{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0001","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=[[0, 0], [1, 0], [0, -1], [-1, 1]]。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":"([0, 1, 0, -1], [0, 0, -1, 1], [是, 是, 否, 否], [是, 否, 是, 否], [原點, x軸, y軸, II])","explanation_zh":"四點有序欄位軸與象限=([0, 1, 0, -1], [0, 0, -1, 1], [是, 是, 否, 否], [是, 否, 是, 否], [原點, x軸, y軸, II])。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":1,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157001,"parameters":{"points":[[0,0],[1,0],[0,-1],[-1,1]],"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/[[0,0],[1,0],[0,-1],[-1,1]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0002","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=[[1, 1], [-1, 1], [-1, -1], [1, -1]]。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":"([1, -1, -1, 1], [1, 1, -1, -1], [否, 否, 否, 否], [否, 否, 否, 否], [I, II, III, IV])","explanation_zh":"四點有序欄位軸與象限=([1, -1, -1, 1], [1, 1, -1, -1], [否, 否, 否, 否], [否, 否, 否, 否], [I, II, III, IV])。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":1,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157002,"parameters":{"points":[[1,1],[-1,1],[-1,-1],[1,-1]],"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/[[1,1],[-1,1],[-1,-1],[1,-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0003","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=[[-10, 1], [1, 0], [0, 1], [-1, -2]]。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":"([-10, 1, 0, -1], [1, 0, 1, -2], [否, 是, 否, 否], [否, 否, 是, 否], [II, x軸, y軸, III])","explanation_zh":"四點有序欄位軸與象限=([-10, 1, 0, -1], [1, 0, 1, -2], [否, 是, 否, 否], [否, 否, 是, 否], [II, 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":1,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157003,"parameters":{"points":[[-10,1],[1,0],[0,1],[-1,-2]],"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/[[-10,1],[1,0],[0,1],[-1,-2]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0004","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=[[-9, 1], [1, 0], [0, 1], [-1, -3]]。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":"([-9, 1, 0, -1], [1, 0, 1, -3], [否, 是, 否, 否], [否, 否, 是, 否], [II, x軸, y軸, III])","explanation_zh":"四點有序欄位軸與象限=([-9, 1, 0, -1], [1, 0, 1, -3], [否, 是, 否, 否], [否, 否, 是, 否], [II, 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":1,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157004,"parameters":{"points":[[-9,1],[1,0],[0,1],[-1,-3]],"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/[[-9,1],[1,0],[0,1],[-1,-3]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0005","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=[[-8, 1], [1, 0], [0, 1], [-1, -4]]。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":"([-8, 1, 0, -1], [1, 0, 1, -4], [否, 是, 否, 否], [否, 否, 是, 否], [II, x軸, y軸, III])","explanation_zh":"四點有序欄位軸與象限=([-8, 1, 0, -1], [1, 0, 1, -4], [否, 是, 否, 否], [否, 否, 是, 否], [II, 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":1,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157005,"parameters":{"points":[[-8,1],[1,0],[0,1],[-1,-4]],"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/[[-8,1],[1,0],[0,1],[-1,-4]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0006","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=[[-7, 1], [1, 0], [0, 1], [-1, -5]]。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":"([-7, 1, 0, -1], [1, 0, 1, -5], [否, 是, 否, 否], [否, 否, 是, 否], [II, x軸, y軸, III])","explanation_zh":"四點有序欄位軸與象限=([-7, 1, 0, -1], [1, 0, 1, -5], [否, 是, 否, 否], [否, 否, 是, 否], [II, 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":1,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157006,"parameters":{"points":[[-7,1],[1,0],[0,1],[-1,-5]],"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/[[-7,1],[1,0],[0,1],[-1,-5]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0007","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=[[-6, 1], [1, 0], [0, 1], [-1, -6]]。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":"([-6, 1, 0, -1], [1, 0, 1, -6], [否, 是, 否, 否], [否, 否, 是, 否], [II, x軸, y軸, III])","explanation_zh":"四點有序欄位軸與象限=([-6, 1, 0, -1], [1, 0, 1, -6], [否, 是, 否, 否], [否, 否, 是, 否], [II, 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":1,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157007,"parameters":{"points":[[-6,1],[1,0],[0,1],[-1,-6]],"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/[[-6,1],[1,0],[0,1],[-1,-6]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0008","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, -7]]。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, -7], [否, 是, 否, 否], [否, 否, 是, 否], [II, x軸, y軸, III])","explanation_zh":"四點有序欄位軸與象限=([-5, 1, 0, -1], [1, 0, 1, -7], [否, 是, 否, 否], [否, 否, 是, 否], [II, 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":1,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157008,"parameters":{"points":[[-5,1],[1,0],[0,1],[-1,-7]],"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,-7]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0009","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=[[-4, 1], [1, 0], [0, 1], [-1, -8]]。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":"([-4, 1, 0, -1], [1, 0, 1, -8], [否, 是, 否, 否], [否, 否, 是, 否], [II, x軸, y軸, III])","explanation_zh":"四點有序欄位軸與象限=([-4, 1, 0, -1], [1, 0, 1, -8], [否, 是, 否, 否], [否, 否, 是, 否], [II, 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":2,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157009,"parameters":{"points":[[-4,1],[1,0],[0,1],[-1,-8]],"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/[[-4,1],[1,0],[0,1],[-1,-8]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0010","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=[[-3, 1], [1, 0], [0, 1], [-1, -9]]。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":"([-3, 1, 0, -1], [1, 0, 1, -9], [否, 是, 否, 否], [否, 否, 是, 否], [II, x軸, y軸, III])","explanation_zh":"四點有序欄位軸與象限=([-3, 1, 0, -1], [1, 0, 1, -9], [否, 是, 否, 否], [否, 否, 是, 否], [II, 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":2,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157010,"parameters":{"points":[[-3,1],[1,0],[0,1],[-1,-9]],"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/[[-3,1],[1,0],[0,1],[-1,-9]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0011","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=[[-2, 1], [1, 0], [0, 1], [-1, -10]]。