{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261010-advance-20261014-r04-linear-equation-0037", "pilot_number": "R0060-30562", "number": 30562, "family_id": "qf-density14-linear-parameter-slice", "title": { "zh-Hant": "第 30562 題：三個參數切片的一次資格", "en": "Question 30562: Parameter-Dependent Linear and Constant Cases" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261010-advance-20261014-r04-linear-equation-0037", "batch_id": "batch-20261010-advance-20261014-r04-linear-equation-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-linear-equation" ], "title_zh": "三個參數切片的一次資格", "stem_zh": "Q上ax+b=0；非零a才是一次；a_i=t_i−k，k=2、b=-1、ts=[1, 14, 2]。依序列 (三係數, 三個一次資格, 三個解集class)，不忽略a_i=0。", "answer": { "kind": "expression", "value": "([-1, 12, 0], [是, 是, 否], [單解 -1/1, 單解 1/12, 無解])", "explanation_zh": "參數切片一次資格與解集=([-1, 12, 0], [是, 是, 否], [單解 -1/1, 單解 1/12, 無解])。逐個形成實際係數，分開非零根與退化常數式。退化常數等式不是一次方程，有限回代非一般線性系統證明。" }, "difficulty": { "band": "lower_secondary", "level": 2, "skills": [ "三個參數切片的一次資格" ] }, "variant": { "family_id": "qf-density14-linear-parameter-slice", "seed": 202610144037, "parameters": { "k": 2, "b": -1, "ts": [ 1, 14, 2 ], "domain": "finite_Q_affine_row_protocol", "operation": "density14_linear_parameter_slice", "semantic_template": "qf-density14-linear-parameter-slice/[[\"-1\",\"12\",\"0\"],[\"單解 -1/1\",\"單解 1/12\",\"無解\"]]" } }, "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-r04-linear-equation-0037", "batch_id": "batch-20261010-advance-20261014-r04-linear-equation-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "608b199b3b644e426f5e239e36095a644445a22a9efc7ebf64bd323fca9e4e1c", "family_id": "qf-density14-linear-parameter-slice", "seed": 202610144037, "semantic_template": "qf-density14-linear-parameter-slice/[[\"-1\",\"12\",\"0\"],[\"單解 -1/1\",\"單解 1/12\",\"無解\"]]" }, "fields": { "title": "Parameter-Dependent Linear and Constant Cases", "stem": "Over Q, ax+b=0 is linear only for a≠0; a=0 is a degenerate constant equation. a_i=t_i−k, k=2, b=-1, ordered ts=[1, 14, 2]. Give (three coefficients, three linear-eligibility values, three solution classes), retaining zero-coefficient cases.", "answer": { "kind": "expression", "value": "([-1, 12, 0], [Yes, Yes, No], [single-solution -1/1, single-solution 1/12, no-solution])", "explanation": "Form each actual coefficient before separating a unique rational root from all-Q/no-solution degeneracies; no general linear-system formal proof is implied. The exact result, retaining the requested order, is ([-1, 12, 0], [Yes, Yes, No], [single-solution -1/1, single-solution 1/12, no-solution])." }, "skills": [ "Parameter-Dependent Linear and Constant Cases" ], "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": "Q上ax+b=0；非零a才是一次；a_i=t_i−k，k=2、b=-1、ts=[1, 14, 2]。依序列 (三係數, 三個一次資格, 三個解集class)，不忽略a_i=0。", "en": "Over Q, ax+b=0 is linear only for a≠0; a=0 is a degenerate constant equation. a_i=t_i−k, k=2, b=-1, ordered ts=[1, 14, 2]. Give (three coefficients, three linear-eligibility values, three solution classes), retaining zero-coefficient cases." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-density14-linear-parameter-slice, density14_linear_parameter_slice, finite_Q_affine_row_protocol]", "after": "derived = [[ALL_derived_coefficients, ALL_linear_flags, ALL_solution_classes]]", "relation": "implies", "rule_id": "R60_EXACT_perbank_operation_domain_FRAME_and_output_roles", "conditions": [], "explanation": { "zh-Hant": "density14/15用full-prefix underscores，density17用local hyphens。coordinate frame與circle frame不同，輸出欄序／型別依本family，不改原中英／JSON／status。", "en": "density14/15 use FULL-prefix underscores;density17 uses LOCAL hyphens.The coordinate and circle frames differ.Retain THIS family ordered answer roles/types and all original bilingual JSON/status." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "Linear parameter ORIGINAL t0 minus k := sub(1, 2)", "after": "Linear parameter ORIGINAL t0 minus k = -1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數做精確整數／有理計算；只有raw輸入驗SAFE或本family明定小界，衍生值不重套界、不作浮點近似。", "en": "Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Linear parameter ORIGINAL t0 minus k，不以小數近似替代。", "en": "Recompute Linear parameter ORIGINAL t0 minus k with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "1", "2" ], "output": "-1", "label": "Linear parameter ORIGINAL t0 minus k" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "Linear parameter original slot0 ORIGINAL negated constant := sub(0, -1)", "after": "Linear parameter original slot0 ORIGINAL negated constant = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數做精確整數／有理計算；只有raw輸入驗SAFE或本family明定小界，衍生值不重套界、不作浮點近似。", "en": "Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Linear parameter original slot0 ORIGINAL negated constant，不以小數近似替代。", "en": "Recompute Linear parameter original slot0 ORIGINAL negated constant with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "0", "-1" ], "output": "1", "label": "Linear parameter original slot0 ORIGINAL negated constant" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "Linear parameter original slot0 ORIGINAL negative b over a := div(1, -1)", "after": "Linear parameter original slot0 ORIGINAL negative b over a = -1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數做精確整數／有理計算；只有raw輸入驗SAFE或本family明定小界，衍生值不重套界、不作浮點近似。", "en": "Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Linear parameter original slot0 ORIGINAL negative b over a，不以小數近似替代。", "en": "Recompute Linear parameter original slot0 ORIGINAL negative b over a with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "div", "inputs": [ "1", "-1" ], "output": "-1", "label": "Linear parameter original slot0 ORIGINAL negative b over a" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "Linear parameter original slot0 reverse ORIGINAL a times root := mul(-1, -1)", "after": "Linear parameter original slot0 reverse ORIGINAL a times root = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數做精確整數／有理計算；只有raw輸入驗SAFE或本family明定小界，衍生值不重套界、不作浮點近似。", "en": "Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Linear parameter original slot0 reverse ORIGINAL a times root，不以小數近似替代。", "en": "Recompute Linear parameter original slot0 reverse ORIGINAL a times root with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "-1", "-1" ], "output": "1", "label": "Linear parameter original slot0 reverse ORIGINAL a times root" } }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "Linear parameter original slot0 reverse ORIGINAL residual plus b := sum(1, -1)", "after": "Linear parameter original slot0 reverse ORIGINAL residual plus b = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數做精確整數／有理計算；只有raw輸入驗SAFE或本family明定小界，衍生值不重套界、不作浮點近似。", "en": "Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Linear parameter original slot0 reverse ORIGINAL residual plus b，不以小數近似替代。", "en": "Recompute Linear parameter original slot0 reverse ORIGINAL residual plus b with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1", "-1" ], "output": "0", "label": "Linear parameter original slot0 reverse ORIGINAL residual plus b" } }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "source roles = [Linear parameter original slot0, -1, -1]", "after": "derived = [-1/1, 0/1]", "relation": "implies", "rule_id": "Linear_NONZERO_a_exact_Q_root_AND_original_substitution", "conditions": [], "explanation": { "zh-Hant": "a非0才可除，ax+b=0 iff x=-b/a；以原係數回代殘差0確認。負a也約成正den，derived root不截SAFE，不用近似。", "en": "ONLY nonzero a permits division:ax+b=0 IFF x=-b/a.Substitute into the ORIGINAL coefficients to verify zero residual.Normalize a negative a to a positive denominator;derived roots are not SAFE-capped or approximated." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "Linear parameter ORIGINAL t1 minus k := sub(14, 2)", "after": "Linear parameter ORIGINAL t1 minus k = 12", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數做精確整數／有理計算；只有raw輸入驗SAFE或本family明定小界，衍生值不重套界、不作浮點近似。", "en": "Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Linear parameter ORIGINAL t1 minus k，不以小數近似替代。", "en": "Recompute Linear parameter ORIGINAL t1 minus k with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "14", "2" ], "output": "12", "label": "Linear parameter ORIGINAL t1 minus k" } }, { "id": "S009", "uses": [ "G001", "S008" ], "before": "Linear parameter original slot1 ORIGINAL negated constant := sub(0, -1)", "after": "Linear parameter original slot1 ORIGINAL negated constant = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數做精確整數／有理計算；只有raw輸入驗SAFE或本family明定小界，衍生值不重套界、不作浮點近似。", "en": "Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Linear parameter original slot1 ORIGINAL negated constant，不以小數近似替代。", "en": "Recompute Linear parameter original slot1 ORIGINAL negated constant with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "0", "-1" ], "output": "1", "label": "Linear parameter original slot1 ORIGINAL negated constant" } }, { "id": "S010", "uses": [ "G001", "S009" ], "before": "Linear parameter original slot1 ORIGINAL negative b over a := div(1, 12)", "after": "Linear parameter original slot1 ORIGINAL negative b over a = 1/12", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數做精確整數／有理計算；只有raw輸入驗SAFE或本family明定小界，衍生值不重套界、不作浮點近似。", "en": "Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Linear parameter original slot1 ORIGINAL negative b over a，不以小數近似替代。", "en": "Recompute Linear parameter original slot1 ORIGINAL negative b over a with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "div", "inputs": [ "1", "12" ], "output": "1/12", "label": "Linear parameter original slot1 ORIGINAL negative b over a" } }, { "id": "S011", "uses": [ "G001", "S010" ], "before": "Linear parameter original slot1 reverse ORIGINAL a times root := mul(12, 1/12)", "after": "Linear parameter original slot1 reverse ORIGINAL a times root = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數做精確整數／有理計算；只有raw輸入驗SAFE或本family明定小界，衍生值不重套界、不作浮點近似。", "en": "Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Linear parameter original slot1 reverse ORIGINAL a times root，不以小數近似替代。", "en": "Recompute Linear parameter original slot1 reverse ORIGINAL a times root with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "12", "1/12" ], "output": "1", "label": "Linear parameter original slot1 reverse ORIGINAL a times root" } }, { "id": "S012", "uses": [ "G001", "S011" ], "before": "Linear parameter original slot1 reverse ORIGINAL residual plus b := sum(1, -1)", "after": "Linear parameter original slot1 reverse ORIGINAL residual plus b = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數做精確整數／有理計算；只有raw輸入驗SAFE或本family明定小界，衍生值不重套界、不作浮點近似。", "en": "Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Linear parameter original slot1 reverse ORIGINAL residual plus b，不以小數近似替代。", "en": "Recompute Linear parameter original slot1 reverse ORIGINAL residual plus b with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1", "-1" ], "output": "0", "label": "Linear parameter original slot1 reverse ORIGINAL residual plus b" } }, { "id": "S013", "uses": [ "G001", "S012" ], "before": "source roles = [Linear parameter original slot1, 12, -1]", "after": "derived = [1/12, 0/1]", "relation": "implies", "rule_id": "Linear_NONZERO_a_exact_Q_root_AND_original_substitution", "conditions": [], "explanation": { "zh-Hant": "a非0才可除，ax+b=0 iff x=-b/a；以原係數回代殘差0確認。負a也約成正den，derived root不截SAFE，不用近似。", "en": "ONLY nonzero a permits division:ax+b=0 IFF x=-b/a.Substitute into the ORIGINAL coefficients to verify zero residual.Normalize a negative a to a positive denominator;derived roots are not SAFE-capped or approximated." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S014", "uses": [ "G001", "S013" ], "before": "Linear parameter ORIGINAL t2 minus k := sub(2, 2)", "after": "Linear parameter ORIGINAL t2 minus k = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數做精確整數／有理計算；只有raw輸入驗SAFE或本family明定小界，衍生值不重套界、不作浮點近似。", "en": "Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Linear parameter ORIGINAL t2 minus k，不以小數近似替代。", "en": "Recompute Linear parameter ORIGINAL t2 minus k with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "2", "2" ], "output": "0", "label": "Linear parameter ORIGINAL t2 minus k" } }, { "id": "S015", "uses": [ "G001", "S014" ], "before": "source roles = [Linear parameter original slot2, 0, -1]", "after": "derived = [否, 無解]", "relation": "implies", "rule_id": "Linear_a0_CONSTANT_equation_separate_ALLQ_vs_NOsolution", "conditions": [], "explanation": { "zh-Hant": "a0時不是一次方程：b0是0=0，全部Q解；b非0則常數矛盾無解，不作0除法。", "en": "At a=0 this is NOT linear:b=0 gives0=0 and all Q solutions;nonzero b is a contradictory constant equation with no solution.Do not divide by0." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S016", "uses": [ "G001", "S015" ], "before": "source roles = [2, -1, [1, 14, 2]]", "after": "derived = [[-1, 12, 0], [是, 是, 否], [單解 -1/1, 單解 1/12, 無解]]", "relation": "implies", "rule_id": "Linear_PARAMETER_derived_a_not_revalidated_RAW_and_ALL_classes", "conditions": [], "explanation": { "zh-Hant": "逐原ts位置先計a_i=t_i-k，derived可超SAFE；再分非零一次、零係數常數兩種。保三個flags與解集，不排序／去重parameters。", "en": "First compute a_i=t_i-k at EACH original position;derived coefficients may exceed SAFE.Then distinguish nonzero linear and zero-coefficient constant equations.Retain all three flags/classes without sorting/deduplicating parameters." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate." } }, "arithmetic": null } ], "math_model": { "result": [ [ "-1", "12", "0" ], [ true, true, false ], [ "單解 -1/1", "單解 1/12", "無解" ] ] }, "conclusion": { "canonical_value": "([-1, 12, 0], [是, 是, 否], [單解 -1/1, 單解 1/12, 無解])", "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-r04-linear-equation-foundations", "batch_path": "public/data/questions/batches/batch-20261010-advance-20261014-r04-linear-equation-foundations/questions.jsonl", "batch_sha256": "2fbe5515808bcc208c053f531c3c0e90d3c29d02bad07d36e1d0e64738410d2e", "original_line": 37, "original_line_sha256": "33343beef126d8e4ed46b77dc2104df45f0ea590648ce8e45268a74848dc5346", "question_compact_sha256": "608b199b3b644e426f5e239e36095a644445a22a9efc7ebf64bd323fca9e4e1c", "english_row_compact_sha256": "d0064b6f9eae610702360cc097c01c025b24c86a70b3ea18294839cf058703b2", "english_manifest_path": "public/data/i18n/editions/batch-20261010-advance-20261014-r04-linear-equation-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261010-advance-20261014-r04-linear-equation-foundations.en.jsonl" }, "mko_bindings": { "mko-linear-equation": { "sha256": "70cc85ab6a989077a196caad95d1800fef7d3e5988f0a9cdc5c0c700600ef109", "english_sha256": "02c486fa9699473d8637ad7a935af439f6824eb0d4d00498a72e210457f394d9", "original_path": "public/data/mko/linear-equation.json", "english_path": "public/data/i18n/editions/mko-linear-equation.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "322533190c1eb10144c4c59b6c70cc2f8105108b5f4f3a39dd577712e7185c02", "original_candidate_sha256": "045393bf597fb17ec4d78658b799f9face661e2a464ccdbc0359ed939352e8cb", "original_candidate_line_sha256": "045393bf597fb17ec4d78658b799f9face661e2a464ccdbc0359ed939352e8cb" }, "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-p61", "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": "d6b5a409bf933281a46617cd715d8016fd5ca3d6fb76f77d179ac2ecd9d608bf", "question_first_witness_sha256": "f80ecf598c6893a580af018e1a82849b33ee6887efb48a6a1d69569aa17f12e4" }, "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": "2d2f42bcce5c70809ae6f6816c6cd8da3528d324f8424accfc62d6177d78b0b6", "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." } }