{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261008-advance-20261011-r03-variable-expression-0020", "pilot_number": "R0008-04795", "number": 4795, "family_id": "qf-density11-expression-two-env-values", "title": { "zh-Hant": "第 4795 題：同一表達式在兩環境的值", "en": "Question 4795: Affine Expression in Two Environments" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261008-advance-20261011-r03-variable-expression-0020", "batch_id": "batch-20261008-advance-20261011-r03-variable-expression-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-variable-expression" ], "title_zh": "同一表達式在兩環境的值", "stem_zh": "有理數Q；表達式非方程式，E(x)=-19x+(12)，有序環境x=[19/3, -10/1]。依序求兩個E值，均寫最簡分數。", "answer": { "kind": "expression", "value": "(-325/3, 202/1)", "explanation_zh": "雙環境求值=(-325/3, 202/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。" }, "difficulty": { "band": "upper_secondary", "level": 3, "skills": [ "同一表達式在兩環境的值" ] }, "variant": { "family_id": "qf-density11-expression-two-env-values", "seed": 202610113020, "parameters": { "a": -19, "b": 12, "inputs": [ [ 19, 3 ], [ -20, 2 ] ], "operation": "density11_expression_two_env_values", "domain": "typed_Q_affine_expression_slice", "semantic_template": "qf-density11-expression-two-env-values/[-19,12,[\"19/3\",\"-10/1\"]]" } }, "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": "2026-10-08", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261008-advance-20261011-r03-variable-expression-0020", "batch_id": "batch-20261008-advance-20261011-r03-variable-expression-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "677050c6f76185db98c86df1b9f1f98114d0957ce694f2355c98532d749d2f8f", "family_id": "qf-density11-expression-two-env-values", "seed": 202610113020, "semantic_template": "qf-density11-expression-two-env-values/[-19,12,[\"19/3\",\"-10/1\"]]" }, "fields": { "title": "Affine Expression in Two Environments", "stem": "All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-19)x+(12) is an expression, not an equation. Ordered x environments=[19/3, -20/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.", "answer": { "kind": "expression", "value": "(-325/3, 202/1)", "explanation": "Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-325/3, 202/1)." }, "skills": [ "Affine Expression in Two Environments" ], "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": "有理數Q；表達式非方程式，E(x)=-19x+(12)，有序環境x=[19/3, -10/1]。依序求兩個E值，均寫最簡分數。", "en": "All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-19)x+(12) is an expression, not an equation. Ordered x environments=[19/3, -20/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "typed rational expression and explicitly given environment", "after": "evaluation,not solving an equation", "relation": "implies", "rule_id": "expression_environment_scope", "conditions": [], "explanation": { "zh-Hant": "表達式求值不是求解方程式；只把明示環境代入，不反推未知根或擅改綁定。", "en": "Evaluating an expression is not solving an equation;substitute only the supplied environment without inventing roots or changing bindings." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "environment0 ax := mul(-19, 19/3)", "after": "environment0 ax = -361/3", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "把本環境的x代入乘法部分。", "en": "Substitute this environment's x into the product term." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 environment0 ax，不以小數近似替代。", "en": "Recompute environment0 ax with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "-19", "19/3" ], "output": "-361/3", "label": "environment0 ax" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "environment0 ax+b := sum(-361/3, 12)", "after": "environment0 ax+b = -325/3", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "再加同一表達式常數b。", "en": "Then add b from the same expression." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 environment0 ax+b，不以小數近似替代。", "en": "Recompute environment0 ax+b with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "-361/3", "12" ], "output": "-325/3", "label": "environment0 ax+b" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "environment1 ax := mul(-19, -10)", "after": "environment1 ax = 190", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "把本環境的x代入乘法部分。", "en": "Substitute this environment's x into the product term." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 environment1 ax，不以小數近似替代。", "en": "Recompute environment1 ax with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "-19", "-10" ], "output": "190", "label": "environment1 ax" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "environment1 ax+b := sum(190, 12)", "after": "environment1 ax+b = 202", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "再加同一表達式常數b。", "en": "Then add b from the same expression." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 environment1 ax+b，不以小數近似替代。", "en": "Recompute environment1 ax+b with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "190", "12" ], "output": "202", "label": "environment1 ax+b" } }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "[-325/3, 202/1]", "after": "ordered independent evaluations of the same expression", "relation": "implies", "rule_id": "separate_expression_environments", "conditions": [], "explanation": { "zh-Hant": "兩個輸入環境分別從原始資料取值，第二次不繼承第一次代換後的數值狀態；a=0時常數式不隨x改變。", "en": "Read both environments from the original data;the second evaluation does not inherit a mutated first substitution.When a=0 the constant expression is independent of x." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null } ], "math_model": { "result": [ "-325/3", "202" ] }, "conclusion": { "canonical_value": "(-325/3, 202/1)", "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-20261008-advance-20261011-r03-variable-expression-foundations", "batch_path": "public/data/questions/batches/batch-20261008-advance-20261011-r03-variable-expression-foundations/questions.jsonl", "batch_sha256": "62cfe30aaffc9d75ac212c2a5a4338aa58a8acb9aa7a328ac228475f96d02fb6", "original_line": 20, "original_line_sha256": "7c377bc3abb6ee21ef3dadb9c100d4ff056b5645c1a84fef339b7d87184e487b", "question_compact_sha256": "677050c6f76185db98c86df1b9f1f98114d0957ce694f2355c98532d749d2f8f", "english_row_compact_sha256": "fbbc5b845cfe7df5d9f43e61cec44bf6065f44e9d6ae656e062812eee8a1987f", "english_manifest_path": "public/data/i18n/editions/batch-20261008-advance-20261011-r03-variable-expression-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261008-advance-20261011-r03-variable-expression-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": "6dc34e24b0f43c50e49365ca1a1153175f8661d5290c9236df5527bb047157eb", "original_candidate_sha256": "01f7e79a6ecc3f30d49bf72386994a4c960f80a2e74b558e7b8d2707aee7b18e", "original_candidate_line_sha256": "01f7e79a6ecc3f30d49bf72386994a4c960f80a2e74b558e7b8d2707aee7b18e" }, "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-20261026-004-p9", "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": "b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289", "question_first_witness_sha256": "caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 6, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "b8be6bc75f9ed5ac44522e4ef1192707a103365eda5450f53599e81dc926a2ef", "arithmetic_steps": 4 }, "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." } }