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":"([-2, 1, 0, -1], [1, 0, 1, -10], [否, 是, 否, 否], [否, 否, 是, 否], [II, x軸, y軸, III])","explanation_zh":"四點有序欄位軸與象限=([-2, 1, 0, -1], [1, 0, 1, -10], [否, 是, 否, 否], [否, 否, 是, 否], [II, 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":2,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157011,"parameters":{"points":[[-2,1],[1,0],[0,1],[-1,-10]],"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/[[-2,1],[1,0],[0,1],[-1,-10]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0012","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=[[-1, 1], [1, 0], [0, 1], [-1, -11]]。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":"([-1, 1, 0, -1], [1, 0, 1, -11], [否, 是, 否, 否], [否, 否, 是, 否], [II, x軸, y軸, III])","explanation_zh":"四點有序欄位軸與象限=([-1, 1, 0, -1], [1, 0, 1, -11], [否, 是, 否, 否], [否, 否, 是, 否], [II, 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":2,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157012,"parameters":{"points":[[-1,1],[1,0],[0,1],[-1,-11]],"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/[[-1,1],[1,0],[0,1],[-1,-11]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0013","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=[[0, 1], [1, 0], [0, 1], [-1, -12]]。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":"([0, 1, 0, -1], [1, 0, 1, -12], [否, 是, 否, 否], [是, 否, 是, 否], [y軸, x軸, y軸, III])","explanation_zh":"四點有序欄位軸與象限=([0, 1, 0, -1], [1, 0, 1, -12], [否, 是, 否, 否], [是, 否, 是, 否], [y軸, 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":2,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157013,"parameters":{"points":[[0,1],[1,0],[0,1],[-1,-12]],"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/[[0,1],[1,0],[0,1],[-1,-12]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0014","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=[[1, 1], [1, 0], [0, 1], [-1, -13]]。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":"([1, 1, 0, -1], [1, 0, 1, -13], [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=([1, 1, 0, -1], [1, 0, 1, -13], [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":2,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157014,"parameters":{"points":[[1,1],[1,0],[0,1],[-1,-13]],"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/[[1,1],[1,0],[0,1],[-1,-13]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0015","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=[[2, 1], [1, 0], [0, 1], [-1, -14]]。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":"([2, 1, 0, -1], [1, 0, 1, -14], [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=([2, 1, 0, -1], [1, 0, 1, -14], [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":2,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157015,"parameters":{"points":[[2,1],[1,0],[0,1],[-1,-14]],"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/[[2,1],[1,0],[0,1],[-1,-14]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0016","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=[[3, 1], [1, 0], [0, 1], [-1, -15]]。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":"([3, 1, 0, -1], [1, 0, 1, -15], [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=([3, 1, 0, -1], [1, 0, 1, -15], [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":2,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157016,"parameters":{"points":[[3,1],[1,0],[0,1],[-1,-15]],"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/[[3,1],[1,0],[0,1],[-1,-15]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0017","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=[[4, 1], [1, 0], [0, 1], [-1, -16]]。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":"([4, 1, 0, -1], [1, 0, 1, -16], [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=([4, 1, 0, -1], [1, 0, 1, -16], [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":2,"skills":["四點欄位軸與象限"]},"variant":{"family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157017,"parameters":{"points":[[4,1],[1,0],[0,1],[-1,-16]],"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/[[4,1],[1,0],[0,1],[-1,-16]]"}},"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"}}
{"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0019","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=[[6, 1], [1, 0], [0, 1], [-1, -18]]。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":"([6, 1, 0, -1], [1, 0, 1, -18], [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=([6, 1, 0, -1], [1, 0, 1, -18], [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":202610157019,"parameters":{"points":[[6,1],[1,0],[0,1],[-1,-18]],"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/[[6,1],[1,0],[0,1],[-1,-18]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0020","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=[[7, 1], [1, 0], [0, 1], [-1, -19]]。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":"([7, 1, 0, -1], [1, 0, 1, -19], [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=([7, 1, 0, -1], [1, 0, 1, -19], [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":202610157020,"parameters":{"points":[[7,1],[1,0],[0,1],[-1,-19]],"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/[[7,1],[1,0],[0,1],[-1,-19]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0021","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=[[8, 1], [1, 0], [0, 1], [-1, -20]]。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":"([8, 1, 0, -1], [1, 0, 1, -20], [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=([8, 1, 0, -1], [1, 0, 1, -20], [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":202610157021,"parameters":{"points":[[8,1],[1,0],[0,1],[-1,-20]],"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/[[8,1],[1,0],[0,1],[-1,-20]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0022","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=[[9, 1], [1, 0], [0, 1], [-1, -21]]。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":"([9, 1, 0, -1], [1, 0, 1, -21], [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=([9, 1, 0, -1], [1, 0, 1, -21], [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":202610157022,"parameters":{"points":[[9,1],[1,0],[0,1],[-1,-21]],"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/[[9,1],[1,0],[0,1],[-1,-21]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0023","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=[[10, 1], [1, 0], [0, 1], [-1, -22]]。