{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0001","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[1,0],[1,2]]、B=[[3,5],[4,5],[4,3]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"是","explanation_zh":"對應平方邊：A=[1, 5, 4]；B=[1, 5, 4]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075001,"parameters":{"A":[[0,0],[1,0],[1,2]],"B":[[3,5],[4,5],[4,3]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"1\",\"5\",\"4\"],[\"1\",\"5\",\"4\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0002","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[2,0],[1,3]]、B=[[0,0],[3,0],[1,3]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[4, 10, 10]；B=[9, 10, 13]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075002,"parameters":{"A":[[0,0],[2,0],[1,3]],"B":[[0,0],[3,0],[1,3]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"4\",\"10\",\"10\"],[\"9\",\"10\",\"13\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0003","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[3,0],[1,4]]、B=[[0,0],[3,0],[1,5]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[9, 17, 20]；B=[9, 26, 29]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075003,"parameters":{"A":[[0,0],[3,0],[1,4]],"B":[[0,0],[3,0],[1,5]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"9\",\"17\",\"20\"],[\"9\",\"26\",\"29\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0004","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[4,0],[1,5]]、B=[[0,0],[4,0],[-1,5]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[16, 26, 34]；B=[16, 26, 50]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075004,"parameters":{"A":[[0,0],[4,0],[1,5]],"B":[[0,0],[4,0],[-1,5]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"16\",\"26\",\"34\"],[\"16\",\"26\",\"50\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0005","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[5,0],[1,6]]、B=[[3,5],[8,5],[4,-1]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"是","explanation_zh":"對應平方邊：A=[25, 37, 52]；B=[25, 37, 52]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075005,"parameters":{"A":[[0,0],[5,0],[1,6]],"B":[[3,5],[8,5],[4,-1]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"25\",\"37\",\"52\"],[\"25\",\"37\",\"52\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0006","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[6,0],[1,7]]、B=[[0,0],[7,0],[1,7]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[36, 50, 74]；B=[49, 50, 85]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075006,"parameters":{"A":[[0,0],[6,0],[1,7]],"B":[[0,0],[7,0],[1,7]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"36\",\"50\",\"74\"],[\"49\",\"50\",\"85\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0007","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[7,0],[1,8]]、B=[[0,0],[7,0],[1,9]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[49, 65, 100]；B=[49, 82, 117]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075007,"parameters":{"A":[[0,0],[7,0],[1,8]],"B":[[0,0],[7,0],[1,9]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"49\",\"65\",\"100\"],[\"49\",\"82\",\"117\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0008","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[8,0],[1,9]]、B=[[0,0],[8,0],[-1,9]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[64, 82, 130]；B=[64, 82, 162]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075008,"parameters":{"A":[[0,0],[8,0],[1,9]],"B":[[0,0],[8,0],[-1,9]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"64\",\"82\",\"130\"],[\"64\",\"82\",\"162\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0009","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[9,0],[1,10]]、B=[[3,5],[12,5],[4,-5]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"是","explanation_zh":"對應平方邊：A=[81, 101, 164]；B=[81, 101, 164]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075009,"parameters":{"A":[[0,0],[9,0],[1,10]],"B":[[3,5],[12,5],[4,-5]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"81\",\"101\",\"164\"],[\"81\",\"101\",\"164\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0010","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[10,0],[1,11]]、B=[[0,0],[11,0],[1,11]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[100, 122, 202]；B=[121, 122, 221]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075010,"parameters":{"A":[[0,0],[10,0],[1,11]],"B":[[0,0],[11,0],[1,11]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"100\",\"122\",\"202\"],[\"121\",\"122\",\"221\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0011","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[11,0],[1,12]]、B=[[0,0],[11,0],[1,13]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[121, 145, 244]；B=[121, 170, 269]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075011,"parameters":{"A":[[0,0],[11,0],[1,12]],"B":[[0,0],[11,0],[1,13]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"121\",\"145\",\"244\"],[\"121\",\"170\",\"269\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0012","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[12,0],[1,13]]、B=[[0,0],[12,0],[-1,13]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[144, 170, 290]；B=[144, 170, 338]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075012,"parameters":{"A":[[0,0],[12,0],[1,13]],"B":[[0,0],[12,0],[-1,13]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"144\",\"170\",\"290\"],[\"144\",\"170\",\"338\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0013","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[13,0],[1,14]]、B=[[3,5],[16,5],[4,-9]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"是","explanation_zh":"對應平方邊：A=[169, 