{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260924-equation-multiplicative-solve-0022", "pilot_number": "R0062-31597", "number": 31597, "family_id": "qf-equation-multiplicative-solve", "title": { "zh-Hant": "第 31597 題：乘法型方程", "en": "Question 31597: Multiplicative Equation" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260924-equation-multiplicative-solve-0022", "batch_id": "batch-20260924-equation-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-equation" ], "title_zh": "乘法型方程", "stem_zh": "在整數論域解 4×x=20；係數 4 已明示非零。", "answer": { "kind": "short_text", "value": "5", "explanation_zh": "4≠0，x=20/4=5；代回 4×5=20。" }, "difficulty": { "band": "lower_secondary", "level": 2, "skills": [ "非零係數", "乘法反運算" ] }, "variant": { "family_id": "qf-equation-multiplicative-solve", "seed": 20261146, "parameters": { "form": "a*x=b", "a": 4, "b": 20, "domain": "integers", "semantic_template": "qf-equation-multiplicative-solve/{\"a\":4,\"b\":20,\"domain\":\"integers\",\"form\":\"a*x=b\"}" } }, "verification": { "status": "candidate", "checks": [ "schema_pending", "independent_recomputation_pending" ], "warning_zh": "本題為 candidate 練習；有限精確重算不是形式證明或人工審查。" }, "provenance": { "generator_role": "question_producer", "generator_model": "GPT-5.6 Terra", "generated_at": "2026-09-24", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20260924-equation-multiplicative-solve-0022", "batch_id": "batch-20260924-equation-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "6ca547adfc099f6becd4db375dab573bd7ea5e4ad46caaa83cf569f3d3b4185c", "family_id": "qf-equation-multiplicative-solve", "seed": 20261146, "semantic_template": "qf-equation-multiplicative-solve/{\"a\":4,\"b\":20,\"domain\":\"integers\",\"form\":\"a*x=b\"}" }, "fields": { "title": "Multiplicative Equation", "stem": "Solve 4×x=20 over the integers; the coefficient 4 is explicitly nonzero.", "answer": { "kind": "short_text", "value": "5", "explanation": "4≠0, so x=20/4=5; substitution verifies the equality." }, "skills": [ "nonzero coefficient", "inverse multiplication" ], "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": "在整數論域解 4×x=20；係數 4 已明示非零。", "en": "Solve 4×x=20 over the integers; the coefficient 4 is explicitly nonzero." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-equation-multiplicative-solve, integers, no-operation-field, a*x=b]", "after": "derived = [[integer_solution_STRING]]", "relation": "implies", "rule_id": "R62_EXACT_source_keys_domain_operation_form_AND_output_types", "conditions": [], "explanation": { "zh-Hant": "按原bank核欄位：BASE方程用form及論域，BASE事件／補集無operation，階乘無domain；ext18用local-hyphen，其他legacy用underscore。輸出型別不統一成tuple或fraction。", "en": "Check THIS bank interface:BASE equations use form/domain;BASE events/complement have no operation;factorials have no domain.ext18 uses local hyphens,other legacy operations underscores.Do not force every answer into a tuple or fraction." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向代回原輸入、欄位角色、論域及本步條件；一致性不表示結論能唯一恢復前提。有限核對、獨立審查、形式證明與發布分開標記。", "en": "Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [4, 20, a*x=b, integers]", "after": "derived = [是]", "relation": "implies", "rule_id": "Equation_BASE_integer_coefficients_declared_Z_OR_Q_NOT_blanket_SAFE", "conditions": [], "explanation": { "zh-Hant": "原BASE bank驗整數而非另訂SAFE界；本候選核對凍結題的精確整數資料，不宣稱任意unsafe JavaScript數值行為已認證。Z解與Q解分開。", "en": "The BASE bank checks integers,not an added SAFE limit.This candidate checks the frozen exact integer slice,not arbitrary unsafe JavaScript-number behavior.Distinguish solutions over Z and Q." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向代回原輸入、欄位角色、論域及本步條件；一致性不表示結論能唯一恢復前提。有限核對、獨立審查、形式證明與發布分開標記。", "en": "Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "Equation multiplicative ORIGINAL b over nonzero a := div(20, 4)", "after": "Equation multiplicative ORIGINAL b over nonzero a = 5", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "使用原操作數與明示次序作精確整數／有理計算，不用浮點近似。