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":"([10, 1, 0, -1], [1, 0, 1, -22], [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=([10, 1, 0, -1], [1, 0, 1, -22], [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":202610157023,"parameters":{"points":[[10,1],[1,0],[0,1],[-1,-22]],"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/[[10,1],[1,0],[0,1],[-1,-22]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0024","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=[[11, 1], [1, 0], [0, 1], [-1, -23]]。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":"([11, 1, 0, -1], [1, 0, 1, -23], [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=([11, 1, 0, -1], [1, 0, 1, -23], [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":202610157024,"parameters":{"points":[[11,1],[1,0],[0,1],[-1,-23]],"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/[[11,1],[1,0],[0,1],[-1,-23]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0025","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=[[12, 1], [1, 0], [0, 1], [-1, -24]]。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":"([12, 1, 0, -1], [1, 0, 1, -24], [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=([12, 1, 0, -1], [1, 0, 1, -24], [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":202610157025,"parameters":{"points":[[12,1],[1,0],[0,1],[-1,-24]],"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/[[12,1],[1,0],[0,1],[-1,-24]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0026","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[0, 0]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(0, 0, 是)","explanation_zh":"同框架逐分量差與相等=(0, 0, 是)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":1,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157026,"parameters":{"P":[0,0],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"0\",\"0\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0027","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[1, 2]、Q=[2, 1]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(-1, 1, 否)","explanation_zh":"同框架逐分量差與相等=(-1, 1, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":1,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157027,"parameters":{"P":[1,2],"Q":[2,1],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-1\",\"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0028","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[-10, 3]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(-10, 3, 否)","explanation_zh":"同框架逐分量差與相等=(-10, 3, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":1,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157028,"parameters":{"P":[-10,3],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-10\",\"3\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0029","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[-9, 4]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(-9, 4, 否)","explanation_zh":"同框架逐分量差與相等=(-9, 4, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":1,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157029,"parameters":{"P":[-9,4],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-9\",\"4\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0030","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[-8, 5]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(-8, 5, 否)","explanation_zh":"同框架逐分量差與相等=(-8, 5, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":1,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157030,"parameters":{"P":[-8,5],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-8\",\"5\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0031","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[-7, 6]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(-7, 6, 否)","explanation_zh":"同框架逐分量差與相等=(-7, 6, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":1,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157031,"parameters":{"P":[-7,6],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-7\",\"6\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0032","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[-6, 7]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(-6, 7, 否)","explanation_zh":"同框架逐分量差與相等=(-6, 7, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":1,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157032,"parameters":{"P":[-6,7],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-6\",\"7\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0033","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[-5, 8]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(-5, 8, 否)","explanation_zh":"同框架逐分量差與相等=(-5, 8, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":1,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157033,"parameters":{"P":[-5,8],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-5\",\"8\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0034","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[-4, 9]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(-4, 9, 否)","explanation_zh":"同框架逐分量差與相等=(-4, 9, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":2,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157034,"parameters":{"P":[-4,9],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-4\",\"9\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0035","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[-3, 10]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(-3, 10, 否)","explanation_zh":"同框架逐分量差與相等=(-3, 10, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":2,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157035,"parameters":{"P":[-3,10],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-3\",\"10\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0036","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[-2, 11]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(-2, 11, 否)","explanation_zh":"同框架逐分量差與相等=(-2, 11, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":2,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157036,"parameters":{"P":[-2,11],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-2\",\"11\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0037","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[-1, 