197, 340]；B=[169, 197, 340]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075013,"parameters":{"A":[[0,0],[13,0],[1,14]],"B":[[3,5],[16,5],[4,-9]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"169\",\"197\",\"340\"],[\"169\",\"197\",\"340\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0014","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[14,0],[1,15]]、B=[[0,0],[15,0],[1,15]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[196, 226, 394]；B=[225, 226, 421]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075014,"parameters":{"A":[[0,0],[14,0],[1,15]],"B":[[0,0],[15,0],[1,15]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"196\",\"226\",\"394\"],[\"225\",\"226\",\"421\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0015","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[15,0],[1,16]]、B=[[0,0],[15,0],[1,17]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[225, 257, 452]；B=[225, 290, 485]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075015,"parameters":{"A":[[0,0],[15,0],[1,16]],"B":[[0,0],[15,0],[1,17]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"225\",\"257\",\"452\"],[\"225\",\"290\",\"485\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0016","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[16,0],[1,17]]、B=[[0,0],[16,0],[-1,17]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[256, 290, 514]；B=[256, 290, 578]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075016,"parameters":{"A":[[0,0],[16,0],[1,17]],"B":[[0,0],[16,0],[-1,17]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"256\",\"290\",\"514\"],[\"256\",\"290\",\"578\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0017","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[17,0],[1,18]]、B=[[3,5],[20,5],[4,-13]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"是","explanation_zh":"對應平方邊：A=[289, 325, 580]；B=[289, 325, 580]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075017,"parameters":{"A":[[0,0],[17,0],[1,18]],"B":[[3,5],[20,5],[4,-13]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"289\",\"325\",\"580\"],[\"289\",\"325\",\"580\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0018","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[18,0],[1,19]]、B=[[0,0],[19,0],[1,19]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[324, 362, 650]；B=[361, 362, 685]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075018,"parameters":{"A":[[0,0],[18,0],[1,19]],"B":[[0,0],[19,0],[1,19]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"324\",\"362\",\"650\"],[\"361\",\"362\",\"685\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0019","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[19,0],[1,20]]、B=[[0,0],[19,0],[1,21]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[361, 401, 724]；B=[361, 442, 765]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075019,"parameters":{"A":[[0,0],[19,0],[1,20]],"B":[[0,0],[19,0],[1,21]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"361\",\"401\",\"724\"],[\"361\",\"442\",\"765\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0020","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[20,0],[1,21]]、B=[[0,0],[20,0],[-1,21]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[400, 442, 802]；B=[400, 442, 882]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075020,"parameters":{"A":[[0,0],[20,0],[1,21]],"B":[[0,0],[20,0],[-1,21]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"400\",\"442\",\"802\"],[\"400\",\"442\",\"882\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0021","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[21,0],[1,22]]、B=[[3,5],[24,5],[4,-17]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"是","explanation_zh":"對應平方邊：A=[441, 485, 884]；B=[441, 485, 884]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075021,"parameters":{"A":[[0,0],[21,0],[1,22]],"B":[[3,5],[24,5],[4,-17]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"441\",\"485\",\"884\"],[\"441\",\"485\",\"884\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0022","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[22,0],[1,23]]、B=[[0,0],[23,0],[1,23]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[484, 530, 970]；B=[529, 530, 1013]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075022,"parameters":{"A":[[0,0],[22,0],[1,23]],"B":[[0,0],[23,0],[1,23]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"484\",\"530\",\"970\"],[\"529\",\"530\",\"1013\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0023","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[23,0],[1,24]]、B=[[0,0],[23,0],[1,25]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[529, 577, 1060]；B=[529, 626, 1109]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075023,"parameters":{"A":[[0,0],[23,0],[1,24]],"B":[[0,0],[23,0],[1,25]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"529\",\"577\",\"1060\"],[\"529\",\"626\",\"1109\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0024","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[24,0],[1,25]]、B=[[0,0],[24,0],[-1,25]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"否","explanation_zh":"對應平方邊：A=[576, 626, 1154]；B=[576, 626, 1250]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075024,"parameters":{"A":[[0,0],[24,0],[1,25]],"B":[[0,0],[24,0],[-1,25]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"576\",\"626\",\"1154\"],[\"576\",\"626\",\"1250\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0025","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"固定標記三邊全等","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[25,0],[1,26]]、B=[[3,5],[28,5],[4,-21]]，兩者明示非退化，明示對應 A1↔B1、A2↔B2、A3↔B3。