{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0001","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-23, -26) 與 Q=(-20, -22)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":5,"explanation_zh":"座標差為 (3, 4)，所以 d=√(3²+4²)=5。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260912,"parameters":{"p":[-23,-26],"q":[-20,-22],"expected_distance":5}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0002","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-16, -15) 與 Q=(-21, -3)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":13,"explanation_zh":"座標差為 (-5, 12)，所以 d=√((-5)²+12²)=13。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260913,"parameters":{"p":[-16,-15],"q":[-21,-3],"expected_distance":13}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0003","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-9, -4) 與 Q=(-1, -19)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":17,"explanation_zh":"座標差為 (8, -15)，所以 d=√(8²+(-15)²)=17。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260914,"parameters":{"p":[-9,-4],"q":[-1,-19],"expected_distance":17}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0004","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-2, 7) 與 Q=(-9, -17)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":25,"explanation_zh":"座標差為 (-7, -24)，所以 d=√((-7)²+(-24)²)=25。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260915,"parameters":{"p":[-2,7],"q":[-9,-17],"expected_distance":25}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0005","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(5, 18) 與 Q=(25, 39)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":29,"explanation_zh":"座標差為 (20, 21)，所以 d=√(20²+21²)=29。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260916,"parameters":{"p":[5,18],"q":[25,39],"expected_distance":29}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0006","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(12, -24) 與 Q=(3, 16)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":41,"explanation_zh":"座標差為 (-9, 40)，所以 d=√((-9)²+40²)=41。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260917,"parameters":{"p":[12,-24],"q":[3,16],"expected_distance":41}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0007","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(19, -13) 與 Q=(31, -48)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":37,"explanation_zh":"座標差為 (12, -35)，所以 d=√(12²+(-35)²)=37。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260918,"parameters":{"p":[19,-13],"q":[31,-48],"expected_distance":37}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0008","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-21, -2) 與 Q=(-32, -62)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":61,"explanation_zh":"座標差為 (-11, -60)，所以 d=√((-11)²+(-60)²)=61。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260919,"parameters":{"p":[-21,-2],"q":[-32,-62],"expected_distance":61}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0009","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-14, 9) 與 Q=(14, 54)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":53,"explanation_zh":"座標差為 (28, 45)，所以 d=√(28²+45²)=53。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260920,"parameters":{"p":[-14,9],"q":[14,54],"expected_distance":53}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0010","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-7, 20) 與 Q=(-40, 76)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":65,"explanation_zh":"座標差為 (-33, 56)，所以 d=√((-33)²+56²)=65。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260921,"parameters":{"p":[-7,20],"q":[-40,76],"expected_distance":65}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0011","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(0, -22) 與 Q=(16, -85)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":65,"explanation_zh":"座標差為 (16, -63)，所以 d=√(16²+(-63)²)=65。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260922,"parameters":{"p":[0,-22],"q":[16,-85],"expected_distance":65}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0012","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(7, -11) 與 Q=(-41, -66)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":73,"explanation_zh":"座標差為 (-48, -55)，所以 d=√((-48)²+(-55)²)=73。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260923,"parameters":{"p":[7,-11],"q":[-41,-66],"expected_distance":73}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0013","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(14, 0) 與 Q=(27, 84)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":85,"explanation_zh":"座標差為 (13, 84)，所以 d=√(13²+84²)=85。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260924,"parameters":{"p":[14,0],"q":[27,84],"expected_distance":85}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0014","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(21, 11) 與 Q=(-15, 88)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":85,"explanation_zh":"座標差為 (-36, 77)，所以 d=√((-36)²+77²)=85。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260925,"parameters":{"p":[21,11],"q":[-15,88],"expected_distance":85}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0015","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-19, 22) 與 Q=(20, -58)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":89,"explanation_zh":"座標差為 (39, -80)，所以 d=√(39²+(-80)²)=89。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260926,"parameters":{"p":[-19,22],"q":[20,-58],"expected_distance":89}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0016","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-12, -20) 與 Q=(-77, -92)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":97,"explanation_zh":"座標差為 (-65, -72)，所以 d=√((-65)²+(-72)²)=97。