12]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(-1, 12, 否)","explanation_zh":"同框架逐分量差與相等=(-1, 12, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":2,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157037,"parameters":{"P":[-1,12],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-1\",\"12\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0038","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[0, 13]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(0, 13, 否)","explanation_zh":"同框架逐分量差與相等=(0, 13, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":2,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157038,"parameters":{"P":[0,13],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"0\",\"13\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0039","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[1, 14]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(1, 14, 否)","explanation_zh":"同框架逐分量差與相等=(1, 14, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":2,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157039,"parameters":{"P":[1,14],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"1\",\"14\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0040","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[2, 15]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(2, 15, 否)","explanation_zh":"同框架逐分量差與相等=(2, 15, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":2,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157040,"parameters":{"P":[2,15],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"2\",\"15\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0041","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[3, 16]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(3, 16, 否)","explanation_zh":"同框架逐分量差與相等=(3, 16, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":2,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157041,"parameters":{"P":[3,16],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"3\",\"16\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0042","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[4, 17]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(4, 17, 否)","explanation_zh":"同框架逐分量差與相等=(4, 17, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":2,"skills":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157042,"parameters":{"P":[4,17],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"4\",\"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0043","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[5, 18]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(5, 18, 否)","explanation_zh":"同框架逐分量差與相等=(5, 18, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157043,"parameters":{"P":[5,18],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"5\",\"18\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0044","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[6, 19]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(6, 19, 否)","explanation_zh":"同框架逐分量差與相等=(6, 19, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157044,"parameters":{"P":[6,19],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"6\",\"19\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0045","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[7, 20]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(7, 20, 否)","explanation_zh":"同框架逐分量差與相等=(7, 20, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157045,"parameters":{"P":[7,20],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"7\",\"20\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0046","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[8, 21]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(8, 21, 否)","explanation_zh":"同框架逐分量差與相等=(8, 21, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157046,"parameters":{"P":[8,21],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"8\",\"21\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0047","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[9, 22]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(9, 22, 否)","explanation_zh":"同框架逐分量差與相等=(9, 22, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157047,"parameters":{"P":[9,22],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"9\",\"22\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0048","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[10, 23]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(10, 23, 否)","explanation_zh":"同框架逐分量差與相等=(10, 23, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157048,"parameters":{"P":[10,23],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"10\",\"23\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0049","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[11, 24]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(11, 24, 否)","explanation_zh":"同框架逐分量差與相等=(11, 24, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157049,"parameters":{"P":[11,24],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"11\",\"24\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0050","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"逐分量差與相等","stem_zh":"同一正交有向xy框架，座標有序對。P=[12, 25]、Q=[0, 0]。求 (P.x−Q.x, P.y−Q.y, 兩點相等資格)，差的兩分量不當L2距離。","answer":{"kind":"expression","value":"(12, 25, 否)","explanation_zh":"同框架逐分量差與相等=(12, 25, 否)。分別相減，只有兩個殘差都為零才是同框架中的相等有序對。