是否符合標記 SSS 全等？","answer":{"kind":"short_text","value":"是","explanation_zh":"對應平方邊：A=[625, 677, 1252]；B=[625, 677, 1252]。按固定 12、13、23 對應比較，允許反射；否定目前對應不否定其他頂點排列。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定標記三邊全等"]},"variant":{"family_id":"qf-congruence-labeled-sss","seed":202610075025,"parameters":{"A":[[0,0],[25,0],[1,26]],"B":[[3,5],[28,5],[4,-21]],"operation":"labeled_sss","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"625\",\"677\",\"1252\"],[\"625\",\"677\",\"1252\"]],\"operation\":\"labeled_sss\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0026","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[0,1],[-1,0]]、B=[[3,5],[3,4],[2,5]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"1","explanation_zh":"對應邊12平方=1。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075026,"parameters":{"A":[[0,0],[0,1],[-1,0]],"B":[[3,5],[3,4],[2,5]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"0\",\"1\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0027","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[1,2],[-2,1]]、B=[[3,5],[4,3],[1,4]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"5","explanation_zh":"對應邊12平方=5。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075027,"parameters":{"A":[[0,0],[1,2],[-2,1]],"B":[[3,5],[4,3],[1,4]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"1\",\"2\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0028","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[2,3],[-3,2]]、B=[[3,5],[5,2],[0,3]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"13","explanation_zh":"對應邊12平方=13。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075028,"parameters":{"A":[[0,0],[2,3],[-3,2]],"B":[[3,5],[5,2],[0,3]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"2\",\"3\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0029","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[3,4],[-4,3]]、B=[[3,5],[6,1],[-1,2]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"25","explanation_zh":"對應邊12平方=25。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075029,"parameters":{"A":[[0,0],[3,4],[-4,3]],"B":[[3,5],[6,1],[-1,2]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"3\",\"4\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0030","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[4,5],[-5,4]]、B=[[3,5],[7,0],[-2,1]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"41","explanation_zh":"對應邊12平方=41。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075030,"parameters":{"A":[[0,0],[4,5],[-5,4]],"B":[[3,5],[7,0],[-2,1]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"4\",\"5\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0031","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[5,6],[-6,5]]、B=[[3,5],[8,-1],[-3,0]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"61","explanation_zh":"對應邊12平方=61。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075031,"parameters":{"A":[[0,0],[5,6],[-6,5]],"B":[[3,5],[8,-1],[-3,0]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"5\",\"6\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0032","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[6,7],[-7,6]]、B=[[3,5],[9,-2],[-4,-1]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"85","explanation_zh":"對應邊12平方=85。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075032,"parameters":{"A":[[0,0],[6,7],[-7,6]],"B":[[3,5],[9,-2],[-4,-1]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"6\",\"7\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0033","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[7,8],[-8,7]]、B=[[3,5],[10,-3],[-5,-2]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"113","explanation_zh":"對應邊12平方=113。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075033,"parameters":{"A":[[0,0],[7,8],[-8,7]],"B":[[3,5],[10,-3],[-5,-2]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"7\",\"8\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0034","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[8,9],[-9,8]]、B=[[3,5],[11,-4],[-6,-3]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"145","explanation_zh":"對應邊12平方=145。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075034,"parameters":{"A":[[0,0],[8,9],[-9,8]],"B":[[3,5],[11,-4],[-6,-3]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"8\",\"9\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0035","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[9,10],[-10,9]]、B=[[3,5],[12,-5],[-7,-4]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"181","explanation_zh":"對應邊12平方=181。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075035,"parameters":{"A":[[0,0],[9,10],[-10,9]],"B":[[3,5],[12,-5],[-7,-4]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"9\",\"10\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0036","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[10,11],[-11,10]]、B=[[3,5],[13,-6],[-8,-5]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"221","explanation_zh":"對應邊12平方=221。