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260927,"parameters":{"p":[-12,-20],"q":[-77,-92],"expected_distance":97}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0017","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-5, -9) 與 Q=(15, 90)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":101,"explanation_zh":"座標差為 (20, 99)，所以 d=√(20²+99²)=101。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260928,"parameters":{"p":[-5,-9],"q":[15,90],"expected_distance":101}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0018","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(2, 2) 與 Q=(-58, 93)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":109,"explanation_zh":"座標差為 (-60, 91)，所以 d=√((-60)²+91²)=109。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260929,"parameters":{"p":[2,2],"q":[-58,93],"expected_distance":109}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0019","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(9, 13) 與 Q=(24, -99)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":113,"explanation_zh":"座標差為 (15, -112)，所以 d=√(15²+(-112)²)=113。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260930,"parameters":{"p":[9,13],"q":[24,-99],"expected_distance":113}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0020","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(16, 24) 與 Q=(-28, -93)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":125,"explanation_zh":"座標差為 (-44, -117)，所以 d=√((-44)²+(-117)²)=125。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260931,"parameters":{"p":[16,24],"q":[-28,-93],"expected_distance":125}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0021","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(23, -18) 與 Q=(29, -10)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":10,"explanation_zh":"座標差為 (6, 8)，所以 d=√(6²+8²)=10。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260932,"parameters":{"p":[23,-18],"q":[29,-10],"expected_distance":10}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0022","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-17, -7) 與 Q=(-27, 17)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":26,"explanation_zh":"座標差為 (-10, 24)，所以 d=√((-10)²+24²)=26。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260933,"parameters":{"p":[-17,-7],"q":[-27,17],"expected_distance":26}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0023","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-10, 4) 與 Q=(6, -26)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":34,"explanation_zh":"座標差為 (16, -30)，所以 d=√(16²+(-30)²)=34。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260934,"parameters":{"p":[-10,4],"q":[6,-26],"expected_distance":34}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0024","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-3, 15) 與 Q=(-17, -33)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":50,"explanation_zh":"座標差為 (-14, -48)，所以 d=√((-14)²+(-48)²)=50。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260935,"parameters":{"p":[-3,15],"q":[-17,-33],"expected_distance":50}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0025","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(4, 26) 與 Q=(44, 68)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":58,"explanation_zh":"座標差為 (40, 42)，所以 d=√(40²+42²)=58。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260936,"parameters":{"p":[4,26],"q":[44,68],"expected_distance":58}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0026","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(11, -16) 與 Q=(-7, 64)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":82,"explanation_zh":"座標差為 (-18, 80)，所以 d=√((-18)²+80²)=82。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260937,"parameters":{"p":[11,-16],"q":[-7,64],"expected_distance":82}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0027","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(18, -5) 與 Q=(42, -75)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":74,"explanation_zh":"座標差為 (24, -70)，所以 d=√(24²+(-70)²)=74。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260938,"parameters":{"p":[18,-5],"q":[42,-75],"expected_distance":74}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0028","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-22, 6) 與 Q=(-44, -114)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":122,"explanation_zh":"座標差為 (-22, -120)，所以 d=√((-22)²+(-120)²)=122。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260939,"parameters":{"p":[-22,6],"q":[-44,-114],"expected_distance":122}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0029","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-15, 17) 與 Q=(41, 107)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":106,"explanation_zh":"座標差為 (56, 90)，所以 d=√(56²+90²)=106。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260940,"parameters":{"p":[-15,17],"q":[41,107],"expected_distance":106}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-distance-coordinate-0030","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclidean-length"],"title_zh":"座標平面距離計算","stem_zh":"在歐幾里得平面上，點 P=(-8, -25) 與 Q=(-74, 87)。求距離 d(P,Q)。","answer":{"kind":"numeric","value":130,"explanation_zh":"座標差為 (-66, 112)，所以 d=√((-66)²+112²)=130。