{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261105-r06-sampling-distribution-0051", "pilot_number": "R0037-19126", "number": 19126, "family_id": "qf-mod36-sampling-observed-estimate-boundary", "title": { "zh-Hant": "第 19126 題：抽樣分布", "en": "Question 19126: An Observed Estimate Is Not the Whole Sampling Law" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261014-advance-20261105-r06-sampling-distribution-0051", "batch_id": "batch-20261014-advance-20261105-r06-sampling-distribution-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-sampling-distribution" ], "title_zh": "抽樣分布", "stem_zh": "共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],\"statistic\":[0,0,1,2],\"parameter\":0,\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "answer": { "kind": "expression", "value": "(0, 0, [[0, 3/8], [1, 3/8], [2, 1/4]], observed_estimate_is_not_sampling_distribution)", "explanation_zh": "Wave5第五層核對=(0, 0, [[0, 3/8], [1, 3/8], [2, 1/4]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。" }, "difficulty": { "band": "undergraduate_core", "level": 1, "skills": [ "抽樣分布" ] }, "variant": { "family_id": "qf-mod36-sampling-observed-estimate-boundary", "seed": 202611056051, "parameters": { "parameter_count": 2, "outcome_count": 4, "laws": [ [ [ 1, 8 ], [ 2, 8 ], [ 3, 8 ], [ 2, 8 ] ], [ [ 2, 12 ], [ 3, 12 ], [ 4, 12 ], [ 3, 12 ] ] ], "statistic": [ 0, 0, 1, 2 ], "parameter": 0, "outcome": 0, "domain": "Finite_parametric_pushforward_laws", "operation": "sampling-observed-estimate-boundary", "semantic_template": "qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],\"outcome\":0,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,1,2]}" } }, "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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、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-20261105-r06-sampling-distribution-0051", "batch_id": "batch-20261014-advance-20261105-r06-sampling-distribution-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "baca53481c4c88d4f46e8c44e2cb294f13bd0527c31d2078d20b996494e2d738", "family_id": "qf-mod36-sampling-observed-estimate-boundary", "seed": 202611056051, "semantic_template": "qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],\"outcome\":0,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,1,2]}" }, "fields": { "title": "An Observed Estimate Is Not the Whole Sampling Law", "stem": "Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/8, 2/8, 3/8, 2/8], [2/12, 3/12, 4/12, 3/12]], and one total parameter-independent statistic T=[0, 0, 1, 2] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=0. Give (outcome, estimate, law, boundary).", "answer": { "kind": "expression", "value": "(0, 0, [[0, 3/8], [1, 3/8], [2, 1/4]], observed_estimate_is_not_sampling_distribution)", "explanation": "Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (0, 0, [[0, 3/8], [1, 3/8], [2, 1/4]], observed_estimate_is_not_sampling_distribution)." }, "skills": [ "An Observed Estimate Is Not the Whole Sampling Law" ], "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模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],\"statistic\":[0,0,1,2],\"parameter\":0,\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "en": "Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/8, 2/8, 3/8, 2/8], [2/12, 3/12, 4/12, 3/12]], and one total parameter-independent statistic T=[0, 0, 1, 2] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=0. Give (outcome, estimate, law, boundary)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source operation=sampling-observed-estimate-boundary;original snapshot and mathematics retained", "after": "explicit ordered source output fields=[outcome, estimate, law, 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": "sampling parameter0 full law mass := sum(1/8, 1/4, 3/8, 1/4)", "after": "sampling 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 sampling parameter0 full law mass，不以小數近似替代。", "en": "Recompute sampling parameter0 full law mass with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1/8", "1/4", "3/8", "1/4" ], "output": "1", "label": "sampling parameter0 full law mass" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "sampling:original parameter SLOT=0;same outcome carrier Fin(4);ALL aligned