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075036,"parameters":{"A":[[0,0],[10,11],[-11,10]],"B":[[3,5],[13,-6],[-8,-5]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"10\",\"11\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0037","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[11,12],[-12,11]]、B=[[3,5],[14,-7],[-9,-6]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"265","explanation_zh":"對應邊12平方=265。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075037,"parameters":{"A":[[0,0],[11,12],[-12,11]],"B":[[3,5],[14,-7],[-9,-6]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"11\",\"12\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0038","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[12,13],[-13,12]]、B=[[3,5],[15,-8],[-10,-7]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"313","explanation_zh":"對應邊12平方=313。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075038,"parameters":{"A":[[0,0],[12,13],[-13,12]],"B":[[3,5],[15,-8],[-10,-7]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"12\",\"13\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0039","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[13,14],[-14,13]]、B=[[3,5],[16,-9],[-11,-8]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"365","explanation_zh":"對應邊12平方=365。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075039,"parameters":{"A":[[0,0],[13,14],[-14,13]],"B":[[3,5],[16,-9],[-11,-8]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"13\",\"14\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0040","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[14,15],[-15,14]]、B=[[3,5],[17,-10],[-12,-9]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"421","explanation_zh":"對應邊12平方=421。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075040,"parameters":{"A":[[0,0],[14,15],[-15,14]],"B":[[3,5],[17,-10],[-12,-9]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"14\",\"15\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0041","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[15,16],[-16,15]]、B=[[3,5],[18,-11],[-13,-10]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"481","explanation_zh":"對應邊12平方=481。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075041,"parameters":{"A":[[0,0],[15,16],[-16,15]],"B":[[3,5],[18,-11],[-13,-10]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"15\",\"16\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0042","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[16,17],[-17,16]]、B=[[3,5],[19,-12],[-14,-11]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"545","explanation_zh":"對應邊12平方=545。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075042,"parameters":{"A":[[0,0],[16,17],[-17,16]],"B":[[3,5],[19,-12],[-14,-11]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"16\",\"17\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0043","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[17,18],[-18,17]]、B=[[3,5],[20,-13],[-15,-12]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"613","explanation_zh":"對應邊12平方=613。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075043,"parameters":{"A":[[0,0],[17,18],[-18,17]],"B":[[3,5],[20,-13],[-15,-12]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"17\",\"18\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0044","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[18,19],[-19,18]]、B=[[3,5],[21,-14],[-16,-13]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"685","explanation_zh":"對應邊12平方=685。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075044,"parameters":{"A":[[0,0],[18,19],[-19,18]],"B":[[3,5],[21,-14],[-16,-13]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"18\",\"19\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0045","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[19,20],[-20,19]]、B=[[3,5],[22,-15],[-17,-14]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"761","explanation_zh":"對應邊12平方=761。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075045,"parameters":{"A":[[0,0],[19,20],[-20,19]],"B":[[3,5],[22,-15],[-17,-14]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"19\",\"20\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0046","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[20,21],[-21,20]]、B=[[3,5],[23,-16],[-18,-15]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"841","explanation_zh":"對應邊12平方=841。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075046,"parameters":{"A":[[0,0],[20,21],[-21,20]],"B":[[3,5],[23,-16],[-18,-15]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"20\",\"21\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0047","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[21,22],[-22,21]]、B=[[3,5],[24,-17],[-19,-16]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"925","explanation_zh":"對應邊12平方=925。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075047,"parameters":{"A":[[0,0],[21,22],[-22,21]],"B":[[3,5],[24,-17],[-19,-16]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"21\",\"22\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0048","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[22,23],[-23,22]]、B=[[3,5],[25,-18],[-20,-17]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"1013","explanation_zh":"對應邊12平方=1013。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075048,"parameters":{"A":[[0,0],[22,23],[-23,22]],"B":[[3,5],[25,-18],[-20,-17]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"22\",\"23\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0049","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[23,24],[-24,23]]、B=[[3,5],[26,-19],[-21,-18]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"1105","explanation_zh":"對應邊12平方=1105。