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["座標差","距離公式"]},"variant":{"family_id":"qf-distance-coordinate","seed":20260941,"parameters":{"p":[-8,-25],"q":[-74,87],"expected_distance":130}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0001","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 10°、90°、80°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260942,"parameters":{"mode":"angles","angles":[10,90,80]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0002","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 15°、80°、85°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260943,"parameters":{"mode":"angles","angles":[15,80,85]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0003","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 20°、90°、70°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260944,"parameters":{"mode":"angles","angles":[20,90,70]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0004","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 25°、80°、75°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260945,"parameters":{"mode":"angles","angles":[25,80,75]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0005","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 30°、90°、60°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260946,"parameters":{"mode":"angles","angles":[30,90,60]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0006","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 35°、80°、65°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260947,"parameters":{"mode":"angles","angles":[35,80,65]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0007","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 40°、90°、50°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260948,"parameters":{"mode":"angles","angles":[40,90,50]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0008","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 45°、80°、55°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260949,"parameters":{"mode":"angles","angles":[45,80,55]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0009","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 50°、90°、40°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260950,"parameters":{"mode":"angles","angles":[50,90,40]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0010","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 55°、80°、45°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260951,"parameters":{"mode":"angles","angles":[55,80,45]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0011","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 60°、90°、30°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260952,"parameters":{"mode":"angles","angles":[60,90,30]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0012","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 65°、80°、35°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260953,"parameters":{"mode":"angles","angles":[65,80,35]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0013","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 70°、90°、20°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260954,"parameters":{"mode":"angles","angles":[70,90,20]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0014","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 75°、80°、25°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260955,"parameters":{"mode":"angles","angles":[75,80,25]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0015","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 80°、90°、10°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260956,"parameters":{"mode":"angles","angles":[80,90,10]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0016","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 80°、11°、89°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260957,"parameters":{"mode":"angles","angles":[80,11,89]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0017","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 90°、15°、75°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260958,"parameters":{"mode":"angles","angles":[90,15,75]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0018","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 80°、19°、81°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260959,"parameters":{"mode":"angles","angles":[80,19,81]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0019","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 90°、23°、67°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260960,"parameters":{"mode":"angles","angles":[90,23,67]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0020","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 80°、27°、73°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260961,"parameters":{"mode":"angles","angles":[80,27,73]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0021","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 90°、31°、59°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260962,"parameters":{"mode":"angles","angles":[90,31,59]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0022","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 80°、35°、65°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260963,"parameters":{"mode":"angles","angles":[80,35,65]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0023","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 90°、39°、51°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260964,"parameters":{"mode":"angles","angles":[90,39,51]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0024","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 80°、43°、57°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260965,"parameters":{"mode":"angles","angles":[80,43,57]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0025","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 