{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261010-advance-20261014-r06-absolute-value-0039", "pilot_number": "R0059-30314", "number": 30314, "family_id": "qf-density14-absolute-three-point-distances", "title": { "zh-Hant": "第 30314 題：三點距離與路徑差", "en": "Question 30314: Three Rational Distances and Path Defect" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261010-advance-20261014-r06-absolute-value-0039", "batch_id": "batch-20261010-advance-20261014-r06-absolute-value-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-absolute-value" ], "title_zh": "三點距離與路徑差", "stem_zh": "有理嵌入的絕對值協議；有序points=[0/1, 13/2, 14/2]。依序求 (d01, d12, d02, d01+d12−d02) 的精確有理數。", "answer": { "kind": "expression", "value": "(13/2, 1/2, 7/1, 0/1)", "explanation_zh": "三點距離與路徑差=(13/2, 1/2, 7/1, 0/1)。各段直接取差的絕對值；路徑量不冒充端點距離，有限差值非三角不等式普遍證明。有限分段核對非全部實數性質證明。" }, "difficulty": { "band": "lower_secondary", "level": 2, "skills": [ "三點距離與路徑差" ] }, "variant": { "family_id": "qf-density14-absolute-three-point-distances", "seed": 202610146039, "parameters": { "points": [ [ 0, 1 ], [ 13, 2 ], [ 14, 2 ] ], "domain": "finite_rational_absolute_protocol", "operation": "density14_absolute_three_point_distances", "semantic_template": "qf-density14-absolute-three-point-distances/[\"13/2\",\"1/2\",\"7/1\"]" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_integer_rational_arithmetic", "producer_finite_enumeration", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-10", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261010-advance-20261014-r06-absolute-value-0039", "batch_id": "batch-20261010-advance-20261014-r06-absolute-value-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "2f376ae98ddd2a1e992b437f2b4acd31de3c9eac5a5093596fe5a49e81554aa5", "family_id": "qf-density14-absolute-three-point-distances", "seed": 202610146039, "semantic_template": "qf-density14-absolute-three-point-distances/[\"13/2\",\"1/2\",\"7/1\"]" }, "fields": { "title": "Three Rational Distances and Path Defect", "stem": "Use exact rational absolute values embedded in R; negative representation denominators are normalized before deciding signs. Ordered points=[0/1, 13/2, 14/2]. Give (d01, d12, d02, d01+d12−d02). Use exact reduced fractions with positive denominators, retaining /1 for integers.", "answer": { "kind": "expression", "value": "(13/2, 1/2, 7/1, 0/1)", "explanation": "Take the absolute difference for each segment separately; a path sum is not an endpoint distance, and finite checks are not a universal triangle-inequality proof. The exact result, retaining the requested order, is (13/2, 1/2, 7/1, 0/1)." }, "skills": [ "Three Rational Distances and Path Defect" ], "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": "有理嵌入的絕對值協議；有序points=[0/1, 13/2, 14/2]。依序求 (d01, d12, d02, d01+d12−d02) 的精確有理數。", "en": "Use exact rational absolute values embedded in R; negative representation denominators are normalized before deciding signs. Ordered points=[0/1, 13/2, 14/2]. Give (d01, d12, d02, d01+d12−d02). Use exact reduced fractions with positive denominators, retaining /1 for integers." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-density14-absolute-three-point-distances, density14_absolute_three_point_distances, finite_rational_absolute_protocol]", "after": "derived = [[distance_01, distance_12, distance_02, path_minus_direct]]", "relation": "implies", "rule_id": "R59_EXACT_family_domain_FULLprefix_operation_and_answer_roles", "conditions": [], "explanation": { "zh-Hant": "保原bank的完整operation前綴、domain及輸出欄序；frame只用orthogonal_equal_unit，角度unit只用degrees。分數整數保/1；不增不存在的參數，不改原中英來源。", "en": "Retain the ORIGINAL bank full operation prefix,domain and ordered answer roles.Use orthogonal_equal_unit only where a frame is declared,and degrees where an angle unit is declared.Integer fractions retain/1.Do not invent parameters or alter original bilingual sources." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [Absolute original point0, [0, 1]]", "after": "derived = [0/1, 0, 1]", "relation": "implies", "rule_id": "Absolute_RAW_SAFE_pair_NONZERO_den_normalize_SIGN_and_gcd", "conditions": [], "explanation": { "zh-Hant": "原pair兩數SAFE且den非0；這個bank允許負den，先正分母約分才按值選sign。不套primitive正den或STR22 component cap。", "en": "Require a RAW SAFE pair with nonzero denominator.This bank ALLOWS negative denominators;normalize sign/gcd BEFORE deciding the value sign.Do not import a primitive positive-denominator rule or a STR22 component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [Absolute original point1, [13, 2]]", "after": "derived = [13/2, 13, 2]", "relation": "implies", "rule_id": "Absolute_RAW_SAFE_pair_NONZERO_den_normalize_SIGN_and_gcd", "conditions": [], "explanation": { "zh-Hant": "原pair兩數SAFE且den非0；這個bank允許負den，先正分母約分才按值選sign。不套primitive正den或STR22 component cap。", "en": "Require a RAW SAFE pair with nonzero denominator.This bank ALLOWS negative denominators;normalize sign/gcd BEFORE deciding the value sign.Do not import a primitive positive-denominator rule or a STR22 component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [Absolute original point2, [14, 2]]", "after": "derived = [7/1, 7, 1]", "relation": "implies", "rule_id": "Absolute_RAW_SAFE_pair_NONZERO_den_normalize_SIGN_and_gcd", "conditions": [], "explanation": { "zh-Hant": "原pair兩數SAFE且den非0；這個bank允許負den，先正分母約分才按值選sign。不套primitive正den或STR22 component cap。", "en": "Require a RAW SAFE pair with nonzero denominator.This bank ALLOWS negative denominators;normalize sign/gcd BEFORE deciding the value sign.Do not import a primitive positive-denominator rule or a STR22 component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "Absolute ORIGINAL point0 minus point1 := sub(0, 13/2)", "after": "Absolute ORIGINAL point0 minus point1 = -13/2", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原角色精確代值，不作浮點近似；SAFE只驗raw輸入，衍生整數／有理數不截斷，不套其他銀行的component cap。", "en": "Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Absolute ORIGINAL point0 minus point1，不以小數近似替代。", "en": "Recompute Absolute ORIGINAL point0 minus point1 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "0", "13/2" ], "output": "-13/2", "label": "Absolute ORIGINAL point0 minus point1" } }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "Absolute segment01 ORIGINAL negative branch negation := sub(0, -13/2)", "after": "Absolute segment01 ORIGINAL negative branch negation = 13/2", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原角色精確代值，不作浮點近似；SAFE只驗raw輸入，衍生整數／有理數不截斷，不套其他銀行的component cap。", "en": "Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Absolute segment01 ORIGINAL negative branch negation，不以小數近似替代。", "en": "Recompute Absolute segment01 ORIGINAL negative branch negation with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "0", "-13/2" ], "output": "13/2", "label": "Absolute segment01 ORIGINAL negative branch negation" } }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "source roles = [Absolute segment01, -13/2]", "after": "derived = [否, 13/2]", "relation": "implies", "rule_id": "Absolute_value_normalized_sign_branch_ZERO_is_nonnegative", "conditions": [], "explanation": { "zh-Hant": "以已正規化數值的sign選分段：x>=0保x，x<0取0-x；zero在非負分支，不因raw負分母而誤判。", "en": "Choose the branch by the NORMALIZED value:x>=0 keeps x;for x<0 use0-x.Zero is in the nonnegative branch;do not misclassify a raw negative denominator." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "Absolute ORIGINAL point1 minus point2 := sub(13/2, 7)", "after": "Absolute ORIGINAL point1 minus point2 = -1/2", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原角色精確代值，不作浮點近似；SAFE只驗raw輸入，衍生整數／有理數不截斷，不套其他銀行的component cap。", "en": "Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Absolute ORIGINAL point1 minus point2，不以小數近似替代。", "en": "Recompute Absolute ORIGINAL point1 minus point2 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "13/2", "7" ], "output": "-1/2", "label": "Absolute ORIGINAL point1 minus point2" } }, { "id": "S009", "uses": [ "G001", "S008" ], "before": "Absolute segment12 ORIGINAL negative branch negation := sub(0, -1/2)", "after": "Absolute segment12 ORIGINAL negative branch negation = 1/2", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原角色精確代值，不作浮點近似；SAFE只驗raw輸入，衍生整數／有理數不截斷，不套其他銀行的component cap。", "en": "Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Absolute segment12 ORIGINAL negative branch negation，不以小數近似替代。", "en": "Recompute Absolute segment12 ORIGINAL negative branch negation with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "0", "-1/2" ], "output": "1/2", "label": "Absolute segment12 ORIGINAL negative branch negation" } }, { "id": "S010", "uses": [ "G001", "S009" ], "before": "source roles = [Absolute segment12, -1/2]", "after": "derived = [否, 1/2]", "relation": "implies", "rule_id": "Absolute_value_normalized_sign_branch_ZERO_is_nonnegative", "conditions": [], "explanation": { "zh-Hant": "以已正規化數值的sign選分段：x>=0保x，x<0取0-x；zero在非負分支，不因raw負分母而誤判。", "en": "Choose the branch by the NORMALIZED value:x>=0 keeps x;for x<0 use0-x.Zero is in the nonnegative branch;do not misclassify a raw negative denominator." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S011", "uses": [ "G001", "S010" ], "before": "Absolute ORIGINAL point0 minus point2 := sub(0, 7)", "after": "Absolute ORIGINAL point0 minus point2 = -7", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原角色精確代值，不作浮點近似；SAFE只驗raw輸入，衍生整數／有理數不截斷，不套其他銀行的component cap。", "en": "Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Absolute ORIGINAL point0 minus point2，不以小數近似替代。", "en": "Recompute Absolute ORIGINAL point0 minus point2 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "0", "7" ], "output": "-7", "label": "Absolute ORIGINAL point0 minus point2" } }, { "id": "S012", "uses": [ "G001", "S011" ], "before": "Absolute segment02 ORIGINAL negative branch negation := sub(0, -7)", "after": "Absolute segment02 ORIGINAL negative branch negation = 7", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原角色精確代值，不作浮點近似；SAFE只驗raw輸入，衍生整數／有理數不截斷，不套其他銀行的component cap。", "en": "Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Absolute segment02 ORIGINAL negative branch negation，不以小數近似替代。", "en": "Recompute Absolute segment02 ORIGINAL negative branch negation with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "0", "-7" ], "output": "7", "label": "Absolute segment02 ORIGINAL negative branch negation" } }, { "id": "S013", "uses": [ "G001", "S012" ], "before": "source roles = [Absolute segment02, -7]", "after": "derived = [否, 7]", "relation": "implies", "rule_id": "Absolute_value_normalized_sign_branch_ZERO_is_nonnegative", "conditions": [], "explanation": { "zh-Hant": "以已正規化數值的sign選分段：x>=0保x，x<0取0-x；zero在非負分支，不因raw負分母而誤判。", "en": "Choose the branch by the NORMALIZED value:x>=0 keeps x;for x<0 use0-x.Zero is in the nonnegative branch;do not misclassify a raw negative denominator." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S014", "uses": [ "G001", "S013" ], "before": "Absolute ORIGINAL two-segment path sum := sum(13/2, 1/2)", "after": "Absolute ORIGINAL two-segment path sum = 7", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原角色精確代值，不作浮點近似；SAFE只驗raw輸入，衍生整數／有理數不截斷，不套其他銀行的component cap。", "en": "Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Absolute ORIGINAL two-segment path sum，不以小數近似替代。", "en": "Recompute Absolute ORIGINAL two-segment path sum with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "13/2", "1/2" ], "output": "7", "label": "Absolute ORIGINAL two-segment path sum" } }, { "id": "S015", "uses": [ "G001", "S014" ], "before": "Absolute ORIGINAL path minus endpoint distance := sub(7, 7)", "after": "Absolute ORIGINAL path minus endpoint distance = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原角色精確代值，不作浮點近似；SAFE只驗raw輸入，衍生整數／有理數不截斷，不套其他銀行的component cap。", "en": "Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Absolute ORIGINAL path minus endpoint distance，不以小數近似替代。", "en": "Recompute Absolute ORIGINAL path minus endpoint distance with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "7", "7" ], "output": "0", "label": "Absolute ORIGINAL path minus endpoint distance" } }, { "id": "S016", "uses": [ "G001", "S015" ], "before": "source roles = [[0/1, 13/2, 7/1]]", "after": "derived = [[13/2, 1/2, 7/1], 0/1]", "relation": "implies", "rule_id": "Absolute_THREE_original_distances_AND_signed_path_defect", "conditions": [], "explanation": { "zh-Hant": "每段各自取abs；前兩段和不是第三段端點距離，gap以原路徑次序求。此完整有限有理實例不冒充一般三角不等式的形式證明。", "en": "Take the absolute value for EACH separate segment.The first-two-leg sum differs from the endpoint distance;retain the ORIGINAL path order for the gap.This complete finite rational instance is not a formal proof of the general triangle inequality." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null } ], "math_model": { "result": [ "13/2", "1/2", "7/1", "0/1" ] }, "conclusion": { "canonical_value": "(13/2, 1/2, 7/1, 0/1)", "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-20261010-advance-20261014-r06-absolute-value-foundations", "batch_path": "public/data/questions/batches/batch-20261010-advance-20261014-r06-absolute-value-foundations/questions.jsonl", "batch_sha256": "6f64d92445cd0622999a4aea7165b9a1bc243bbea1361e5440354586968dac04", "original_line": 39, "original_line_sha256": "2b989d4ad02df4d2dfe9bb8e35eec051a51fc16163630659df02b7f02e011d14", "question_compact_sha256": "2f376ae98ddd2a1e992b437f2b4acd31de3c9eac5a5093596fe5a49e81554aa5", "english_row_compact_sha256": "5d8b5904dcc948b25cba7d52e04f17dc91e7e4c2d4fc00208b75c9381db9581e", "english_manifest_path": "public/data/i18n/editions/batch-20261010-advance-20261014-r06-absolute-value-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261010-advance-20261014-r06-absolute-value-foundations.en.jsonl" }, "mko_bindings": { "mko-absolute-value": { "sha256": "7df0aed9ca41a0e67b84a464f450422348753d1171802220b41a103488fb5f95", "english_sha256": "7f191b7dbbd24ac7ec2a252a08d3178f961ef31414f76098c51f5f01d63473f6", "original_path": "public/data/mko/absolute-value.json", "english_path": "public/data/i18n/editions/mko-absolute-value.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "17d593a551933064f195bd9277d5085fe2b6c98e11cbda0c8aa27d11b7b07949", "original_candidate_sha256": "d30cd576bc238bd3b5104b07d8c78d2abf2728d32fd02ea14a241940459be63b", "original_candidate_line_sha256": "d30cd576bc238bd3b5104b07d8c78d2abf2728d32fd02ea14a241940459be63b" }, "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-20261026-011-p60", "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": "4c93dea3956f58509e20b3b8bbbf716dbc340b424a2a5177bc04aba9e8ea9ec5", "question_first_witness_sha256": "a5e56e0d64d622d7202840cef7019839c5a99244c602694190779155207dafdf" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 16, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "e9823c2be76dbf54560b09b374edbb86260e1f0a82599b6c282bdf3a1da312aa", "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." } }