{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261003-r04-quadratic-equation-0066", "pilot_number": "R0068-34616", "number": 34616, "family_id": "qf-quadratic-root-verification", "title": { "zh-Hant": "第 34616 題：精確有理根代入驗證", "en": "Question 34616: Exact Substitution of a Rational Root Candidate" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261003-r04-quadratic-equation-0066", "batch_id": "batch-20261003-r04-quadratic-equation-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-quadratic-equation" ], "title_zh": "精確有理根代入驗證", "stem_zh": "在實數論域，(-2)x²+(-1)x+(6)=0 的 a≠0。最簡正分母候選 x=2/1 是否為解？", "answer": { "kind": "short_text", "value": "否", "explanation_zh": "分母清除後=-4。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是否。" }, "difficulty": { "band": "upper_secondary", "level": 2, "skills": [ "精確有理根代入驗證" ] }, "variant": { "family_id": "qf-quadratic-root-verification", "seed": 202610034066, "parameters": { "a": -2, "b": -1, "c": 6, "p": 2, "q": 1, "domain": "reals", "operation": "root_verification", "semantic_template": "qf-quadratic-root-verification/{\"a\":-2,\"b\":-1,\"c\":6,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"2\",\"q\":\"1\"}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_integer_rational_arithmetic", "producer_source_snapshot_check", "producer_substantive_template_deduplication" ], "warning_zh": "僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。" }, "provenance": { "generator_role": "question_producer", "generator_model": "Codex independent peer (inherited model; exact runtime model not exposed)", "generated_at": "2026-10-03", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261003-r04-quadratic-equation-0066", "batch_id": "batch-20261003-r04-quadratic-equation-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "e417f62c702c1946871c4fc71ba8a118733ea43245c90b2e2597163f851f94e0", "family_id": "qf-quadratic-root-verification", "seed": 202610034066, "semantic_template": "qf-quadratic-root-verification/{\"a\":-2,\"b\":-1,\"c\":6,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"2\",\"q\":\"1\"}" }, "fields": { "title": "Exact Substitution of a Rational Root Candidate", "stem": "Over the reals, (-2)x²+(-1)x+(6)=0 has a≠0. Is the reduced rational candidate x=2/1, with positive denominator, a solution?", "answer": { "kind": "short_text", "value": "No", "explanation": "Since q=1>0, clear denominators by multiplying the substituted expression by q². Its numerator is -4; comparison with zero gives No." }, "skills": [ "Exact Substitution of a Rational Root Candidate" ], "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": "在實數論域，(-2)x²+(-1)x+(6)=0 的 a≠0。最簡正分母候選 x=2/1 是否為解？", "en": "Over the reals, (-2)x²+(-1)x+(6)=0 has a≠0. Is the reduced rational candidate x=2/1, with positive denominator, a solution?" } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-quadratic-root-verification, [a, b, c, domain, operation, p, q]]", "after": "derived = [root_verification, reals]", "relation": "implies", "rule_id": "R68_BANK_specific_keys_operations_and_numeric_guards", "conditions": [], "explanation": { "zh-Hant": "按來源分bank：legacy raw SAFE/衍生BigInt無界，BASE Number.isInteger不偷加SAFE/百萬界。underscore operation、domain及寬/嚴keys各依本bank；原JSON完整保存。", "en": "Separate source banks:legacy RAW SAFE with unbounded derived BigInts versus BASE Number.isInteger without invented SAFE/million caps.Operations,domains and permissive/exact keys follow THIS bank.Keep ORIGINAL JSON intact." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [-2, -1, 6, 2, 1]", "after": "derived = [2/1, 是]", "relation": "implies", "rule_id": "Quadratic_ROOT_candidate_ALREADY_reduced_positive_DEN", "conditions": [], "explanation": { "zh-Hant": "先驗a非0、candidate原表示已最簡且den正；0候選只能是0/1。此題只驗此candidate，No是合法結果，不強求D非負或完全平方。", "en": "FIRST qualify a≠0 and an ALREADY reduced candidate with POSITIVE denominator.Zero can only be0/1.This task checks THIS candidate;No is legal and does not require a nonnegative or square discriminant." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "Root verification SOURCE unused discriminant b squared := mul(-1, -1)", "after": "Root verification SOURCE unused discriminant b squared = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Root verification SOURCE unused discriminant b squared，不以小數近似替代。", "en": "Recompute Root verification SOURCE unused discriminant b squared with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "-1", "-1" ], "output": "1", "label": "Root verification SOURCE unused discriminant b squared" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "Root verification SOURCE discriminant ORIGINAL a times c := mul(-2, 6)", "after": "Root verification SOURCE discriminant ORIGINAL a times c = -12", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Root verification SOURCE discriminant ORIGINAL a times c，不以小數近似替代。", "en": "Recompute Root verification SOURCE discriminant ORIGINAL a times c with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "-2", "6" ], "output": "-12", "label": "Root verification SOURCE discriminant ORIGINAL a times c" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "Root verification SOURCE unused discriminant four a c := mul(4, -12)", "after": "Root verification SOURCE unused discriminant four a c = -48", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Root verification SOURCE unused discriminant four a c，不以小數近似替代。", "en": "Recompute Root verification SOURCE unused discriminant four a c with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "4", "-12" ], "output": "-48", "label": "Root verification SOURCE unused discriminant four a c" } }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "Root verification SOURCE unused signed discriminant := sub(1, -48)", "after": "Root verification SOURCE unused signed discriminant = 49", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Root verification SOURCE unused signed discriminant，不以小數近似替代。", "en": "Recompute Root verification SOURCE unused signed discriminant with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "1", "-48" ], "output": "49", "label": "Root verification SOURCE unused signed discriminant" } }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "Root verification ORIGINAL candidate numerator squared := mul(2, 2)", "after": "Root verification ORIGINAL candidate numerator squared = 4", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Root verification ORIGINAL candidate numerator squared，不以小數近似替代。", "en": "Recompute Root verification ORIGINAL candidate numerator squared with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "2", "2" ], "output": "4", "label": "Root verification ORIGINAL candidate numerator squared" } }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "Root verification ORIGINAL candidate denominator squared := mul(1, 1)", "after": "Root verification ORIGINAL candidate denominator squared = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Root verification ORIGINAL candidate denominator squared，不以小數近似替代。", "en": "Recompute Root verification ORIGINAL candidate denominator squared with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "1" ], "output": "1", "label": "Root verification ORIGINAL candidate denominator squared" } }, { "id": "S009", "uses": [ "G001", "S008" ], "before": "Root verification ORIGINAL a times numerator squared := mul(-2, 4)", "after": "Root verification ORIGINAL a times numerator squared = -8", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Root verification ORIGINAL a times numerator squared，不以小數近似替代。", "en": "Recompute Root verification ORIGINAL a times numerator squared with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "-2", "4" ], "output": "-8", "label": "Root verification ORIGINAL a times numerator squared" } }, { "id": "S010", "uses": [ "G001", "S009" ], "before": "Root verification ORIGINAL b times candidate numerator := mul(-1, 2)", "after": "Root verification ORIGINAL b times candidate numerator = -2", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Root verification ORIGINAL b times candidate numerator，不以小數近似替代。", "en": "Recompute Root verification ORIGINAL b times candidate numerator with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "-1", "2" ], "output": "-2", "label": "Root verification ORIGINAL b times candidate numerator" } }, { "id": "S011", "uses": [ "G001", "S010" ], "before": "Root verification ORIGINAL b numerator denominator := mul(-2, 1)", "after": "Root verification ORIGINAL b