90°、47°、43°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260966,"parameters":{"mode":"angles","angles":[90,47,43]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0026","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 80°、51°、49°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260967,"parameters":{"mode":"angles","angles":[80,51,49]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0027","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 90°、55°、35°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260968,"parameters":{"mode":"angles","angles":[90,55,35]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0028","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 80°、59°、41°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260969,"parameters":{"mode":"angles","angles":[80,59,41]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0029","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 90°、63°、27°。它是否為直角三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260970,"parameters":{"mode":"angles","angles":[90,63,27]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-right-triangle-determination-0030","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"直角三角形判定","stem_zh":"一個非退化三角形的三內角依序為 80°、67°、33°。它是否為直角三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"雖然三角形內角和為 180°，但沒有任何一角是 90°，故不是直角三角形。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["內角判定","三角形內角和"]},"variant":{"family_id":"qf-right-triangle-determination","seed":20260971,"parameters":{"mode":"angles","angles":[80,67,33]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0001","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 3 與 4。求斜邊長 c。","answer":{"kind":"numeric","value":5,"explanation_zh":"c=√(3²+4²)=5。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260972,"parameters":{"mode":"hypotenuse","legs":[3,4],"hypotenuse":5,"known":[3,4]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0002","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，一股長為 12，斜邊長為 13。求另一股長 a。","answer":{"kind":"numeric","value":5,"explanation_zh":"a=√(13²-12²)=5。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260973,"parameters":{"mode":"leg","legs":[5,12],"hypotenuse":13,"known":[12,13]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0003","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 8 與 15。求斜邊長 c。","answer":{"kind":"numeric","value":17,"explanation_zh":"c=√(8²+15²)=17。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260974,"parameters":{"mode":"hypotenuse","legs":[8,15],"hypotenuse":17,"known":[8,15]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0004","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，一股長為 24，斜邊長為 25。求另一股長 a。","answer":{"kind":"numeric","value":7,"explanation_zh":"a=√(25²-24²)=7。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260975,"parameters":{"mode":"leg","legs":[7,24],"hypotenuse":25,"known":[24,25]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0005","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 20 與 21。求斜邊長 c。","answer":{"kind":"numeric","value":29,"explanation_zh":"c=√(20²+21²)=29。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260976,"parameters":{"mode":"hypotenuse","legs":[20,21],"hypotenuse":29,"known":[20,21]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0006","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，一股長為 40，斜邊長為 41。求另一股長 a。","answer":{"kind":"numeric","value":9,"explanation_zh":"a=√(41²-40²)=9。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260977,"parameters":{"mode":"leg","legs":[9,40],"hypotenuse":41,"known":[40,41]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0007","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 12 與 35。求斜邊長 c。","answer":{"kind":"numeric","value":37,"explanation_zh":"c=√(12²+35²)=37。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260978,"parameters":{"mode":"hypotenuse","legs":[12,35],"hypotenuse":37,"known":[12,35]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0008","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，一股長為 60，斜邊長為 61。求另一股長 a。","answer":{"kind":"numeric","value":11,"explanation_zh":"a=√(61²-60²)=11。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260979,"parameters":{"mode":"leg","legs":[11,60],"hypotenuse":61,"known":[60,61]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0009","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 28 與 45。求斜邊長 c。","answer":{"kind":"numeric","value":53,"explanation_zh":"c=√(28²+45²)=53。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260980,"parameters":{"mode":"hypotenuse","legs":[28,45],"hypotenuse":53,"known":[28,45]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0010","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，一股長為 56，斜邊長為 65。求另一股長 a。","answer":{"kind":"numeric","value":33,"explanation_zh":"a=√(65²-56²)=33。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260981,"parameters":{"mode":"leg","legs":[33,56],"hypotenuse":65,"known":[56,65]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0011","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 16 與 63。求斜邊長 c。","answer":{"kind":"numeric","value":65,"explanation_zh":"c=√(16²+63²)=65。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260982,"parameters":{"mode":"hypotenuse","legs":[16,63],"hypotenuse":65,"known":[16,63]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0012","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，一股長為 55，斜邊長為 73。求另一股長 a。","answer":{"kind":"numeric","value":48,"explanation_zh":"a=√(73²-55²)=48。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260983,"parameters":{"mode":"leg","legs":[48,55],"hypotenuse":73,"known":[55,73]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0013","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 13 與 84。