{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261006-advance-20261007-r07-geometric-transformations-0018", "pilot_number": "R0058-29768", "number": 29768, "family_id": "qf-transform-translation-point", "title": { "zh-Hant": "第 29768 題：平移後的精確像點", "en": "Question 29768: Exact Image Point under Translation" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261006-advance-20261007-r07-geometric-transformations-0018", "batch_id": "batch-20261006-advance-20261007-r07-geometric-transformations-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-geometric-transformations" ], "title_zh": "平移後的精確像點", "stem_zh": "等單位正交座標系，兩軸採同一長度單位。P=(5, -16)、平移向量 t=[1, 2]。求 P+t 的點座標。", "answer": { "kind": "expression", "value": "(6, -14)", "explanation_zh": "像點=(6, -14)。兩分量按明示向量相加，像點位置須保留，不能只算兩點間差。" }, "difficulty": { "band": "upper_secondary", "level": 3, "skills": [ "平移後的精確像點" ] }, "variant": { "family_id": "qf-transform-translation-point", "seed": 202610077018, "parameters": { "P": [ 5, -16 ], "t": [ 1, 2 ], "operation": "translation_point", "frame": "euclidean_orthonormal_equal_units", "semantic_template": "qf-transform-translation-point/{\"inputs\":[[\"5\",\"-16\"],[\"1\",\"2\"]],\"operation\":\"translation_point\"}" } }, "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": "2026-10-06", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261006-advance-20261007-r07-geometric-transformations-0018", "batch_id": "batch-20261006-advance-20261007-r07-geometric-transformations-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "dba0255a16525739d99237c55118b2d210c26e6b7c8bbc5c61ff8f1fc3f2d2e9", "family_id": "qf-transform-translation-point", "seed": 202610077018, "semantic_template": "qf-transform-translation-point/{\"inputs\":[[\"5\",\"-16\"],[\"1\",\"2\"]],\"operation\":\"translation_point\"}" }, "fields": { "title": "Exact Image Point under Translation", "stem": "Use one equal-unit orthonormal Euclidean Cartesian frame. The point is P=(5, -16) and translation vector t=[1, 2]. Find the coordinates of P+t.", "answer": { "kind": "expression", "value": "(6, -14)", "explanation": "Add the two components of the specified translation, obtaining the exact image (6, -14). Retain the actual image position rather than only a difference between points." }, "skills": [ "Exact Image Point under Translation" ], "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": "等單位正交座標系，兩軸採同一長度單位。P=(5, -16)、平移向量 t=[1, 2]。求 P+t 的點座標。", "en": "Use one equal-unit orthonormal Euclidean Cartesian frame. The point is P=(5, -16) and translation vector t=[1, 2]. Find the coordinates of P+t." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-transform-translation-point, translation_point]", "after": "derived = [[image_POINT_string]]", "relation": "implies", "rule_id": "R58_EXACT_source_interface_and_answer_ROLE", "conditions": [], "explanation": { "zh-Hant": "依本題銀行的keys、domain或frame、operation與輸出角色。STR22/App20 tuple與legacy scalar不同；分數是否保/1按原契約，不能用共同外觀改題。", "en": "Follow THIS bank exact keys,domain/frame,operation and answer role.STR22/App20 tuples differ from legacy scalars;retain or omit/1 by the ORIGINAL contract,not a generic visual convention." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。", "en": "Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "Transform ORIGINAL translation coordinate0 := sum(5, 1)", "after": "Transform ORIGINAL translation coordinate0 = 6", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。", "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Transform ORIGINAL translation coordinate0，不以小數近似替代。", "en": "Recompute Transform ORIGINAL translation coordinate0 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "5", "1" ], "output": "6", "label": "Transform ORIGINAL translation coordinate0" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "Transform ORIGINAL translation coordinate1 := sum(-16, 2)", "after": "Transform ORIGINAL translation coordinate1 = -14", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。", "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Transform ORIGINAL translation coordinate1，不以小數近似替代。", "en": "Recompute Transform ORIGINAL translation coordinate1 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "-16", "2" ], "output": "-14", "label": "Transform ORIGINAL translation coordinate1" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [[5, -16], [1, 2]]", "after": "derived = [[6, -14]]", "relation": "implies", "rule_id": "Transform_translation_ACTUAL_image_not_only_displacement", "conditions": [], "explanation": { "zh-Hant": "保持同一原點／basis，加原translation每一coordinate得真正image；只輸出v並非P+t。derived和可以超SAFE，原輸入仍SAFE。", "en": "In the SAME origin/basis,add each original translation component to obtain the ACTUAL image.Returning only v is not P+t.Derived sums may exceed SAFE while raw inputs remain SAFE." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。", "en": "Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null } ], "math_model": { "result": "(6, -14)" }, "conclusion": { "canonical_value": "(6, -14)", "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-20261006-advance-20261007-r07-geometric-transformations-foundations", "batch_path": "public/data/questions/batches/batch-20261006-advance-20261007-r07-geometric-transformations-foundations/questions.jsonl", "batch_sha256": "ba809546e64880b47dffa9a5e44ba757e9a0ce452af4b03745db86f595cb6b57", "original_line": 18, "original_line_sha256": "0b2f7e03077d38018e2186406891f7d1b4e03fc06dd446dd2fab637d5f40aa8b", "question_compact_sha256": "dba0255a16525739d99237c55118b2d210c26e6b7c8bbc5c61ff8f1fc3f2d2e9", "english_row_compact_sha256": "c7c505ef5a35d46b6d2c19199630ea8b9bf22ca196cdf5810d5df3c00dc2a3b3", "english_manifest_path": "public/data/i18n/editions/batch-20261006-advance-20261007-r07-geometric-transformations-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261006-advance-20261007-r07-geometric-transformations-foundations.en.jsonl" }, "mko_bindings": { "mko-geometric-transformations": { "sha256": "13176ddfbd967892818086ef2859a68ada71d09c120c932f688634fbec64e489", "english_sha256": "403883e15b18bf9b23ff01fe8eec209041ce5774af2f19c72ec39d5e53538c31", "original_path": "public/data/mko/geometric-transformations.json", "english_path": "public/data/i18n/editions/mko-geometric-transformations.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "623c23f45586b08629c5a347ffbc994cf8dbff2133c4f4cdb227b851d74ea6b6", "original_candidate_sha256": "129758d8ab7c734856c39103bf1f0d28104eacdd4f0aa234809da0875f3daac6", "original_candidate_line_sha256": "129758d8ab7c734856c39103bf1f0d28104eacdd4f0aa234809da0875f3daac6" }, "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-p59", "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": "66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05df", "question_first_witness_sha256": "b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7" }, "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": "179974c44bbf15fd527302d56beab6d9f10f8e7b1308b6e8908914d2dfae614c", "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." } }