence,and No retains the operation's specific claim scope." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "bias parameter0 full law mass := sum(1/32, 1/16, 3/32, 13/16)", "after": "bias parameter0 full law mass = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色與已核中間量精確代值，保留參數、樣本、目標與分母，不交換未授權的聲稱。", "en": "Substitute original roles and established intermediates exactly,retaining parameter,outcome,target and denominator roles without replacing the claim." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 bias parameter0 full law mass，不以小數近似替代。", "en": "Recompute bias parameter0 full law mass with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1/32", "1/16", "3/32", "13/16" ], "output": "1", "label": "bias parameter0 full law mass" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "bias:original parameter SLOT=0;same outcome carrier Fin(4);ALL aligned law masses=[1/32, 1/16, 3/32, 13/16]", "after": "full sum=1;all masses nonnegative=是;qualified probability law;zero-mass outcomes retained", "relation": "implies", "rule_id": "finite_statistical_full_law_not_partial_or_prior", "conditions": [], "explanation": { "zh-Hant": "每一參數的完整law須各自非負且總和1；零質量結果仍在原表，不能把參數列相加正規化來捏一個prior或posterior。", "en": "Each complete parameter law must separately be nonnegative and total1.Keep zero-mass outcomes in the original table;do not normalize across parameter rows to invent a prior or posterior." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "bias parameter1 full law mass := sum(1/18, 1/12, 1/9, 3/4)", "after": "bias parameter1 full law mass = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色與已核中間量精確代值，保留參數、樣本、目標與分母，不交換未授權的聲稱。", "en": "Substitute original roles and established intermediates exactly,retaining parameter,outcome,target and denominator roles without replacing the claim." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 bias parameter1 full law mass，不以小數近似替代。", "en": "Recompute bias parameter1 full law mass with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1/18", "1/12", "1/9", "3/4" ], "output": "1", "label": "bias parameter1 full law mass" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "bias:original parameter SLOT=1;same outcome carrier Fin(4);ALL aligned law masses=[1/18, 1/12, 1/9, 3/4]", "after": "full sum=1;all masses nonnegative=是;qualified probability law;zero-mass outcomes retained", "relation": "implies", "rule_id": "finite_statistical_full_law_not_partial_or_prior", "conditions": [], "explanation": { "zh-Hant": "每一參數的完整law須各自非負且總和1；零質量結果仍在原表，不能把參數列相加正規化來捏一個prior或posterior。", "en": "Each complete parameter law must separately be nonnegative and total1.Keep zero-mass outcomes in the original table;do not normalize across parameter rows to invent a prior or posterior." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "bias:parameter SLOT carrier Fin(2);common outcome carrier Fin(4);ONE total original statistic array=[0, 1, 24, 25]", "after": "T takes only the observation index,not the unknown parameter;SAME function at all parameter slots;its sampling law may still vary with the slot", "relation": "implies", "rule_id": "finite_statistic_definition_not_distribution_free", "conditions": [], "explanation": { "zh-Hant": "T函數定義不吃未知參數，與T(X)分布是否依參數是不同事。每個outcome只有一個原T值，不用每列另換一個T來調答案。", "en": "Functional parameter-independence is different from a parameter-free distribution of T(X).Use the same original statistic value at every outcome rather than changing T between laws." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "original parameter SLOT order0..1;aligned exact theta_values=[1/2, 23/25]", "after": "declared target g(theta)=theta;indices are not targets;claims range over THIS supplied finite parameter model only", "relation": "implies", "rule_id": "bias_declared_target_and_finite_parameter_scope", "conditions": [], "explanation": { "zh-Hant": "目標值與參數索引分開，theta值不必互異。沒有未提供的連續參數空間、prior或統計量序列，不能把有限模型內的全稱結論外推。", "en": "Keep target values separate from parameter indices;theta values need not be distinct.No unprovided continuous parameter space,prior or sequence of statistics is supplied,so a universal claim within this finite model is not extended beyond it." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "bias parameter0 original outcome0 weighted statistic := mul(1/32, 0)", "after": "bias parameter0 original outcome0 weighted statistic = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色與已核中間量精確代值，保留參數、樣本、目標與分母，不交換未授權的聲稱。", "en": "Substitute original roles and established intermediates exactly,retaining parameter,outcome,target and denominator roles without replacing the claim." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 bias parameter0 original outcome0 weighted statistic，不以小數近似替代。", "en": "Recompute bias parameter0 original outcome0 weighted statistic with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1/32", "0" ], "output": "0", "label": "bias parameter0 original outcome0 weighted statistic" } }, { "id": "S009", "uses": [ "G001", "S008" ], "before": "bias parameter0 original outcome1 weighted statistic := mul(1/16, 1)", "after": "bias parameter0 original outcome1 weighted statistic = 1/16", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色與已核中間量精確代值，保留參數、樣本、目標與分母，不交換未授權的聲稱。", "en": "Substitute original roles and established intermediates exactly,retaining parameter,outcome,target and denominator roles without replacing the claim." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 bias parameter0 original outcome1 weighted statistic，不以小數近似替代。", "en": "Recompute bias parameter0 original outcome1 weighted statistic with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1/16", "1" ], "output": "1/16", "label": "bias parameter0 original outcome1 weighted statistic" } }, { "id": "S010", "uses": [ "G001", "S009" ], "before": "bias parameter0 original outcome2 weighted statistic := mul(3/32, 24)", "after": "bias parameter0 original outcome2 weighted statistic = 9/4", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色與已核中間量精確代值，保留參數、樣本、目標與分母，不交換未授權的聲稱。", "en": "Substitute original roles and established intermediates exactly,retaining parameter,outcome,target and denominator roles without replacing the claim." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 bias parameter0 original outcome2 weighted statistic，不以小數近似替代。", "en": "Recompute bias parameter0 original outcome2 weighted statistic with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "3/32", "24" ], "output": "9/4", "label": "bias parameter0 original outcome2 weighted statistic" } }, { "id": "S011", "uses": [ "G001", "S010" ], "before": "bias parameter0 original outcome3 weighted statistic := mul(13/16, 25)", "after": "bias parameter0 original outcome3 weighted statistic = 325/16", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色與已核中間量精確代值，保留參數、樣本、目標與分母，不交換未授權的聲稱。", "en": "Substitute original roles and established intermediates exactly,retaining parameter,outcome,target and denominator roles without replacing the claim." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 bias parameter0 original outcome3 weighted statistic，不以小數近似替代。", "en": "Recompute bias parameter0 original outcome3 weighted statistic with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "13/16", "25" ], "output": "325/16", "label": "bias parameter0 original outcome3 weighted statistic" } }, { "id": "S012", "uses": [ "G001", "S011" ], "before": "bias parameter0 same-law expectation := sum(0, 1/16, 9/4, 325/16)", "after": "bias parameter0 same-law expectation = 181/8", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色與已核中間量精確代值，保留參數、樣本、目標與分母，不交換未授權的聲稱。", "en": "Substitute original roles and established intermediates exactly,retaining parameter,outcome,target and denominator roles without replacing the claim." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 bias parameter0 same-law expectation，不以小數近似替代。", "en": "Recompute bias parameter0 same-law expectation with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "0", "1/16", "9/4", "325/16" ], "output": "181/8", "label": "bias parameter0 same-law expectation" } }, { "id": "S013", "uses": [ "G001", "S012" ], "before": "bias parameter0 expectation minus actual target := sub(181/8, 1/2)", "after": "bias parameter0 expectation minus actual target = 177/8", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色與已核中間量精確代值，保留參數、樣本、目標與分母，不交換未授權的聲稱。", "en": "Substitute original roles and established intermediates exactly,retaining parameter,outcome,target and denominator roles without replacing the claim." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 bias parameter0 expectation minus actual target，不以小數近似替代。", "en": "Recompute bias parameter0 expectation minus actual target with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "181/8", "1/2" ], "output": "177/8", "label": "bias parameter0 expectation minus actual target" } }, { "id": "S014", "uses": [ "G001", "S013" ], "before": "fixed original parameter SLOT=0;actual aligned theta VALUE=1/2;SAME complete law=[1/32, 1/16, 3/32, 13/16];same statistic=[0, 1, 24, 25];weighted terms=[0, 1/16, 9/4, 325/16]", "after": "E_at_slot[T]=181/8;Bias=E_at_slot[T]-ACTUAL theta value=177/8", "relation": "implies", "rule_id": "bias_same_law_expectation_minus_target_not_index", "conditions": [], "explanation": { "zh-Hant": "這裡已明示g(theta)=theta，所以減原theta_values裡的目標值，不減slot索引、不減一次estimate，也不混別參數的law。", "en": "The target g(theta)=theta is now declared.Subtract the aligned theta_values entry,not its slot index or one observed estimate,and use no other parameter's law." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S015", "uses": [ "G001", "S014" ], "before": "original parameter SLOT=0;original outcome=2;observed estimate=24;SEPARATE same-law bias=177/8", "after": "single-observation property sufficiency=否;NOT a comparison of whether estimate numerically equals bias;no zero-variance/consistency/sufficiency/minimum-MSE claim", "relation": "implies", "rule_id": "bias_observed_No_nonclaim_not_numerical_inequality", "conditions": [], "explanation": { "zh-Hant": "No只是不從一次觀察推出其他性質，並非宣稱這次estimate數值必不等bias。無偏本身也不推出零變異、一致性、充分性或最小MSE；需要各自目標與抽樣架構。", "en": "The No withholds property claims from one observation;it does not assert numerical inequality of estimate and bias.Unbiasedness itself does not imply zero variance,consistency,sufficiency or minimum MSE;these require their own target and sampling framework." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null } ], "math_model": { "result": [ 0, 2, 24, "177/8", false, "observed_estimate_not_bias_and_unbiased_not_zero_variance_consistency_sufficiency_or_minimum_MSE" ] }, "conclusion": { "canonical_value": "(0, 2, 24, 177/8, 否, observed_estimate_not_bias_and_unbiased_not_zero_variance_consistency_sufficiency_or_minimum_MSE)", "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-20261106-r03-estimator-bias-foundations", "batch_path": "public/data/questions/batches/batch-20261014-advance-20261106-r03-estimator-bias-foundations/questions.jsonl", "batch_sha256": "e354f494661b143d421db9a0858f697e75c0a01262179ea2aa35c0979e07a1d8", "original_line": 98, "original_line_sha256": "c92dedb681d66cebed2213880191e5c3f407b67197b7df0684eb8fa1a14b3db1", "question_compact_sha256": "0184de19ca2cead94946aabd389da85c52ab7ea318645c734b2cbbe9e9f970c2", "english_row_compact_sha256": "45abd140b7c8482e42d3b6856cf36536d55aa32c4642b34e1c8b08a4eb2934df", "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261106-r03-estimator-bias-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261106-r03-estimator-bias-foundations.en.jsonl" }, "mko_bindings": { "mko-estimator-bias": { "sha256": "be64de19751560ba6bd5142b5efa74407be5c35def263eb936120c6b63925da6", "english_sha256": "20825b4dd1d176eec9f31fe0ce7332c60f17ef65eae2ce83800f43e122f82a68", "original_path": "public/data/mko/estimator-bias.json", "english_path": "public/data/i18n/editions/mko-estimator-bias.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "7be57d88eceb13736454f82dd18bb3c4ec9d30c0367f974dcefdf8990dc4e3cb", "original_candidate_sha256": "19098159f225823e3855fe26199917bf90f238c6c0184a8faa2f9e8215149f61", "original_candidate_line_sha256": "19098159f225823e3855fe26199917bf90f238c6c0184a8faa2f9e8215149f61" }, "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-20261026-008-p38", "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": "065507b602ceee60cf47a700d387a51940e0c6724c35a3336a7a7948a199ed80", "question_first_witness_sha256": "7203f33b030792559673b0fee520a8c0e70903c4dd970b35293aa40852f333d6" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 15, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "c65b92932430cbcec332766a5f75d2abb984064eea224d1c89cfa194c5a71a69", "arithmetic_steps": 8 }, "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." } }