{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261011-advance-20261015-r07-coordinate-plane-0018", "pilot_number": "R0060-30768", "number": 30768, "family_id": "qf-density15-coordinate-four-point-axis-masks", "title": { "zh-Hant": "第 30768 題：四點欄位軸與象限", "en": "Question 30768: Four Ordered Coordinate Columns, Axes, and Locations" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261011-advance-20261015-r07-coordinate-plane-0018", "batch_id": "batch-20261011-advance-20261015-r07-coordinate-plane-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-coordinate-plane" ], "title_zh": "四點欄位軸與象限", "stem_zh": "同一正交有向xy框架，座標有序對。原序四點=[[5, 1], [1, 0], [0, 1], [-1, -17]]。求 (x欄, y欄, x軸資格, y軸資格, 原點/x軸/y軸/I/II/III/IV分類)，原點不歸象限。", "answer": { "kind": "expression", "value": "([5, 1, 0, -1], [1, 0, 1, -17], [否, 是, 否, 否], [否, 否, 是, 否], [I, x軸, y軸, III])", "explanation_zh": "四點有序欄位軸與象限=([5, 1, 0, -1], [1, 0, 1, -17], [否, 是, 否, 否], [否, 否, 是, 否], [I, x軸, y軸, III])。先讀有序兩欄，零分量先核軸，再按非零分量符號分類。軸點不屬象限原點同屬兩軸，逐分量差不當距離或圖形尺寸，不由示意圖猜座標。" }, "difficulty": { "band": "lower_secondary", "level": 3, "skills": [ "四點欄位軸與象限" ] }, "variant": { "family_id": "qf-density15-coordinate-four-point-axis-masks", "seed": 202610157018, "parameters": { "points": [ [ 5, 1 ], [ 1, 0 ], [ 0, 1 ], [ -1, -17 ] ], "frame": "same_orthogonal_xy_axes", "domain": "finite_ordered_coordinate_protocol", "operation": "density15_coordinate_four_point_axis_masks", "semantic_template": "qf-density15-coordinate-four-point-axis-masks/[[5,1],[1,0],[0,1],[-1,-17]]" } }, "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": "2026-10-11", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261011-advance-20261015-r07-coordinate-plane-0018", "batch_id": "batch-20261011-advance-20261015-r07-coordinate-plane-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "69b3fdfb6da3e55d5847515053e47800697722a6d00d1ccd4f00384f83e6415b", "family_id": "qf-density15-coordinate-four-point-axis-masks", "seed": 202610157018, "semantic_template": "qf-density15-coordinate-four-point-axis-masks/[[5,1],[1,0],[0,1],[-1,-17]]" }, "fields": { "title": "Four Ordered Coordinate Columns, Axes, and Locations", "stem": "Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[5, 1], [1, 0], [0, 1], [-1, -17]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).", "answer": { "kind": "expression", "value": "([5, 1, 0, -1], [1, 0, 1, -17], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])", "explanation": "Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([5, 1, 0, -1], [1, 0, 1, -17], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])." }, "skills": [ "Four Ordered Coordinate Columns, Axes, and Locations" ], "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": "同一正交有向xy框架，座標有序對。原序四點=[[5, 1], [1, 0], [0, 1], [-1, -17]]。求 (x欄, y欄, x軸資格, y軸資格, 原點/x軸/y軸/I/II/III/IV分類)，原點不歸象限。", "en": "Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[5, 1], [1, 0], [0, 1], [-1, -17]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-density15-coordinate-four-point-axis-masks, density15_coordinate_four_point_axis_masks, finite_ordered_coordinate_protocol]", "after": "derived = [[x_column, y_column, x_axis_mask, y_axis_mask, locations]]", "relation": "implies", "rule_id": "R60_EXACT_perbank_operation_domain_FRAME_and_output_roles", "conditions": [], "explanation": { "zh-Hant": "density14/15用full-prefix underscores，density17用local hyphens。coordinate frame與circle frame不同，輸出欄序／型別依本family，不改原中英／JSON／status。", "en": "density14/15 use FULL-prefix underscores;density17 uses LOCAL hyphens.The coordinate and circle frames differ.Retain THIS family ordered answer roles/types and all original bilingual JSON/status." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [0, 5, 1]", "after": "derived = [否, 否, I]", "relation": "implies", "rule_id": "Coordinate_EACH_original_point_axes_BEFORE_quadrants", "conditions": [], "explanation": { "zh-Hant": "先判zero coordinates再判象限；原點同屬兩軸且不在象限，axis點也不在象限。