輸入界依題族：不把衍生值重驗成raw輸入，也不給BASE題庫另加SAFE或n64界。", "en": "Use ORIGINAL operands and declared order for exact integer/rational arithmetic,not floats.Bounds are family-specific:do not revalidate derived values as RAW inputs or add blanket SAFE/n64 caps to BASE families." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Equation multiplicative ORIGINAL b over nonzero a，不以小數近似替代。", "en": "Recompute Equation multiplicative ORIGINAL b over nonzero a with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "div", "inputs": [ "20", "4" ], "output": "5", "label": "Equation multiplicative ORIGINAL b over nonzero a" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "Equation multiplicative reverse ORIGINAL a times solution := mul(4, 5)", "after": "Equation multiplicative reverse ORIGINAL a times solution = 20", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "使用原操作數與明示次序作精確整數／有理計算，不用浮點近似。輸入界依題族：不把衍生值重驗成raw輸入，也不給BASE題庫另加SAFE或n64界。", "en": "Use ORIGINAL operands and declared order for exact integer/rational arithmetic,not floats.Bounds are family-specific:do not revalidate derived values as RAW inputs or add blanket SAFE/n64 caps to BASE families." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Equation multiplicative reverse ORIGINAL a times solution，不以小數近似替代。", "en": "Recompute Equation multiplicative reverse ORIGINAL a times solution with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "4", "5" ], "output": "20", "label": "Equation multiplicative reverse ORIGINAL a times solution" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "source roles = [4, 20]", "after": "derived = [0, 5, 20]", "relation": "implies", "rule_id": "Equation_MULT_Z_nonzero_AND_divisibility_BEFORE_division", "conditions": [], "explanation": { "zh-Hant": "先驗a非0及a整除b，才可在Z內解x=b/a；負a合法。若不整除是此Z解題族的來源資格不合，不把有理數解冒充整數解。", "en": "FIRST require a≠0 AND a divides b,then solve x=b/a IN Z.Negative a is legal.Nondivisibility fails this source family qualification;do not present a rational answer as an integer solution." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向代回原輸入、欄位角色、論域及本步條件；一致性不表示結論能唯一恢復前提。有限核對、獨立審查、形式證明與發布分開標記。", "en": "Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate." } }, "arithmetic": null } ], "math_model": { "result": "5" }, "conclusion": { "canonical_value": "5", "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-20260924-equation-foundations", "batch_path": "public/data/questions/batches/batch-20260924-equation-foundations/questions.jsonl", "batch_sha256": "6d31f2307850ca273164b6b9024cb43f5b2102f0834c5fef9c5dd2285ffb256a", "original_line": 72, "original_line_sha256": "4a4f20aceaaf6524b9e639222f9ed47632781c4ed4649c5e1446f09f8682876b", "question_compact_sha256": "6ca547adfc099f6becd4db375dab573bd7ea5e4ad46caaa83cf569f3d3b4185c", "english_row_compact_sha256": "1bf0853a33b679b9d5e66a1a0e3a78433419b48e83514b3f9f93a67e5a725521", "english_manifest_path": "public/data/i18n/editions/batch-20260924-equation-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20260924-equation-foundations.en.jsonl" }, "mko_bindings": { "mko-equation": { "sha256": "6f8d6ca379da35727c14f320d99d0bc8c53c47ad478d0f462d30a4127aea0a78", "english_sha256": "de50265f38fde7fafcc45aa22db603721664273dbafb01a18c77a7d51b393bdd", "original_path": "public/data/mko/equation.json", "english_path": "public/data/i18n/editions/mko-equation.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "59d384ca3d958b27165f4295ff96efb155e7b12d3fb70bcdd0ed68148513c05a", "original_candidate_sha256": "5728bf015ddd71858a9eee6e2947c202c82e75f7d2c5aaf71bc68430c84189be", "original_candidate_line_sha256": "5728bf015ddd71858a9eee6e2947c202c82e75f7d2c5aaf71bc68430c84189be" }, "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-p63", "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": "963099ffc9f754069fdce6792949a85ed350472465eaceb3038fa8011cf672bd", "question_first_witness_sha256": "d7655324c5d11528e1af90b757384cebd3313e19dc5f6f5b9b8ea7624fb06f6f" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 5, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "a0c8e400c882bf281a3c69080c0263ed9f0ad232328b70cb8ee6d99d2e8c897b", "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." } }