{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261005-advance-20261006-r06-area-0050", "pilot_number": "R0004-02725", "number": 2725, "family_id": "qf-area-coordinate-rectangle", "title": { "zh-Hant": "第 2725 題：整數端點半開矩形的面積", "en": "Question 2725: Area of a Half-Open Integer-Endpoint Rectangle" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261005-advance-20261006-r06-area-0050", "batch_id": "batch-20261005-advance-20261006-r06-area-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-area" ], "title_zh": "整數端點半開矩形的面積", "stem_zh": "在等單位正交座標系中，兩軸使用同一長度單位，半開矩形 [-28,-27)×[12,37) 端點有序。求面積的精確平方單位數。", "answer": { "kind": "short_text", "value": "25", "explanation_zh": "面積=25 平方單位。先取兩個非負邊長，再相乘；零邊長是空矩形，座標原點移動不增加面積。" }, "difficulty": { "band": "lower_secondary", "level": 3, "skills": [ "整數端點半開矩形的面積" ] }, "variant": { "family_id": "qf-area-coordinate-rectangle", "seed": 202610066050, "parameters": { "frame": "euclidean_orthonormal_equal_units", "boundary": "half_open", "rect": [ -28, -27, 12, 37 ], "operation": "coordinate_rectangle", "semantic_template": "qf-area-coordinate-rectangle/{\"inputs\":[\"1\",\"25\"],\"operation\":\"coordinate_rectangle\"}" } }, "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": "2026-10-05", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261005-advance-20261006-r06-area-0050", "batch_id": "batch-20261005-advance-20261006-r06-area-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "da1a7cb125a0c6cc8d62cc12e3068da902a24b0af56ee299b67506ae1acf292b", "family_id": "qf-area-coordinate-rectangle", "seed": 202610066050, "semantic_template": "qf-area-coordinate-rectangle/{\"inputs\":[\"1\",\"25\"],\"operation\":\"coordinate_rectangle\"}" }, "fields": { "title": "Area of a Half-Open Integer-Endpoint Rectangle", "stem": "Use one equal-unit orthonormal Euclidean Cartesian frame. For the half-open rectangle [-28, -27)×[12, 37), find the exact area in squared length units.", "answer": { "kind": "short_text", "value": "25", "explanation": "Subtract each lower endpoint from its upper endpoint and multiply the two nonnegative extents, obtaining 25 squared units. A zero width or height makes the rectangle empty." }, "skills": [ "Area of a Half-Open Integer-Endpoint Rectangle" ], "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": "在等單位正交座標系中，兩軸使用同一長度單位，半開矩形 [-28,-27)×[12,37) 端點有序。求面積的精確平方單位數。", "en": "Use one equal-unit orthonormal Euclidean Cartesian frame. For the half-open rectangle [-28, -27)×[12, 37), find the exact area in squared length units." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "orthonormal equal-length coordinate units;half-open regions", "after": "area in squared length units", "relation": "implies", "rule_id": "half_open_area_convention", "conditions": [], "explanation": { "zh-Hant": "兩軸正交且使用相同長度單位；半開邊界避免相鄰單位格重複包含邊，面積單位是平方單位而非長度。", "en": "Axes are orthogonal with equal length units;half-open boundaries make adjacent unit cells disjoint.Area uses squared units,not length units." }, "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": "coordinate rectangle width := sub(-27, -28)", "after": "coordinate rectangle width = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "有序端點的右減左是非負寬度，不把原點位移當面積。", "en": "Right minus left is the nonnegative width;translation of the origin contributes no area." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 coordinate rectangle width，不以小數近似替代。", "en": "Recompute coordinate rectangle width with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "-27", "-28" ], "output": "1", "label": "coordinate rectangle width" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "coordinate rectangle height := sub(37, 12)", "after": "coordinate rectangle height = 25", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "上減下是非負高度，必使用同一矩形的端點。", "en": "Top minus bottom is the nonnegative height,using endpoints of the same rectangle." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 coordinate rectangle height，不以小數近似替代。", "en": "Recompute coordinate rectangle height with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "37", "12" ], "output": "25", "label": "coordinate rectangle height" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "coordinate rectangle area := mul(1, 25)", "after": "coordinate rectangle area = 25", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "矩形面積為寬乘高；任一零邊長表示空的半開矩形，面積0。", "en": "Rectangle area is width times height;a zero side makes the half-open rectangle empty,with area0." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 coordinate rectangle area，不以小數近似替代。", "en": "Recompute coordinate rectangle area with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "25" ], "output": "25", "label": "coordinate rectangle area" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "[-28, -27, 12, 37]", "after": "area=25", "relation": "implies", "rule_id": "rectangle_area_boundary", "conditions": [], "explanation": { "zh-Hant": "端點可以相等，但不可顛倒；先求邊長再乘，不直接把座標相乘。", "en": "Endpoints may coincide but may not be reversed;compute side lengths before multiplying,not products of coordinates." }, "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": "25" }, "conclusion": { "canonical_value": "25", "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-20261005-advance-20261006-r06-area-foundations", "batch_path": "public/data/questions/batches/batch-20261005-advance-20261006-r06-area-foundations/questions.jsonl", "batch_sha256": "ae5e68190a9fbefa299612f8a40e9c091f12108ad9798ec677bf34c4df61c45e", "original_line": 50, "original_line_sha256": "5949d1c83b80fc582823384c1bd3bb8043ba4d5392076a0e983b672082fdb1f5", "question_compact_sha256": "da1a7cb125a0c6cc8d62cc12e3068da902a24b0af56ee299b67506ae1acf292b", "english_row_compact_sha256": "ad042620b44b2f7dbe329e2fd5df844eac063b9d32fbadff185a0fb635704dd3", "english_manifest_path": "public/data/i18n/editions/batch-20261005-advance-20261006-r06-area-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261005-advance-20261006-r06-area-foundations.en.jsonl" }, "mko_bindings": { "mko-area": { "sha256": "dd727d645461b67b46876e9fedc6a33242ba8cb9ef182cf6bd74290b45ac1b58", "english_sha256": "3c701b4dcaf9e9568dd937b5470cb18f890bd452abc9d2716d75a66401416371", "original_path": "public/data/mko/area.json", "english_path": "public/data/i18n/editions/mko-area.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "b254245aa10315455f756d4620a6ac0243e0146bccea5d89e872f1359bb32a1d", "original_candidate_sha256": "4fa11405619a528ef2cdab5263cc861934e25e2e010a9ef88bee505d7f09d73e", "original_candidate_line_sha256": "4fa11405619a528ef2cdab5263cc861934e25e2e010a9ef88bee505d7f09d73e" }, "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-p5", "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": "312ae86315346b8955842a547cb2d09246e1f826755f72c2a51f042e5c7d5c56", "question_first_witness_sha256": "831f449ed41ff9144a290e534aa32adf7252d15b81c16ed5886a7dfd65dee70c" }, "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": "cea1f1cdb2647d4d74d1a50bfec6069bd83e4810f33052fd4db575257018b6eb", "arithmetic_steps": 3 }, "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." } }