law masses=[1/8, 1/4, 3/8, 1/4]", "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": "S004", "uses": [ "G001", "S003" ], "before": "sampling parameter1 full law mass := sum(1/6, 1/4, 1/3, 1/4)", "after": "sampling 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 sampling parameter1 full law mass，不以小數近似替代。", "en": "Recompute sampling parameter1 full law mass with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1/6", "1/4", "1/3", "1/4" ], "output": "1", "label": "sampling parameter1 full law mass" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "sampling:original parameter SLOT=1;same outcome carrier Fin(4);ALL aligned law masses=[1/6, 1/4, 1/3, 1/4]", "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": "sampling:parameter SLOT carrier Fin(2);common outcome carrier Fin(4);ONE total original statistic array=[0, 0, 1, 2]", "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": "sampling parameter0 statistic value0 full fibre mass := sum(1/8, 1/4)", "after": "sampling parameter0 statistic value0 full fibre mass = 3/8", "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 sampling parameter0 statistic value0 full fibre mass，不以小數近似替代。", "en": "Recompute sampling parameter0 statistic value0 full fibre mass with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1/8", "1/4" ], "output": "3/8", "label": "sampling parameter0 statistic value0 full fibre mass" } }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "FIXED original parameter SLOT=0;statistic value=0;FULL original fibre outcome indices=[0, 1];aligned law masses=[1/8, 1/4]", "after": "pushforward mass at value0=3/8;retain this row even if mass0", "relation": "implies", "rule_id": "sampling_complete_fibre_not_one_representative_or_null_deletion", "conditions": [], "explanation": { "zh-Hant": "相同T值的所有結果都加質量，不只選一個代表；原statistic有此值即留該列，即使本參數下其fibre質量為0。", "en": "Add masses from every outcome with the same statistic value,not one representative.Retain every value present in the original statistic even when its fibre has mass0 under this parameter." }, "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": "S009", "uses": [ "G001", "S008" ], "before": "sampling parameter0 statistic value1 full fibre mass := sum(3/8)", "after": "sampling parameter0 statistic value1 full fibre mass = 3/8", "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 sampling parameter0 statistic value1 full fibre mass，不以小數近似替代。", "en": "Recompute sampling parameter0 statistic value1 full fibre mass with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "3/8" ], "output": "3/8", "label": "sampling parameter0 statistic value1 full fibre mass" } }, { "id": "S010", "uses": [ "G001", "S009" ], "before": "FIXED original parameter SLOT=0;statistic value=1;FULL original fibre outcome indices=[2];aligned law masses=[3/8]", "after": "pushforward mass at value1=3/8;retain this row even if mass0", "relation": "implies", "rule_id": "sampling_complete_fibre_not_one_representative_or_null_deletion", "conditions": [], "explanation": { "zh-Hant": "相同T值的所有結果都加質量，不只選一個代表；原statistic有此值即留該列，即使本參數下其fibre質量為0。", "en": "Add masses from every outcome with the same statistic value,not one representative.Retain every value present in the original statistic even when its fibre has mass0 under this parameter." }, "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": "S011", "uses": [ "G001", "S010" ], "before": "sampling parameter0 statistic value2 full fibre mass := sum(1/4)", "after": "sampling parameter0 statistic value2 full fibre mass = 1/4", "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 sampling parameter0 statistic value2 full fibre mass，不以小數近似替代。", "en": "Recompute sampling parameter0 statistic value2 full fibre mass with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1/4" ], "output": "1/4", "label": "sampling parameter0 statistic value2 full fibre mass" } }, { "id": "S012", "uses": [ "G001", "S011" ], "before": "FIXED original parameter SLOT=0;statistic value=2;FULL original fibre outcome indices=[3];aligned law masses=[1/4]", "after": "pushforward mass at value2=1/4;retain this row even if mass0", "relation": "implies", "rule_id": "sampling_complete_fibre_not_one_representative_or_null_deletion", "conditions": [], "explanation": { "zh-Hant": "相同T值的所有結果都加質量，不只選一個代表；原statistic有此值即留該列，即使本參數下其fibre質量為0。", "en": "Add