保四點位置及x/y兩欄，不能從圖猜數字。", "en": "Check zero coordinates BEFORE quadrants.The origin lies on BOTH axes and in NO quadrant;axis points are not quadrant points.Keep all four positions and separate x/y columns without diagram guesses." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [1, 1, 0]", "after": "derived = [是, 否, x軸]", "relation": "implies", "rule_id": "Coordinate_EACH_original_point_axes_BEFORE_quadrants", "conditions": [], "explanation": { "zh-Hant": "先判zero coordinates再判象限；原點同屬兩軸且不在象限，axis點也不在象限。保四點位置及x/y兩欄，不能從圖猜數字。", "en": "Check zero coordinates BEFORE quadrants.The origin lies on BOTH axes and in NO quadrant;axis points are not quadrant points.Keep all four positions and separate x/y columns without diagram guesses." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [2, 0, 1]", "after": "derived = [否, 是, y軸]", "relation": "implies", "rule_id": "Coordinate_EACH_original_point_axes_BEFORE_quadrants", "conditions": [], "explanation": { "zh-Hant": "先判zero coordinates再判象限；原點同屬兩軸且不在象限，axis點也不在象限。保四點位置及x/y兩欄，不能從圖猜數字。", "en": "Check zero coordinates BEFORE quadrants.The origin lies on BOTH axes and in NO quadrant;axis points are not quadrant points.Keep all four positions and separate x/y columns without diagram guesses." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "source roles = [3, -1, -17]", "after": "derived = [否, 否, III]", "relation": "implies", "rule_id": "Coordinate_EACH_original_point_axes_BEFORE_quadrants", "conditions": [], "explanation": { "zh-Hant": "先判zero coordinates再判象限；原點同屬兩軸且不在象限，axis點也不在象限。保四點位置及x/y兩欄，不能從圖猜數字。", "en": "Check zero coordinates BEFORE quadrants.The origin lies on BOTH axes and in NO quadrant;axis points are not quadrant points.Keep all four positions and separate x/y columns without diagram guesses." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate." } }, "arithmetic": null } ], "math_model": { "result": [ [ "5", "1", "0", "-1" ], [ "1", "0", "1", "-17" ], [ false, true, false, false ], [ false, false, true, false ], [ "I", "x軸", "y軸", "III" ] ] }, "conclusion": { "canonical_value": "([5, 1, 0, -1], [1, 0, 1, -17], [否, 是, 否, 否], [否, 否, 是, 否], [I, x軸, y軸, III])", "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-20261011-advance-20261015-r07-coordinate-plane-foundations", "batch_path": "public/data/questions/batches/batch-20261011-advance-20261015-r07-coordinate-plane-foundations/questions.jsonl", "batch_sha256": "123b8ceaa888b690a0ae676ad07f8bab359ecadb66103e52a232095b913b44ff", "original_line": 18, "original_line_sha256": "01a3583dcccae94ed5fd026b91a001e6d5d12abd3fbb868bc6737fa29877e894", "question_compact_sha256": "69b3fdfb6da3e55d5847515053e47800697722a6d00d1ccd4f00384f83e6415b", "english_row_compact_sha256": "6f4e8afba3fe6ebd86c0d69f11868ff47203b807ff835c87ab70ace172cd680c", "english_manifest_path": "public/data/i18n/editions/batch-20261011-advance-20261015-r07-coordinate-plane-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261011-advance-20261015-r07-coordinate-plane-foundations.en.jsonl" }, "mko_bindings": { "mko-coordinate-plane": { "sha256": "eb010001cb85a8fe8eee5a876ee1ec40caddc67fe621f671741caacf48ab3c78", "english_sha256": "5da6135768256b641dcda707cae4d1c9b7a425ea489f9b1e850eaa6bf67fa0b3", "original_path": "public/data/mko/coordinate-plane.json", "english_path": "public/data/i18n/editions/mko-coordinate-plane.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "322533190c1eb10144c4c59b6c70cc2f8105108b5f4f3a39dd577712e7185c02", "original_candidate_sha256": "87115b77528253daef89977726d33420dd130a8c0f7ccebeca3d257ed2cc3de9", "original_candidate_line_sha256": "87115b77528253daef89977726d33420dd130a8c0f7ccebeca3d257ed2cc3de9" }, "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-p61", "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": "d6b5a409bf933281a46617cd715d8016fd5ca3d6fb76f77d179ac2ecd9d608bf", "question_first_witness_sha256": "f80ecf598c6893a580af018e1a82849b33ee6887efb48a6a1d69569aa17f12e4" }, "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": "c5fc0961fff8609f45f80ddb872424a708f2c7413d95f222cc6511f4a0ec236f", "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." } }