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075049,"parameters":{"A":[[0,0],[23,24],[-24,23]],"B":[[3,5],[26,-19],[-21,-18]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"23\",\"24\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0050","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"已全等的對應邊平方","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[24,25],[-25,24]]、B=[[3,5],[27,-20],[-22,-19]]，已確認非退化且全三邊標記全等；明示對應按同索引。求 A1A2 與對應 B1B2 的共同平方長度。","answer":{"kind":"short_text","value":"1201","explanation_zh":"對應邊12平方=1201。先守住完整三邊全等，再讀指定邊；不以只相等一邊冒充全等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已全等的對應邊平方"]},"variant":{"family_id":"qf-congruence-corresponding-squared-side","seed":202610075050,"parameters":{"A":[[0,0],[24,25],[-25,24]],"B":[[3,5],[27,-20],[-22,-19]],"i":1,"j":2,"operation":"corresponding_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"24\",\"25\"],\"operation\":\"corresponding_squared_side\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0051","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[1,0],[1,2]]、B=[[3,5],[4,5],[4,3]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"無","explanation_zh":"對應平方邊：A=[1, 5, 4]；B=[1, 5, 4]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075051,"parameters":{"A":[[0,0],[1,0],[1,2]],"B":[[3,5],[4,5],[4,3]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"1\",\"5\",\"4\"],[\"1\",\"5\",\"4\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0052","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[2,0],[1,3]]、B=[[0,0],[3,0],[1,3]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"12","explanation_zh":"對應平方邊：A=[4, 10, 10]；B=[9, 10, 13]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075052,"parameters":{"A":[[0,0],[2,0],[1,3]],"B":[[0,0],[3,0],[1,3]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"4\",\"10\",\"10\"],[\"9\",\"10\",\"13\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0053","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[3,0],[1,4]]、B=[[0,0],[3,0],[1,5]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"13","explanation_zh":"對應平方邊：A=[9, 17, 20]；B=[9, 26, 29]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075053,"parameters":{"A":[[0,0],[3,0],[1,4]],"B":[[0,0],[3,0],[1,5]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"9\",\"17\",\"20\"],[\"9\",\"26\",\"29\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0054","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[4,0],[1,5]]、B=[[0,0],[4,0],[-1,5]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"23","explanation_zh":"對應平方邊：A=[16, 26, 34]；B=[16, 26, 50]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075054,"parameters":{"A":[[0,0],[4,0],[1,5]],"B":[[0,0],[4,0],[-1,5]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"16\",\"26\",\"34\"],[\"16\",\"26\",\"50\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0055","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[5,0],[1,6]]、B=[[3,5],[8,5],[4,-1]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"無","explanation_zh":"對應平方邊：A=[25, 37, 52]；B=[25, 37, 52]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075055,"parameters":{"A":[[0,0],[5,0],[1,6]],"B":[[3,5],[8,5],[4,-1]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"25\",\"37\",\"52\"],[\"25\",\"37\",\"52\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0056","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[6,0],[1,7]]、B=[[0,0],[7,0],[1,7]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"12","explanation_zh":"對應平方邊：A=[36, 50, 74]；B=[49, 50, 85]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075056,"parameters":{"A":[[0,0],[6,0],[1,7]],"B":[[0,0],[7,0],[1,7]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"36\",\"50\",\"74\"],[\"49\",\"50\",\"85\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0057","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[7,0],[1,8]]、B=[[0,0],[7,0],[1,9]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"13","explanation_zh":"對應平方邊：A=[49, 65, 100]；B=[49, 82, 117]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075057,"parameters":{"A":[[0,0],[7,0],[1,8]],"B":[[0,0],[7,0],[1,9]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"49\",\"65\",\"100\"],[\"49\",\"82\",\"117\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0058","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[8,0],[1,9]]、B=[[0,0],[8,0],[-1,9]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"23","explanation_zh":"對應平方邊：A=[64, 82, 130]；B=[64, 82, 162]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075058,"parameters":{"A":[[0,0],[8,0],[1,9]],"B":[[0,0],[8,0],[-1,9]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"64\",\"82\",\"130\"],[\"64\",\"82\",\"162\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0059","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[9,0],[1,10]]、B=[[3,5],[12,5],[4,-5]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"無","explanation_zh":"對應平方邊：A=[81, 101, 164]；B=[81, 101, 164]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075059,"parameters":{"A":[[0,0],[9,0],[1,10]],"B":[[3,5],[12,5],[4,-5]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"81\",\"101\",\"164\"],[\"81\",\"101\",\"164\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0060","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[10,0],[1,11]]、B=[[0,0],[11,0],[1,11]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"12","explanation_zh":"對應平方邊：A=[100, 