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":["逐分量差與相等"]},"variant":{"family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157050,"parameters":{"P":[12,25],"Q":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_ordered_pair_compare","semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"12\",\"25\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0051","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[0, 0]、候選=[0, 0]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([0, 0], [0, 0], 是, 是)","explanation_zh":"交換欄位候選與殘差=([0, 0], [0, 0], 是, 是)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":1,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157051,"parameters":{"P":[0,0],"candidate":[0,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[0,0],[\"0\",\"0\"]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0052","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[1, 1]、候選=[1, 1]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([1, 1], [0, 0], 是, 是)","explanation_zh":"交換欄位候選與殘差=([1, 1], [0, 0], 是, 是)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":1,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157052,"parameters":{"P":[1,1],"candidate":[1,1],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[1,1],[\"0\",\"0\"]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0053","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[1, 2]、候選=[2, 1]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([2, 1], [0, 0], 是, 否)","explanation_zh":"交換欄位候選與殘差=([2, 1], [0, 0], 是, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":1,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157053,"parameters":{"P":[1,2],"candidate":[2,1],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[1,2],[\"0\",\"0\"]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0054","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[1, 2]、候選=[1, 2]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([2, 1], [-1, 1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([2, 1], [-1, 1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":1,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157054,"parameters":{"P":[1,2],"candidate":[1,2],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[1,2],[\"-1\",\"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0055","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[-8, 5]、候選=[6, -9]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([5, -8], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([5, -8], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":1,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157055,"parameters":{"P":[-8,5],"candidate":[6,-9],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-8,5],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0056","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[-7, 6]、候選=[7, -8]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([6, -7], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([6, -7], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":1,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157056,"parameters":{"P":[-7,6],"candidate":[7,-8],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-7,6],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0057","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[-6, 7]、候選=[8, -7]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([7, -6], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([7, -6], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":1,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157057,"parameters":{"P":[-6,7],"candidate":[8,-7],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-6,7],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0058","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[-5, 8]、候選=[9, -6]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([8, -5], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([8, -5], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":1,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157058,"parameters":{"P":[-5,8],"candidate":[9,-6],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-5,8],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0059","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[-4, 9]、候選=[10, -5]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([9, -4], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([9, -4], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":2,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157059,"parameters":{"P":[-4,9],"candidate":[10,-5],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-4,9],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0060","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[-3, 10]、候選=[11, -4]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([10, -3], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([10, -3], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":2,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157060,"parameters":{"P":[-3,10],"candidate":[11,-4],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-3,10],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0061","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[-2, 11]、候選=[12, -3]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([11, -2], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([11, -2], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":2,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157061,"parameters":{"P":[-2,11],"candidate":[12,-3],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-2,11],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0062","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[-1, 12]、候選=[13, -2]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([12, -1], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([12, -1], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":2,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157062,"parameters":{"P":[-1,12],"candidate":[13,-2],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-1,12],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0063","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[0, 13]、候選=[14, -1]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([13, 0], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([13, 0], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":2,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157063,"parameters":{"P":[0,13],"candidate":[14,-1],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[0,13],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0064","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[1, 14]、候選=[15, 0]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([14, 1], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([14, 1], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":2,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157064,"parameters":{"P":[1,14],"candidate":[15,0],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[1,14],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0065","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[2, 15]、候選=[16, 1]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([15, 2], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([15, 2], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":2,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157065,"parameters":{"P":[2,15],"candidate":[16,1],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[2,15],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0066","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[3, 16]、候選=[17, 2]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([16, 3], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([16, 3], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":2,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157066,"parameters":{"P":[3,16],"candidate":[17,2],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[3,16],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0067","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[4, 17]、候選=[18, 3]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([17, 4], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([17, 4], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":2,"skills":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157067,"parameters":{"P":[4,17],"candidate":[18,3],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[4,17],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0068","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[5, 18]、候選=[19, 4]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([18, 5], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([18, 5], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157068,"parameters":{"P":[5,18],"candidate":[19,4],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[5,18],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0069","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[6, 19]、候選=[20, 5]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([19, 6], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([19, 6], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157069,"parameters":{"P":[6,19],"candidate":[20,5],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[6,19],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0070","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[7, 20]、候選=[21, 6]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([20, 7], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([20, 7], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157070,"parameters":{"P":[7,20],"candidate":[21,6],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[7,20],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0071","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[8, 21]、候選=[22, 7]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([21, 8], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([21, 8], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157071,"parameters":{"P":[8,21],"candidate":[22,7],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[8,21],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0072","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[9, 22]、候選=[23, 8]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([22, 9], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([22, 9], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157072,"parameters":{"P":[9,22],"candidate":[23,8],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[9,22],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0073","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[10, 23]、候選=[24, 9]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([23, 10], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([23, 10], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157073,"parameters":{"P":[10,23],"candidate":[24,9],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[10,23],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0074","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[11, 24]、候選=[25, 10]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([24, 11], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([24, 11], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157074,"parameters":{"P":[11,24],"candidate":[25,10],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[11,24],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0075","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"字面交換欄位的候選","stem_zh":"同一正交有向xy框架，座標有序對。P=[12, 25]、候選=[26, 11]。expected=(P.y,P.x)。求 (expected列, 候選減expected兩分量, 候選真交換資格, P本身等於expected資格)。","answer":{"kind":"expression","value":"([25, 12], [1, -1], 否, 否)","explanation_zh":"交換欄位候選與殘差=([25, 12], [1, -1], 否, 否)。只交換資料欄位後逐分量核對候選，另核原兩欄是否相同。交換欄位非幾何反射形式橋。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":["字面交換欄位的候選"]},"variant":{"family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157075,"parameters":{"P":[12,25],"candidate":[26,11],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_swap_candidate_audit","semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[12,25],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0076","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[0, 0], [0, 0]], [[0, 0], [0, 0]], [[0, 0], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[0, 0], [0, 0], [0, 0]], [是, 是, 是], 無)","explanation_zh":"三對分量差與首個不等=([[0, 0], [0, 0], [0, 0]], [是, 是, 是], 無)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":1,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157076,"parameters":{"pairs":[[[0,0],[0,0]],[[0,0],[0,0]],[[0,0],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"0\",\"0\"],[\"0\",\"0\"],[\"0\",\"0\"]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0077","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[1, 0], [0, 0]], [[0, 0], [0, 0]], [[0, 0], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[1, 0], [0, 0], [0, 0]], [否, 是, 是], 0)","explanation_zh":"三對分量差與首個不等=([[1, 0], [0, 0], [0, 0]], [否, 是, 是], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":1,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157077,"parameters":{"pairs":[[[1,0],[0,0]],[[0,0],[0,0]],[[0,0],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"1\",\"0\"],[\"0\",\"0\"],[\"0\",\"0\"]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0078","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[0, 0], [0, 0]], [[0, -1], [0, 0]], [[0, 0], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[0, 0], [0, -1], [0, 