numerator denominator = -2", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Root verification ORIGINAL b numerator denominator，不以小數近似替代。", "en": "Recompute Root verification ORIGINAL b numerator denominator with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "-2", "1" ], "output": "-2", "label": "Root verification ORIGINAL b numerator denominator" } }, { "id": "S012", "uses": [ "G001", "S011" ], "before": "Root verification ORIGINAL c times denominator squared := mul(6, 1)", "after": "Root verification ORIGINAL c times denominator squared = 6", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Root verification ORIGINAL c times denominator squared，不以小數近似替代。", "en": "Recompute Root verification ORIGINAL c times denominator squared with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "6", "1" ], "output": "6", "label": "Root verification ORIGINAL c times denominator squared" } }, { "id": "S013", "uses": [ "G001", "S012" ], "before": "Root verification ORIGINAL all denominator-cleared terms := sum(-8, -2, 6)", "after": "Root verification ORIGINAL all denominator-cleared terms = -4", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Root verification ORIGINAL all denominator-cleared terms，不以小數近似替代。", "en": "Recompute Root verification ORIGINAL all denominator-cleared terms with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "-8", "-2", "6" ], "output": "-4", "label": "Root verification ORIGINAL all denominator-cleared terms" } }, { "id": "S014", "uses": [ "G001", "S013" ], "before": "source roles = [-2, -1, 6, 2, 1, 49]", "after": "derived = [-4, 否]", "relation": "implies", "rule_id": "Quadratic_ROOT_clear_NONzero_denominator_ALL_three_terms", "conditions": [], "explanation": { "zh-Hant": "將原式在x=p/q代入，再乘非零q²，等價於a*p²+b*p*q+c*q²=0。保全部三項含0項；SOURCE也先算D但此family不以D符號/平方性限制驗根，更不由單一候選宣稱所有根。", "en": "Substitute x=p/q into the ORIGINAL equation and multiply by NONZERO q².This is equivalent to a*p²+b*p*q+c*q²=0.Retain ALL three terms,including zeros.The SOURCE computes D but this family does not gate its sign/squareness or infer the complete root set." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null } ], "math_model": { "result": "否" }, "conclusion": { "canonical_value": "否", "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-20261003-r04-quadratic-equation-foundations", "batch_path": "public/data/questions/batches/batch-20261003-r04-quadratic-equation-foundations/questions.jsonl", "batch_sha256": "66a176b962ca84e02bebfdfca16c81ee9677788154f1765c2bfa965a41fce5f6", "original_line": 66, "original_line_sha256": "6710b3aae5130ee5038baa04cf7cc0ee989988664b4c9ec9a8174525304e481f", "question_compact_sha256": "e417f62c702c1946871c4fc71ba8a118733ea43245c90b2e2597163f851f94e0", "english_row_compact_sha256": "1cb766ee304eb0bd03dcc1887a4eeb3a9ca7d9464d87fc3d800d09d9f49b1e06", "english_manifest_path": "public/data/i18n/editions/batch-20261003-r04-quadratic-equation-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261003-r04-quadratic-equation-foundations.en.jsonl" }, "mko_bindings": { "mko-quadratic-equation": { "sha256": "d04aa30d9e57bfe7e7df1f57f60f8361ce982217aa4548374680659f56b38851", "english_sha256": "733cbb98c4349ec66f14ef06f4f713641d49d16ee06b555538ec686c7756deaa", "original_path": "public/data/mko/quadratic-equation.json", "english_path": "public/data/i18n/editions/mko-quadratic-equation.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "345142be27643acca9d0fec2422ac7311b85bf142709391cd6b5b3a33c03cf8e", "original_candidate_sha256": "3751e88ee9c9e8b36984bc966148b82f44cb11f6a433085d23c28203e12d7bd7", "original_candidate_line_sha256": "3751e88ee9c9e8b36984bc966148b82f44cb11f6a433085d23c28203e12d7bd7" }, "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-p69", "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": "e7a54104fa02c235f7591329bd6db8d626dd74bf0fae29c557b1f269c85066ed", "question_first_witness_sha256": "8401a3c2064c1275a6a7ea8f00412fa12286cec7b2db6c305ff9dba3724ae229" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 14, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "bca71e82a3b603522a7c8b63fcbc81f6ac763288e5b122c1663da40e54865d65", "arithmetic_steps": 11 }, "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." } }