{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261104-r04-statistical-estimator-0083", "pilot_number": "R0035-18158", "number": 18158, "family_id": "qf-mod35-estimator-property-nonconclusion", "title": { "zh-Hant": "第 18158 題：統計估計量", "en": "Question 18158: Withholding Statistical Claims Does Not Prove Their Negations" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261014-advance-20261104-r04-statistical-estimator-0083", "batch_id": "batch-20261014-advance-20261104-r04-statistical-estimator-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-statistical-estimator" ], "title_zh": "統計估計量", "stem_zh": "同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,8,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "answer": { "kind": "expression", "value": "([0, 8, 16], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)", "explanation_zh": "Wave5第四層核對=([0, 8, 16], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。" }, "difficulty": { "band": "undergraduate_core", "level": 1, "skills": [ "統計估計量" ] }, "variant": { "family_id": "qf-mod35-estimator-property-nonconclusion", "seed": 202611044083, "parameters": { "parameter_count": 2, "outcome_count": 3, "laws": [ [ [ 1, 11 ], [ 1, 11 ], [ 9, 11 ] ], [ [ 1, 2 ], [ 1, 3 ], [ 1, 6 ] ] ], "statistic": [ 0, 8, 16 ], "domain": "Finite_model_total_statistic", "operation": "estimator-property-nonconclusion", "semantic_template": "qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,8,16]}" } }, "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、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、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-20261104-r04-statistical-estimator-0083", "batch_id": "batch-20261014-advance-20261104-r04-statistical-estimator-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "5c640791920c9482f976f0b0a048c20673f2e1147275cdd0344237df927eb818", "family_id": "qf-mod35-estimator-property-nonconclusion", "seed": 202611044083, "semantic_template": "qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,8,16]}" }, "fields": { "title": "Withholding Statistical Claims Does Not Prove Their Negations", "stem": "Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 8, 16] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).", "answer": { "kind": "expression", "value": "([0, 8, 16], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)", "explanation": "These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 8, 16], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)." }, "skills": [ "Withholding Statistical Claims Does Not Prove Their Negations" ], "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parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,8,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "en": "Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 8, 16] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source operation=estimator-property-nonconclusion;original snapshot and mathematics retained", "after": "explicit ordered source output fields=[statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary]", "relation": "implies", "rule_id": "source_ordered_interface_explicit_without_javascript", "conditions": [], "explanation": { "zh-Hant": "原題的歷史介面標記保留在快照；本頁直接列原始欄位順序，不需JavaScript或外部表。欄位描述不自動成為數學證據，No標記須依本題的聲稱範圍解讀。", "en": "Keep the historical interface marker in the original snapshot while giving ordered fields here,without JavaScript or an external table.Labels are not mathematical evidence,and each No marker retains the operation's 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": "estimator parameter0 complete law sum := sum(1/11, 1/11, 9/11)", "after": "estimator parameter0 complete law sum = 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計算，保留索引、分母、正負號及所屬載體。", "en": "Compute exactly from original roles and established intermediates,retaining indices,denominators,signs and the relevant carrier." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 estimator parameter0 complete law sum，不以小數近似替代。", "en": "Recompute estimator parameter0 complete law sum with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1/11", "1/11", "9/11" ], "output": "1", "label": "estimator parameter0 complete law sum" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "original parameter=0;SAME outcome carrier Fin(3);aligned reduced candidate law=[1/11, 1/11, 9/11]", "after": "sum=1;nonnegative=是;law qualified=是", "relation": "implies", "rule_id": "estimator_complete_laws_separate_from_total_statistic", "conditions": [], "explanation": { "zh-Hant": "模型每列須非負且總和1，無效候選仍帶False保留；一個total statistic本身不能修好機率模型。", "en": "Every model row must be nonnegative and total1.Invalid candidate rows retain false flags;a total statistic does not repair a probability model." }, "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": "estimator parameter1 complete law sum := sum(1/2, 1/3, 1/6)", "after": "estimator parameter1 complete law sum = 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計算，保留索引、分母、正負號及所屬載體。", "en": "Compute exactly from original roles and established intermediates,retaining indices,denominators,signs and the relevant carrier." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 estimator parameter1 complete law sum，不以小數近似替代。", "en": "Recompute estimator parameter1 complete law sum with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1/2", "1/3", "1/6" ], "output": "1", "label": "estimator parameter1 complete law sum" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "original parameter=1;SAME outcome carrier Fin(3);aligned reduced candidate law=[1/2, 1/3, 1/6]", "after": "sum=1;nonnegative=是;law qualified=是", "relation": "implies", "rule_id": "estimator_complete_laws_separate_from_total_statistic", "conditions": [], "explanation": { "zh-Hant": "模型每列須非負且總和1，無效候選仍帶False保留；一個total statistic本身不能修好機率模型。", "en": "Every model row must be nonnegative and total1.Invalid candidate rows retain false flags;a total statistic does not repair a probability model." }, "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": "original parameter carrier Fin(2);common outcome carrier Fin(3);ONE original statistic array=[0, 8, 16]", "after": "all model laws qualified=是;one value per outcome=是;SAME statistic map T(o) at EVERY parameter", "relation": "implies", "rule_id": "estimator_definition_parameter_independence_not_distribution_free", "conditions": [], "explanation": { "zh-Hant": "T的定義只吃觀察索引，不吃未知parameter；這是函數定義不依θ，不表示T(X)的分布或期望不能隨θ變。此有限模型沒有給estimand、prior或posterior。", "en": "The statistic definition takes an observation index,not the unknown parameter.This is functional parameter-independence,not a claim that the law or expectation of T(X) is parameter-free.No estimand,prior or posterior has been supplied." }, "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": "single total statistic=[0, 8, 16];model qualified=是;no estimand/prior/asymptotic sampling sequence supplied", "after": "four literal No markers WITHHOLD claims;not four failed tests;no_unbiased_consistent_sufficient_identifiable_or_posterior_claim", "relation": "implies", "rule_id": "estimator_property_nonconclusions_not_negations", "conditions": [], "explanation": { "zh-Hant": "四個否是定義層級不作聲稱的標記，不是證明有偏、不一致或其他性質為假。沒有estimand與漸近抽樣架構，不自行補出這些問題再作判決。", "en": "The four No values withhold definition-level claims;they do not prove bias,inconsistency or other negated properties.Without an estimand and asymptotic sampling setup,do not invent and decide those questions." }, "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, 8, 16 ], false, false, false, false, "no_unbiased_consistent_sufficient_identifiable_or_posterior_claim" ] }, "conclusion": { "canonical_value": "([0, 8, 16], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)", "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-20261104-r04-statistical-estimator-foundations", "batch_path": "public/data/questions/batches/batch-20261014-advance-20261104-r04-statistical-estimator-foundations/questions.jsonl", "batch_sha256": "afc2520e7f5cce5bf9888e56cb262e8e9239f04f3d0b35b124ac57d94cd259c3", "original_line": 83, "original_line_sha256": "2a691da717846f4b5c68a5d66c900592418dfaa65b0eea712edca54c1638accf", "question_compact_sha256": "5c640791920c9482f976f0b0a048c20673f2e1147275cdd0344237df927eb818", "english_row_compact_sha256": "577d3b8dcb4cdb8a83c3c866c906ee88ad5df3571766d70336f709e36d9031af", "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261104-r04-statistical-estimator-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261104-r04-statistical-estimator-foundations.en.jsonl" }, "mko_bindings": { "mko-statistical-estimator": { "sha256": "ba7fbdff9e10ebc9977253d4edccfcba77e5e47c0404aae6d00ad578d8bf6d2f", "english_sha256": "d391d517379756c16fdbbb5518416c50d6391c8b6b189ea66e1178dbe90b2c2a", "original_path": "public/data/mko/statistical-estimator.json", "english_path": "public/data/i18n/editions/mko-statistical-estimator.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "9adff0bbee39d9c3dec346304161ea9633576ccd5ca954f6b64ad482d2533a8a", "original_candidate_sha256": "9ae3217b58008be63b50a21b08fbb2edf84625c5c276cec077aca6a68a03865c", "original_candidate_line_sha256": "9ae3217b58008be63b50a21b08fbb2edf84625c5c276cec077aca6a68a03865c" }, "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-p36", "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": "713db6309b22bf8b31f0253d4aaa7aca9011ab908587ae0e9d4a365edce1f9bc", "question_first_witness_sha256": "0338a3db344ab237113fc63be29153c3684da96e388109e9dcd913a0a693aed2" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 7, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "03628a8e3798081b247e65001bed72b7947b5dd97881f5f7936cb657acdcefe2", "arithmetic_steps": 2 }, "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." } }