masses from every outcome with the same statistic value,not one representative.Retain every value present in the original statistic even when its fibre has mass0 under this parameter." }, "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": "S013", "uses": [ "G001", "S012" ], "before": "sampling parameter0 complete pushforward mass := sum(3/8, 3/8, 1/4)", "after": "sampling parameter0 complete pushforward 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 sampling parameter0 complete pushforward mass，不以小數近似替代。", "en": "Recompute sampling parameter0 complete pushforward mass with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "3/8", "3/8", "1/4" ], "output": "1", "label": "sampling parameter0 complete pushforward mass" } }, { "id": "S014", "uses": [ "G001", "S013" ], "before": "fixed parameter SLOT=0;ALL increasingly ordered statistic values=[0, 1, 2];disjoint complete fibres=[[0, 1], [2], [3]]", "after": "pushforward law=[[0, 3/8], [1, 3/8], [2, 1/4]];total mass=1;ANY set of statistic values has preimage equal to the union of its fibres", "relation": "implies", "rule_id": "sampling_pushforward_full_partition_probability_law", "conditions": [], "explanation": { "zh-Hant": "fibres互不相交且覆蓋共同樣本全集，所以任意事件的逆像質量就是相應各列和；這證整個離散抽樣law，不是幾次觀察的頻率或參數分布。", "en": "The disjoint fibres cover the entire common sample carrier,so the preimage probability of any set of statistic values is the sum of its rows.This gives the complete discrete sampling law,not observed frequencies or a distribution over parameters." }, "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": "supplied original outcome index=0;observed T(o)=0;SEPARATE full law at parameter SLOT=0", "after": "estimate VALUE=0;sampling LAW=[[0, 3/8], [1, 3/8], [2, 1/4]];observed_estimate_is_not_sampling_distribution", "relation": "implies", "rule_id": "sampling_observed_number_not_function_or_full_law", "conditions": [], "explanation": { "zh-Hant": "原觀察位置讀出一個數值，不把它當整個T函數、整張sampling law或未知參數。即使觀察值剛好等某參數數字，角色也不同。", "en": "Read one number at the original outcome index.Do not replace the estimator function,the full sampling law or the unknown parameter with that number;coinciding numeric labels do not merge their roles." }, "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, 0, [ [ 0, "3/8" ], [ 1, "3/8" ], [ 2, "1/4" ] ], "observed_estimate_is_not_sampling_distribution" ] }, "conclusion": { "canonical_value": "(0, 0, [[0, 3/8], [1, 3/8], [2, 1/4]], observed_estimate_is_not_sampling_distribution)", "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-20261105-r06-sampling-distribution-foundations", "batch_path": "public/data/questions/batches/batch-20261014-advance-20261105-r06-sampling-distribution-foundations/questions.jsonl", "batch_sha256": "192d93bc14e7cdc40ea1764c613e8a1ebc100ea960efbbf8a6ebdbb86d545379", "original_line": 51, "original_line_sha256": "2cae9d2e3a664749cea60f85a22d0d5d1b09a257dc4c5b96cd638a0aacd4f722", "question_compact_sha256": "baca53481c4c88d4f46e8c44e2cb294f13bd0527c31d2078d20b996494e2d738", "english_row_compact_sha256": "9d4aadd1fd0e7da34b118da5e61dc16fe3f807807c739dc54745e0d7a6d6c3e5", "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261105-r06-sampling-distribution-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261105-r06-sampling-distribution-foundations.en.jsonl" }, "mko_bindings": { "mko-sampling-distribution": { "sha256": "0878462afb0517679eb337ad1d5f12bd6025d7039d27a541544de8493ab9cdc9", "english_sha256": "1872de8113252797ce3bf87aa73156e94042d971e9ca7591f474298d6905770c", "original_path": "public/data/mko/sampling-distribution.json", "english_path": "public/data/i18n/editions/mko-sampling-distribution.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "7be57d88eceb13736454f82dd18bb3c4ec9d30c0367f974dcefdf8990dc4e3cb", "original_candidate_sha256": "27eb5b4d39907bd35fa64ba9e4188b387be0f02df2776606a78a100d8add0a52", "original_candidate_line_sha256": "27eb5b4d39907bd35fa64ba9e4188b387be0f02df2776606a78a100d8add0a52" }, "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": "c203c39a714db13c569cfa56cc274edf4747174c47700fb363f49955c2728c93", "arithmetic_steps": 6 }, "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." } }