求斜邊長 c。","answer":{"kind":"numeric","value":85,"explanation_zh":"c=√(13²+84²)=85。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260984,"parameters":{"mode":"hypotenuse","legs":[13,84],"hypotenuse":85,"known":[13,84]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0014","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，一股長為 77，斜邊長為 85。求另一股長 a。","answer":{"kind":"numeric","value":36,"explanation_zh":"a=√(85²-77²)=36。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260985,"parameters":{"mode":"leg","legs":[36,77],"hypotenuse":85,"known":[77,85]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0015","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 39 與 80。求斜邊長 c。","answer":{"kind":"numeric","value":89,"explanation_zh":"c=√(39²+80²)=89。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260986,"parameters":{"mode":"hypotenuse","legs":[39,80],"hypotenuse":89,"known":[39,80]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0016","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，一股長為 72，斜邊長為 97。求另一股長 a。","answer":{"kind":"numeric","value":65,"explanation_zh":"a=√(97²-72²)=65。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260987,"parameters":{"mode":"leg","legs":[65,72],"hypotenuse":97,"known":[72,97]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0017","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 20 與 99。求斜邊長 c。","answer":{"kind":"numeric","value":101,"explanation_zh":"c=√(20²+99²)=101。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260988,"parameters":{"mode":"hypotenuse","legs":[20,99],"hypotenuse":101,"known":[20,99]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0018","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，一股長為 91，斜邊長為 109。求另一股長 a。","answer":{"kind":"numeric","value":60,"explanation_zh":"a=√(109²-91²)=60。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260989,"parameters":{"mode":"leg","legs":[60,91],"hypotenuse":109,"known":[91,109]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0019","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 15 與 112。求斜邊長 c。","answer":{"kind":"numeric","value":113,"explanation_zh":"c=√(15²+112²)=113。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260990,"parameters":{"mode":"hypotenuse","legs":[15,112],"hypotenuse":113,"known":[15,112]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0020","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，一股長為 117，斜邊長為 125。求另一股長 a。","answer":{"kind":"numeric","value":44,"explanation_zh":"a=√(125²-117²)=44。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260991,"parameters":{"mode":"leg","legs":[44,117],"hypotenuse":125,"known":[117,125]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0021","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 6 與 8。求斜邊長 c。","answer":{"kind":"numeric","value":10,"explanation_zh":"c=√(6²+8²)=10。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260992,"parameters":{"mode":"hypotenuse","legs":[6,8],"hypotenuse":10,"known":[6,8]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0022","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，一股長為 24，斜邊長為 26。求另一股長 a。","answer":{"kind":"numeric","value":10,"explanation_zh":"a=√(26²-24²)=10。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260993,"parameters":{"mode":"leg","legs":[10,24],"hypotenuse":26,"known":[24,26]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0023","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 16 與 30。求斜邊長 c。","answer":{"kind":"numeric","value":34,"explanation_zh":"c=√(16²+30²)=34。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260994,"parameters":{"mode":"hypotenuse","legs":[16,30],"hypotenuse":34,"known":[16,30]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0024","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，一股長為 48，斜邊長為 50。求另一股長 a。","answer":{"kind":"numeric","value":14,"explanation_zh":"a=√(50²-48²)=14。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260995,"parameters":{"mode":"leg","legs":[14,48],"hypotenuse":50,"known":[48,50]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-missing-side-0025","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯定理缺邊計算","stem_zh":"在一個直角三角形中，兩股長分別為 40 與 42。求斜邊長 c。","answer":{"kind":"numeric","value":58,"explanation_zh":"c=√(40²+42²)=58。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["畢達哥拉斯定理","平方根"]},"variant":{"family_id":"qf-pythagorean-missing-side","seed":20260996,"parameters":{"mode":"hypotenuse","legs":[40,42],"hypotenuse":58,"known":[40,42]}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0001","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：3、4、7；乙：3、4、5；丙：3、4、5；丁：3、4、5","answer":{"kind":"choice","value":"甲","choices":["甲","乙","丙","丁"],"explanation_zh":"甲 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20260997,"parameters":{"mode":"counterexample","options":[[3,4,7],[3,4,5],[3,4,5],[3,4,5]],"counterexample_index":0}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0002","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：5、12、13；乙：5、13、13；丙：5、12、13；丁：5、12、13","answer":{"kind":"choice","value":"乙","choices":["甲","乙","丙","丁"],"explanation_zh":"乙 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20260998,"parameters":{"mode":"counterexample","options":[[5,12,13],[5,13,13],[5,12,13],[5,12,13]],"counterexample_index":1}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0003","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：8、15、17；乙：8、15、17；丙：10、15、17；丁：8、15、17","answer":{"kind":"choice","value":"丙","choices":["甲","乙","丙","丁"],"explanation_zh":"丙 