0]], [是, 否, 是], 1)","explanation_zh":"三對分量差與首個不等=([[0, 0], [0, -1], [0, 0]], [是, 否, 是], 1)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":1,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157078,"parameters":{"pairs":[[[0,0],[0,0]],[[0,-1],[0,0]],[[0,0],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"0\",\"0\"],[\"0\",\"-1\"],[\"0\",\"0\"]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0079","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[0, 0], [0, 0]], [[0, 0], [0, 0]], [[1, 1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[0, 0], [0, 0], [1, 1]], [是, 是, 否], 2)","explanation_zh":"三對分量差與首個不等=([[0, 0], [0, 0], [1, 1]], [是, 是, 否], 2)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":1,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157079,"parameters":{"pairs":[[[0,0],[0,0]],[[0,0],[0,0]],[[1,1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"0\",\"0\"],[\"0\",\"0\"],[\"1\",\"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0080","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[-8, 1], [0, 0]], [[0, 4], [0, 0]], [[0, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[-8, 1], [0, 4], [0, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[-8, 1], [0, 4], [0, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":1,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157080,"parameters":{"pairs":[[[-8,1],[0,0]],[[0,4],[0,0]],[[0,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-8\",\"1\"],[\"0\",\"4\"],[\"0\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0081","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[-7, 1], [0, 0]], [[0, 5], [0, 0]], [[1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[-7, 1], [0, 5], [1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[-7, 1], [0, 5], [1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":1,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157081,"parameters":{"pairs":[[[-7,1],[0,0]],[[0,5],[0,0]],[[1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-7\",\"1\"],[\"0\",\"5\"],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0082","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[-6, 1], [0, 0]], [[0, 6], [0, 0]], [[-1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[-6, 1], [0, 6], [-1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[-6, 1], [0, 6], [-1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":1,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157082,"parameters":{"pairs":[[[-6,1],[0,0]],[[0,6],[0,0]],[[-1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-6\",\"1\"],[\"0\",\"6\"],[\"-1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0083","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[-5, 1], [0, 0]], [[0, 7], [0, 0]], [[0, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[-5, 1], [0, 7], [0, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[-5, 1], [0, 7], [0, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":1,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157083,"parameters":{"pairs":[[[-5,1],[0,0]],[[0,7],[0,0]],[[0,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-5\",\"1\"],[\"0\",\"7\"],[\"0\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0084","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[-4, 1], [0, 0]], [[0, 8], [0, 0]], [[1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[-4, 1], [0, 8], [1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[-4, 1], [0, 8], [1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":2,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157084,"parameters":{"pairs":[[[-4,1],[0,0]],[[0,8],[0,0]],[[1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-4\",\"1\"],[\"0\",\"8\"],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0085","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[-3, 1], [0, 0]], [[0, 9], [0, 0]], [[-1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[-3, 1], [0, 9], [-1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[-3, 1], [0, 9], [-1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":2,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157085,"parameters":{"pairs":[[[-3,1],[0,0]],[[0,9],[0,0]],[[-1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-3\",\"1\"],[\"0\",\"9\"],[\"-1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0086","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[-2, 1], [0, 0]], [[0, 10], [0, 0]], [[0, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[-2, 1], [0, 10], [0, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[-2, 1], [0, 10], [0, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":2,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157086,"parameters":{"pairs":[[[-2,1],[0,0]],[[0,10],[0,0]],[[0,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-2\",\"1\"],[\"0\",\"10\"],[\"0\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0087","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[-1, 1], [0, 0]], [[0, 11], [0, 0]], [[1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[-1, 1], [0, 11], [1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[-1, 1], [0, 11], [1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":2,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157087,"parameters":{"pairs":[[[-1,1],[0,0]],[[0,11],[0,0]],[[1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-1\",\"1\"],[\"0\",\"11\"],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0088","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[0, 1], [0, 0]], [[0, 12], [0, 0]], [[-1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[0, 1], [0, 12], [-1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[0, 1], [0, 12], [-1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":2,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157088,"parameters":{"pairs":[[[0,1],[0,0]],[[0,12],[0,0]],[[-1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"0\",\"1\"],[\"0\",\"12\"],[\"-1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0089","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[1, 1], [0, 0]], [[0, 13], [0, 0]], [[0, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[1, 1], [0, 13], [0, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[1, 1], [0, 