122, 202]；B=[121, 122, 221]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075060,"parameters":{"A":[[0,0],[10,0],[1,11]],"B":[[0,0],[11,0],[1,11]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"100\",\"122\",\"202\"],[\"121\",\"122\",\"221\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0061","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[11,0],[1,12]]、B=[[0,0],[11,0],[1,13]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"13","explanation_zh":"對應平方邊：A=[121, 145, 244]；B=[121, 170, 269]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075061,"parameters":{"A":[[0,0],[11,0],[1,12]],"B":[[0,0],[11,0],[1,13]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"121\",\"145\",\"244\"],[\"121\",\"170\",\"269\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0062","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[12,0],[1,13]]、B=[[0,0],[12,0],[-1,13]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"23","explanation_zh":"對應平方邊：A=[144, 170, 290]；B=[144, 170, 338]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075062,"parameters":{"A":[[0,0],[12,0],[1,13]],"B":[[0,0],[12,0],[-1,13]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"144\",\"170\",\"290\"],[\"144\",\"170\",\"338\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0063","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[13,0],[1,14]]、B=[[3,5],[16,5],[4,-9]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"無","explanation_zh":"對應平方邊：A=[169, 197, 340]；B=[169, 197, 340]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075063,"parameters":{"A":[[0,0],[13,0],[1,14]],"B":[[3,5],[16,5],[4,-9]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"169\",\"197\",\"340\"],[\"169\",\"197\",\"340\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0064","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[14,0],[1,15]]、B=[[0,0],[15,0],[1,15]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"12","explanation_zh":"對應平方邊：A=[196, 226, 394]；B=[225, 226, 421]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075064,"parameters":{"A":[[0,0],[14,0],[1,15]],"B":[[0,0],[15,0],[1,15]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"196\",\"226\",\"394\"],[\"225\",\"226\",\"421\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0065","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[15,0],[1,16]]、B=[[0,0],[15,0],[1,17]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"13","explanation_zh":"對應平方邊：A=[225, 257, 452]；B=[225, 290, 485]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075065,"parameters":{"A":[[0,0],[15,0],[1,16]],"B":[[0,0],[15,0],[1,17]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"225\",\"257\",\"452\"],[\"225\",\"290\",\"485\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0066","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[16,0],[1,17]]、B=[[0,0],[16,0],[-1,17]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"23","explanation_zh":"對應平方邊：A=[256, 290, 514]；B=[256, 290, 578]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075066,"parameters":{"A":[[0,0],[16,0],[1,17]],"B":[[0,0],[16,0],[-1,17]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"256\",\"290\",\"514\"],[\"256\",\"290\",\"578\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0067","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[17,0],[1,18]]、B=[[3,5],[20,5],[4,-13]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"無","explanation_zh":"對應平方邊：A=[289, 325, 580]；B=[289, 325, 580]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075067,"parameters":{"A":[[0,0],[17,0],[1,18]],"B":[[3,5],[20,5],[4,-13]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"289\",\"325\",\"580\"],[\"289\",\"325\",\"580\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0068","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[18,0],[1,19]]、B=[[0,0],[19,0],[1,19]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"12","explanation_zh":"對應平方邊：A=[324, 362, 650]；B=[361, 362, 685]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075068,"parameters":{"A":[[0,0],[18,0],[1,19]],"B":[[0,0],[19,0],[1,19]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"324\",\"362\",\"650\"],[\"361\",\"362\",\"685\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0069","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[19,0],[1,20]]、B=[[0,0],[19,0],[1,21]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"13","explanation_zh":"對應平方邊：A=[361, 401, 724]；B=[361, 442, 765]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075069,"parameters":{"A":[[0,0],[19,0],[1,20]],"B":[[0,0],[19,0],[1,21]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"361\",\"401\",\"724\"],[\"361\",\"442\",\"765\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0070","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[20,0],[1,21]]、B=[[0,0],[20,0],[-1,21]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"23","explanation_zh":"對應平方邊：A=[400, 442, 802]；B=[400, 442, 882]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075070,"parameters":{"A":[[0,0],[20,0],[1,21]],"B":[[0,0],[20,0],[-1,21]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"400\",\"442\",\"802\"],[\"400\",\"442\",\"882\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0071","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[21,0],[1,22]]、B=[[3,5],[24,5],[4,-17]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"無","explanation_zh":"對應平方邊：A=[441, 