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20260999,"parameters":{"mode":"counterexample","options":[[8,15,17],[8,15,17],[10,15,17],[8,15,17]],"counterexample_index":2}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0004","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：7、24、25；乙：7、24、25；丙：7、24、25；丁：7、24、27","answer":{"kind":"choice","value":"丁","choices":["甲","乙","丙","丁"],"explanation_zh":"丁 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20261000,"parameters":{"mode":"counterexample","options":[[7,24,25],[7,24,25],[7,24,25],[7,24,27]],"counterexample_index":3}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0005","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：20、22、29；乙：20、21、29；丙：20、21、29；丁：20、21、29","answer":{"kind":"choice","value":"甲","choices":["甲","乙","丙","丁"],"explanation_zh":"甲 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20261001,"parameters":{"mode":"counterexample","options":[[20,22,29],[20,21,29],[20,21,29],[20,21,29]],"counterexample_index":0}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0006","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：9、40、41；乙：11、40、41；丙：9、40、41；丁：9、40、41","answer":{"kind":"choice","value":"乙","choices":["甲","乙","丙","丁"],"explanation_zh":"乙 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20261002,"parameters":{"mode":"counterexample","options":[[9,40,41],[11,40,41],[9,40,41],[9,40,41]],"counterexample_index":1}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0007","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：12、35、37；乙：12、35、37；丙：12、35、39；丁：12、35、37","answer":{"kind":"choice","value":"丙","choices":["甲","乙","丙","丁"],"explanation_zh":"丙 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20261003,"parameters":{"mode":"counterexample","options":[[12,35,37],[12,35,37],[12,35,39],[12,35,37]],"counterexample_index":2}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0008","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：11、60、61；乙：11、60、61；丙：11、60、61；丁：11、61、61","answer":{"kind":"choice","value":"丁","choices":["甲","乙","丙","丁"],"explanation_zh":"丁 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20261004,"parameters":{"mode":"counterexample","options":[[11,60,61],[11,60,61],[11,60,61],[11,61,61]],"counterexample_index":3}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0009","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：30、45、53；乙：28、45、53；丙：28、45、53；丁：28、45、53","answer":{"kind":"choice","value":"甲","choices":["甲","乙","丙","丁"],"explanation_zh":"甲 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20261005,"parameters":{"mode":"counterexample","options":[[30,45,53],[28,45,53],[28,45,53],[28,45,53]],"counterexample_index":0}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0010","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：33、56、65；乙：33、56、67；丙：33、56、65；丁：33、56、65","answer":{"kind":"choice","value":"乙","choices":["甲","乙","丙","丁"],"explanation_zh":"乙 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20261006,"parameters":{"mode":"counterexample","options":[[33,56,65],[33,56,67],[33,56,65],[33,56,65]],"counterexample_index":1}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0011","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：16、63、65；乙：16、63、65；丙：16、64、65；丁：16、63、65","answer":{"kind":"choice","value":"丙","choices":["甲","乙","丙","丁"],"explanation_zh":"丙 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20261007,"parameters":{"mode":"counterexample","options":[[16,63,65],[16,63,65],[16,64,65],[16,63,65]],"counterexample_index":2}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0012","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：48、55、73；乙：48、55、73；丙：48、55、73；丁：50、55、73","answer":{"kind":"choice","value":"丁","choices":["甲","乙","丙","丁"],"explanation_zh":"丁 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20261008,"parameters":{"mode":"counterexample","options":[[48,55,73],[48,55,73],[48,55,73],[50,55,73]],"counterexample_index":3}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0013","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：13、84、87；乙：13、84、85；丙：13、84、85；丁：13、84、85","answer":{"kind":"choice","value":"甲","choices":["甲","乙","丙","丁"],"explanation_zh":"甲 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20261009,"parameters":{"mode":"counterexample","options":[[13,84,87],[13,84,85],[13,84,85],[13,84,85]],"counterexample_index":0}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0014","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：36、77、85；乙：36、78、85；丙：36、77、85；丁：36、77、85","answer":{"kind":"choice","value":"乙","choices":["甲","乙","丙","丁"],"explanation_zh":"乙 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20261010,"parameters":{"mode":"counterexample","options":[[36,77,85],[36,78,85],[36,77,85],[36,77,85]],"counterexample_index":1}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260912-pythagorean-counterexample-0015","batch_id":"batch-20260912-geometry-foundations","language":"zh-Hant","source_mko_ids":["mko-euclid-pythagorean-theorem"],"title_zh":"畢達哥拉斯關係反例辨識","stem_zh":"下列哪一組正數不滿足平方關係 a²+b²=c²（各組最後一個數作為 c）？\n甲：39、80、89；乙：39、80、89；丙：41、80、89；丁：39、80、89","answer":{"kind":"choice","value":"丙","choices":["甲","乙","丙","丁"],"explanation_zh":"丙 組的 a²+b² 不等於 c²，因此不滿足本題列出的平方關係。"},"difficulty":{"band":"lower_secondary","level":4,"skills":["平方關係","反例辨識"]},"variant":{"family_id":"qf-pythagorean-counterexample","seed":20261011,"parameters":{"mode":"counterexample","options":[[39,80,89],[39,80,89],[41,80,89],[39,80,89]],"counterexample_index":2}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-12","contract_version":"ocme-question-factory-v0.1"}}