{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261003-advance-20261004-r05-vector-0090", "pilot_number": "R0070-35965", "number": 35965, "family_id": "qf-vector-coordinate-equality", "title": { "zh-Hant": "第 35965 題：固定基底向量的分量相等", "en": "Question 35965: Vector Equality in a Fixed Basis" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261003-advance-20261004-r05-vector-0090", "batch_id": "batch-20261003-advance-20261004-r05-vector-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-vector" ], "title_zh": "固定基底向量的分量相等", "stem_zh": "在固定基底下的實數平面向量 R²，u=(2, 2)，v=(2, 2)。u 與 v 是否相等？", "answer": { "kind": "short_text", "value": "是", "explanation_zh": "分量結果=是。須兩個對應位置的分量都相等，分量和相等或任意交換不夠。" }, "difficulty": { "band": "upper_secondary", "level": 2, "skills": [ "固定基底向量的分量相等" ] }, "variant": { "family_id": "qf-vector-coordinate-equality", "seed": 202610045090, "parameters": { "u": [ 2, 2 ], "domain": "reals", "operation": "vector_equality", "v": [ 2, 2 ], "semantic_template": "qf-vector-coordinate-equality/{\"domain\":\"reals\",\"operation\":\"vector_equality\",\"u\":[2,2],\"v\":[2,2]}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_integer_rational_arithmetic", "producer_finite_enumeration", "producer_source_snapshot_check", "producer_substantive_template_deduplication" ], "warning_zh": "僅為產生端候選及自檢；主架構者須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "Codex independent peer (inherited model; exact runtime model not exposed)", "generated_at": "2026-10-03", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261003-advance-20261004-r05-vector-0090", "batch_id": "batch-20261003-advance-20261004-r05-vector-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "ea35cd130d6cce73977c815d3ac0f47ebada091f3ea97305e721f59e18f11934", "family_id": "qf-vector-coordinate-equality", "seed": 202610045090, "semantic_template": "qf-vector-coordinate-equality/{\"domain\":\"reals\",\"operation\":\"vector_equality\",\"u\":[2,2],\"v\":[2,2]}" }, "fields": { "title": "Vector Equality in a Fixed Basis", "stem": "In the fixed basis of the real plane R², u=(2, 2) and v=(2, 2). Are u and v equal?", "answer": { "kind": "short_text", "value": "Yes", "explanation": "Equality requires both corresponding components to agree, giving Yes. Equality of component sums or arbitrary exchange of components is insufficient." }, "skills": [ "Vector Equality in a Fixed Basis" ], "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": "在固定基底下的實數平面向量 R²，u=(2, 2)，v=(2, 2)。u 與 v 是否相等？", "en": "In the fixed basis of the real plane R², u=(2, 2) and v=(2, 2). Are u and v equal?" } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-vector-coordinate-equality, [domain, operation, u, v]]", "after": "derived = [vector, vector_equality, reals]", "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 = [[2, 2], [2, 2], null]", "after": "derived = [two real coordinates in ONE ordered basis]", "relation": "implies", "rule_id": "Vector_GIVEN_common_ordered_basis_RAW_two_SAFE_components", "conditions": [], "explanation": { "zh-Hant": "兩向量座標在同一有序基底，每個raw分量與k驗SAFE；此題向量不是幾何點、長度或內積，不能只比較分量和。", "en": "The vectors use ONE ordered basis.Type ALL TWO RAW SAFE components and k.These are vector coordinates,not points,lengths or a dot product.Component sums alone do not determine equality." }, "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": "source roles = [0, 2, 2]", "after": "derived = [是]", "relation": "implies", "rule_id": "Vector_EQUALITY_EACH_corresponding_coordinate", "conditions": [], "explanation": { "zh-Hant": "逐相同位置比較，不任意交換座標；向量相等需要兩分量都相同。", "en": "Compare EACH corresponding position without permuting coordinates.Vector equality requires BOTH components to match." }, "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": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [1, 2, 2]", "after": "derived = [是]", "relation": "implies", "rule_id": "Vector_EQUALITY_EACH_corresponding_coordinate", "conditions": [], "explanation": { "zh-Hant": "逐相同位置比較，不任意交換座標；向量相等需要兩分量都相同。", "en": "Compare EACH corresponding position without permuting coordinates.Vector equality requires BOTH components to match." }, "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": "S005", "uses": [ "G001", "S004" ], "before": "source roles = [[是, 是]]", "after": "derived = [是]", "relation": "implies", "rule_id": "Vector_EQUALITY_conjunction_not_component_sum", "conditions": [], "explanation": { "zh-Hant": "合取兩個逐分量條件，不能以任一相等或總和相同替代。", "en": "Conjoin BOTH coordinate equalities;neither one match nor equal component sums is enough." }, "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": "是" }, "conclusion": { "canonical_value": "是", "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-20261003-advance-20261004-r05-vector-foundations", "batch_path": "public/data/questions/batches/batch-20261003-advance-20261004-r05-vector-foundations/questions.jsonl", "batch_sha256": "dcec7d66d887707f0c830babd46721978583fb3c50e70c97f0049d83f1576701", "original_line": 90, "original_line_sha256": "9929770067643962f72dd11295269563caccf1e871c0fefac5df46fa7e0286cf", "question_compact_sha256": "ea35cd130d6cce73977c815d3ac0f47ebada091f3ea97305e721f59e18f11934", "english_row_compact_sha256": "4a8e1995ca80675e2dd9afef2ba6bfb23ea970f9267171e96cf445e909778407", "english_manifest_path": "public/data/i18n/editions/batch-20261003-advance-20261004-r05-vector-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261003-advance-20261004-r05-vector-foundations.en.jsonl" }, "mko_bindings": { "mko-vector": { "sha256": "0d8db0f5e7511aaa8401ebe39e808af23991063892ca349e742b0551c91cba3d", "english_sha256": "8b23c6e9698bb13ffb12ef863fc1ba12d88c96f880c720e6504681e634fcd99d", "original_path": "public/data/mko/vector.json", "english_path": "public/data/i18n/editions/mko-vector.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "20c37a7e64ee5969e7606c5cc3a00e575002ebebdfe82873521cc3d7c608caff", "original_candidate_sha256": "e5ce79a43ebf08d6f9836b2553131664ef2e47e0171e98a14498d14912b49862", "original_candidate_line_sha256": "e5ce79a43ebf08d6f9836b2553131664ef2e47e0171e98a14498d14912b49862" }, "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": 5, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "04d3f7b1b53a2175e0fd8707acf3c0dbdc2b84c660bca89bf8f716e25f5ad050", "arithmetic_steps": 0 }, "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." } }