485, 884]；B=[441, 485, 884]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075071,"parameters":{"A":[[0,0],[21,0],[1,22]],"B":[[3,5],[24,5],[4,-17]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"441\",\"485\",\"884\"],[\"441\",\"485\",\"884\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0072","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[22,0],[1,23]]、B=[[0,0],[23,0],[1,23]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"12","explanation_zh":"對應平方邊：A=[484, 530, 970]；B=[529, 530, 1013]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075072,"parameters":{"A":[[0,0],[22,0],[1,23]],"B":[[0,0],[23,0],[1,23]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"484\",\"530\",\"970\"],[\"529\",\"530\",\"1013\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0073","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[23,0],[1,24]]、B=[[0,0],[23,0],[1,25]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"13","explanation_zh":"對應平方邊：A=[529, 577, 1060]；B=[529, 626, 1109]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075073,"parameters":{"A":[[0,0],[23,0],[1,24]],"B":[[0,0],[23,0],[1,25]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"529\",\"577\",\"1060\"],[\"529\",\"626\",\"1109\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0074","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[24,0],[1,25]]、B=[[0,0],[24,0],[-1,25]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"23","explanation_zh":"對應平方邊：A=[576, 626, 1154]；B=[576, 626, 1250]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075074,"parameters":{"A":[[0,0],[24,0],[1,25]],"B":[[0,0],[24,0],[-1,25]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"576\",\"626\",\"1154\"],[\"576\",\"626\",\"1250\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0075","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"首個不符的固定標記邊","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[25,0],[1,26]]、B=[[3,5],[28,5],[4,-21]]，兩者非退化且明示對應同索引。按 12、13、23 次序求首個平方長度不相等的邊標記，全相等答「無」。","answer":{"kind":"short_text","value":"無","explanation_zh":"對應平方邊：A=[625, 677, 1252]；B=[625, 677, 1252]。「無」恰指本次三邊對應全相等；不偷偷重排頂點以消除不符。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["首個不符的固定標記邊"]},"variant":{"family_id":"qf-congruence-first-mismatch","seed":202610075075,"parameters":{"A":[[0,0],[25,0],[1,26]],"B":[[3,5],[28,5],[4,-21]],"operation":"first_mismatch","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"625\",\"677\",\"1252\"],[\"625\",\"677\",\"1252\"]],\"operation\":\"first_mismatch\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0076","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[0,0],[0,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075076,"parameters":{"A":[[0,0],[0,0],[0,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"0\",\"0\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0077","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[0,0],[1,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075077,"parameters":{"A":[[0,0],[0,0],[1,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"1\",\"1\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0078","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[1,0],[2,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075078,"parameters":{"A":[[0,0],[1,0],[2,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"1\",\"4\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0079","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[3,0],[1,4]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"是","explanation_zh":"共線判別行列式=12。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075079,"parameters":{"A":[[0,0],[3,0],[1,4]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"9\",\"17\",\"20\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0080","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[4,0],[5,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075080,"parameters":{"A":[[0,0],[4,0],[5,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"16\",\"25\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0081","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[5,0],[5,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075081,"parameters":{"A":[[0,0],[5,0],[5,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"25\",\"25\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0082","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[6,0],[1,7]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"是","explanation_zh":"共線判別行列式=42。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075082,"parameters":{"A":[[0,0],[6,0],[1,7]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"36\",\"50\",\"74\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0083","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[7,0],[8,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075083,"parameters":{"A":[[0,0],[7,0],[8,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"49\",\"64\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0084","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[8,0],[8,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075084,"parameters":{"A":[[0,0],[8,0],[8,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"64\",\"64\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0085","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[9,0],[1,10]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"是","explanation_zh":"共線判別行列式=90。