{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260914-variable-expression-evaluation-0005", "pilot_number": "R0070-35785", "number": 35785, "family_id": "qf-variable-expression-evaluation", "title": { "zh-Hant": "第 35785 題：代數式明示求值", "en": "Question 35785: Explicit Evaluation of an Algebraic Expression" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260914-variable-expression-evaluation-0005", "batch_id": "batch-20260914-domain-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-variable-expression" ], "title_zh": "代數式明示求值", "stem_zh": "在數系 N 中，給定 x=12。求代數式 x+5 的值（這是表達式，不是方程式）。", "answer": { "kind": "numeric", "value": 17, "explanation_zh": "代入明示值 x=12，得到 12+5=17；題目只使用已明示的加法。" }, "difficulty": { "band": "upper_secondary", "level": 2, "skills": [ "代數式", "代入求值" ] }, "variant": { "family_id": "qf-variable-expression-evaluation", "seed": 20260938, "parameters": { "number_system": "N", "variable": "x", "assigned_value": 12, "operator": "+", "constant": 5, "expression_form": "x_plus_constant", "semantic_template": "qf-variable-expression-evaluation/{\"assigned_value\":12,\"constant\":5,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}" } }, "verification": { "status": "candidate", "checks": [ "schema_pending", "independent_recomputation_pending" ], "warning_zh": "本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。" }, "provenance": { "generator_role": "question_producer", "generator_model": "GPT-5.6 Terra", "generated_at": "2026-09-14", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20260914-variable-expression-evaluation-0005", "batch_id": "batch-20260914-domain-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "85b4bfab9b2f8f2485e9eff6293f0cc31bc349b0ccb64d78a93448ce15008847", "family_id": "qf-variable-expression-evaluation", "seed": 20260938, "semantic_template": "qf-variable-expression-evaluation/{\"assigned_value\":12,\"constant\":5,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}" }, "fields": { "title": "Explicit Evaluation of an Algebraic Expression", "stem": "In N, let x=12. Evaluate the algebraic expression x+5; this is an expression, not an equation.", "answer": { "kind": "numeric", "value": 17, "explanation": "Substitution gives 12+5=17; only the explicitly stated addition is used." }, "skills": [ "algebraic expressions", "evaluation by substitution" ], "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": "在數系 N 中，給定 x=12。求代數式 x+5 的值（這是表達式，不是方程式）。", "en": "In N, let x=12. Evaluate the algebraic expression x+5; this is an expression, not an equation." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-variable-expression-evaluation, [assigned_value, constant, expression_form, number_system, operator, variable]]", "after": "derived = [variable, null, null]", "relation": "implies", "rule_id": "R70_SOURCE_bank_specific_interface", "conditions": [], "explanation": { "zh-Hant": "只使用此bank真正明示的欄位、operation/domain與型別；BASE容許保留額外metadata，不把LDL SAFE/集合上限或其他bank的去重規則搬來。", "en": "Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [12, 5]", "after": "derived = [x := 12, x + 5]", "relation": "implies", "rule_id": "Variable_GIVEN_assignment_not_equation_solving", "conditions": [], "explanation": { "zh-Hant": "把已明示x值代入x+常數，x只是此題已賦值的變數；不是求未知方程，也不是從一個例子證明任意代數恆等式。", "en": "Substitute the GIVEN assignment into x+constant.The variable already has a value;this is not solving an unknown equation or proving a universal identity from one example." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "Variable ORIGINAL assignment plus constant := sum(12, 5)", "after": "Variable ORIGINAL assignment plus constant = 17", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "本步精確列出原操作數與運算；乘、減、除恰兩項。分數保持精確，衍生BigInt不重套raw SAFE，不用近似值湊答案。", "en": "This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Variable ORIGINAL assignment plus constant，不以小數近似替代。", "en": "Recompute Variable ORIGINAL assignment plus constant with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "12", "5" ], "output": "17", "label": "Variable ORIGINAL assignment plus constant" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [12, 5]", "after": "derived = [17]", "relation": "implies", "rule_id": "Variable_substituted_nonnegative_sum", "conditions": [], "explanation": { "zh-Hant": "兩項皆在N，所以精確加總仍在N；保留數值答案的NUMBER型別。", "en": "Both terms lie in N,so their exact sum remains in N.Retain the NUMBER type of the numerical answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null } ], "math_model": { "result": 17 }, "conclusion": { "canonical_value": "17", "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-20260914-domain-foundations", "batch_path": "public/data/questions/batches/batch-20260914-domain-foundations/questions.jsonl", "batch_sha256": "726b3f94ccd05d8c91cc7e306b42fd71b6d9040e194db91739a250d488fd1de7", "original_line": 25, "original_line_sha256": "3afe5383cf90513a9912640ef224d379cb9aab1d17fb09b6d42f3b77682c0f92", "question_compact_sha256": "85b4bfab9b2f8f2485e9eff6293f0cc31bc349b0ccb64d78a93448ce15008847", "english_row_compact_sha256": "f5875834920ea8337bd7e4059e5292b400bea25c67e1235add2bb0429332c997", "english_manifest_path": "public/data/i18n/editions/batch-20260914-domain-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20260914-domain-foundations.en.jsonl" }, "mko_bindings": { "mko-variable-expression": { "sha256": "da4b6e4a4edfd379a38b6535fd3030cc5c552e2b549572c0d4733d68974a292c", "english_sha256": "4a8cfbcc1fa5d73c360d18a95f35f69578250d0104baf76036f4efc8de9d7e81", "original_path": "public/data/mko/variable-expression.json", "english_path": "public/data/i18n/editions/mko-variable-expression.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "20c37a7e64ee5969e7606c5cc3a00e575002ebebdfe82873521cc3d7c608caff", "original_candidate_sha256": "179bd0a171223213d3d4e4d309fcad69385006d96dd6567c2d38213a2e65ced9", "original_candidate_line_sha256": "179bd0a171223213d3d4e4d309fcad69385006d96dd6567c2d38213a2e65ced9" }, "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-p71", "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": "9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80", "question_first_witness_sha256": "c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dab" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 4, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "5f048c2c6035ec9d51aec80bc2806478466276ea496664b78fc355e633a2993e", "arithmetic_steps": 1 }, "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." } }