13], [0, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":2,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157089,"parameters":{"pairs":[[[1,1],[0,0]],[[0,13],[0,0]],[[0,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"1\",\"1\"],[\"0\",\"13\"],[\"0\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0090","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[2, 1], [0, 0]], [[0, 14], [0, 0]], [[1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[2, 1], [0, 14], [1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[2, 1], [0, 14], [1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":2,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157090,"parameters":{"pairs":[[[2,1],[0,0]],[[0,14],[0,0]],[[1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"2\",\"1\"],[\"0\",\"14\"],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0091","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[3, 1], [0, 0]], [[0, 15], [0, 0]], [[-1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[3, 1], [0, 15], [-1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[3, 1], [0, 15], [-1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":2,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157091,"parameters":{"pairs":[[[3,1],[0,0]],[[0,15],[0,0]],[[-1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"3\",\"1\"],[\"0\",\"15\"],[\"-1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0092","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[4, 1], [0, 0]], [[0, 16], [0, 0]], [[0, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[4, 1], [0, 16], [0, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[4, 1], [0, 16], [0, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":2,"skills":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157092,"parameters":{"pairs":[[[4,1],[0,0]],[[0,16],[0,0]],[[0,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"4\",\"1\"],[\"0\",\"16\"],[\"0\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0093","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[5, 1], [0, 0]], [[0, 17], [0, 0]], [[1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[5, 1], [0, 17], [1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[5, 1], [0, 17], [1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157093,"parameters":{"pairs":[[[5,1],[0,0]],[[0,17],[0,0]],[[1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"5\",\"1\"],[\"0\",\"17\"],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0094","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[6, 1], [0, 0]], [[0, 18], [0, 0]], [[-1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[6, 1], [0, 18], [-1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[6, 1], [0, 18], [-1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157094,"parameters":{"pairs":[[[6,1],[0,0]],[[0,18],[0,0]],[[-1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"6\",\"1\"],[\"0\",\"18\"],[\"-1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0095","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[7, 1], [0, 0]], [[0, 19], [0, 0]], [[0, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[7, 1], [0, 19], [0, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[7, 1], [0, 19], [0, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157095,"parameters":{"pairs":[[[7,1],[0,0]],[[0,19],[0,0]],[[0,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"7\",\"1\"],[\"0\",\"19\"],[\"0\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0096","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[8, 1], [0, 0]], [[0, 20], [0, 0]], [[1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[8, 1], [0, 20], [1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[8, 1], [0, 20], [1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157096,"parameters":{"pairs":[[[8,1],[0,0]],[[0,20],[0,0]],[[1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"8\",\"1\"],[\"0\",\"20\"],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0097","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[9, 1], [0, 0]], [[0, 21], [0, 0]], [[-1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[9, 1], [0, 21], [-1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[9, 1], [0, 21], [-1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157097,"parameters":{"pairs":[[[9,1],[0,0]],[[0,21],[0,0]],[[-1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"9\",\"1\"],[\"0\",\"21\"],[\"-1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0098","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[10, 1], [0, 0]], [[0, 22], [0, 0]], [[0, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[10, 1], [0, 22], [0, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[10, 1], [0, 22], [0, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157098,"parameters":{"pairs":[[[10,1],[0,0]],[[0,22],[0,0]],[[0,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"10\",\"1\"],[\"0\",\"22\"],[\"0\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0099","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[11, 1], [0, 0]], [[0, 23], [0, 0]], [[1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[11, 1], [0, 23], [1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[11, 1], [0, 23], [1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157099,"parameters":{"pairs":[[[11,1],[0,0]],[[0,23],[0,0]],[[1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"11\",\"1\"],[\"0\",\"23\"],[\"1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r07-coordinate-plane-0100","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","language":"zh-Hant","source_mko_ids":["mko-coordinate-plane"],"title_zh":"三對座標的首個不等","stem_zh":"同一正交有向xy框架，座標有序對。原序三對[P,Q]=[[[12, 1], [0, 0]], [[0, 24], [0, 0]], [[-1, -1], [0, 0]]]。求 (每對P−Q分量殘差, 逐對相等資格, 首個不等0索引或無)。","answer":{"kind":"expression","value":"([[12, 1], [0, 24], [-1, -1]], [否, 否, 否], 0)","explanation_zh":"三對分量差與首個不等=([[12, 1], [0, 24], [-1, -1]], [否, 否, 否], 0)。每對都核兩個分量，按原序取第一個失配；若全相同答無。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":["三對座標的首個不等"]},"variant":{"family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157100,"parameters":{"pairs":[[[12,1],[0,0]],[[0,24],[0,0]],[[-1,-1],[0,0]]],"frame":"same_orthogonal_xy_axes","domain":"finite_ordered_coordinate_protocol","operation":"density15_coordinate_first_mismatch_index","semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"12\",\"1\"],[\"0\",\"24\"],[\"-1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}