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075085,"parameters":{"A":[[0,0],[9,0],[1,10]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"81\",\"101\",\"164\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0086","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[10,0],[11,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075086,"parameters":{"A":[[0,0],[10,0],[11,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"100\",\"121\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0087","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[11,0],[11,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075087,"parameters":{"A":[[0,0],[11,0],[11,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"121\",\"121\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0088","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[12,0],[1,13]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"是","explanation_zh":"共線判別行列式=156。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075088,"parameters":{"A":[[0,0],[12,0],[1,13]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"144\",\"170\",\"290\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0089","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[13,0],[14,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075089,"parameters":{"A":[[0,0],[13,0],[14,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"169\",\"196\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0090","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[14,0],[14,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075090,"parameters":{"A":[[0,0],[14,0],[14,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"196\",\"196\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0091","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[15,0],[1,16]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"是","explanation_zh":"共線判別行列式=240。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075091,"parameters":{"A":[[0,0],[15,0],[1,16]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"225\",\"257\",\"452\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0092","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[16,0],[17,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075092,"parameters":{"A":[[0,0],[16,0],[17,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"256\",\"289\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0093","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[17,0],[17,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075093,"parameters":{"A":[[0,0],[17,0],[17,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"289\",\"289\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0094","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[18,0],[1,19]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"是","explanation_zh":"共線判別行列式=342。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075094,"parameters":{"A":[[0,0],[18,0],[1,19]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"324\",\"362\",\"650\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0095","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[19,0],[20,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075095,"parameters":{"A":[[0,0],[19,0],[20,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"361\",\"400\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0096","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[20,0],[20,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075096,"parameters":{"A":[[0,0],[20,0],[20,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"400\",\"400\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0097","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[21,0],[1,22]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"是","explanation_zh":"共線判別行列式=462。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075097,"parameters":{"A":[[0,0],[21,0],[1,22]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"441\",\"485\",\"884\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0098","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[22,0],[23,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075098,"parameters":{"A":[[0,0],[22,0],[23,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"484\",\"529\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0099","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[23,0],[23,0]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"否","explanation_zh":"共線判別行列式=0。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075099,"parameters":{"A":[[0,0],[23,0],[23,0]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"529\",\"529\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r05-congruence-0100","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","language":"zh-Hant","source_mko_ids":["mko-congruence"],"title_zh":"有序三點的三角形資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。有序頂點 A=[[0,0],[24,0],[1,25]]。是否為相異不共線的非退化三角形？重複或共線資料回答否。","answer":{"kind":"short_text","value":"是","explanation_zh":"共線判別行列式=600。用有序 shoelace 的非零判別式檢查，與圖形目測分開；不把退化資料拿去做 SSS。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有序三點的三角形資格"]},"variant":{"family_id":"qf-congruence-triangle-validity","seed":202610075100,"parameters":{"A":[[0,0],[24,0],[1,25]],"operation":"triangle_validity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"576\",\"626\",\"1154\"],\"operation\":\"triangle_validity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}