{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r06-similarity-0001","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[6,-4],[4,-6]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=1/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=1/1；A平方邊=[9, 5, 8]；B平方邊=[9, 5, 8]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076001,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[6,-4],[4,-6]],"p":1,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"1/1\",\"1/1\",\"1/1\"],\"1/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0002","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[9,-4],[5,-8]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=3/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"否","explanation_zh":"指定倍率=3/1；A平方邊=[9, 5, 8]；B平方邊=[36, 20, 32]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076002,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[9,-4],[5,-8]],"p":3,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"4/1\",\"4/1\",\"4/1\"],\"3/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0003","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[12,-4],[6,-10]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=3/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=3/1；A平方邊=[9, 5, 8]；B平方邊=[81, 45, 72]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076003,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[12,-4],[6,-10]],"p":3,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"9/1\",\"9/1\",\"9/1\"],\"3/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0004","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[2,4]]、B=[[3,-4],[24,-4],[10,-18]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=7/2。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=7/2；A平方邊=[36, 20, 32]；B平方邊=[441, 245, 392]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076004,"parameters":{"A":[[0,0],[6,0],[2,4]],"B":[[3,-4],[24,-4],[10,-18]],"p":7,"q":2,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"49/4\",\"49/4\",\"49/4\"],\"7/2\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0005","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[18,-4],[8,-14]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=5/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=5/1；A平方邊=[9, 5, 8]；B平方邊=[225, 125, 200]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076005,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[18,-4],[8,-14]],"p":5,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"25/1\",\"25/1\",\"25/1\"],\"5/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0006","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[21,-4],[9,-16]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=7/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"否","explanation_zh":"指定倍率=7/1；A平方邊=[9, 5, 8]；B平方邊=[324, 180, 288]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076006,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[21,-4],[9,-16]],"p":7,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"36/1\",\"36/1\",\"36/1\"],\"7/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0007","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[24,-4],[11,-18]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=7/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"否","explanation_zh":"指定倍率=7/1；A平方邊=[9, 5, 8]；B平方邊=[441, 260, 365]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076007,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[24,-4],[11,-18]],"p":7,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"49/1\",\"52/1\",\"365/8\"],\"7/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0008","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[27,-4],[11,-20]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=9/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"否","explanation_zh":"指定倍率=9/1；A平方邊=[9, 5, 8]；B平方邊=[576, 320, 512]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076008,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[27,-4],[11,-20]],"p":9,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"64/1\",\"64/1\",\"64/1\"],\"9/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0009","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[2,4]]、B=[[3,-4],[54,-4],[20,-38]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=17/2。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=17/2；A平方邊=[36, 20, 32]；B平方邊=[2601, 1445, 2312]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076009,"parameters":{"A":[[0,0],[6,0],[2,4]],"B":[[3,-4],[54,-4],[20,-38]],"p":17,"q":2,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"289/4\",\"289/4\",\"289/4\"],\"17/2\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0010","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[33,-4],[13,-24]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=11/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"否","explanation_zh":"指定倍率=11/1；A平方邊=[9, 5, 8]；B平方邊=[900, 500, 800]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076010,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[33,-4],[13,-24]],"p":11,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"100/1\",\"100/1\",\"100/1\"],\"11/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0011","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[36,-4],[14,-26]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=11/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=11/1；A平方邊=[9, 5, 8]；B平方邊=[1089, 605, 968]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076011,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[36,-4],[14,-26]],"p":11,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"121/1\",\"121/1\",\"121/1\"],\"11/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0012","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[39,-4],[15,-28]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=13/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"否","explanation_zh":"指定倍率=13/1；A平方邊=[9, 5, 8]；B平方邊=[1296, 720, 1152]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076012,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[39,-4],[15,-28]],"p":13,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"144/1\",\"144/1\",\"144/1\"],\"13/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0013","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[42,-4],[16,-30]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=13/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=13/1；A平方邊=[9, 5, 8]；B平方邊=[1521, 845, 1352]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076013,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[42,-4],[16,-30]],"p":13,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"169/1\",\"169/1\",\"169/1\"],\"13/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0014","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[2,4]]、B=[[3,-4],[84,-4],[31,-58]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=27/2。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"否","explanation_zh":"指定倍率=27/2；A平方邊=[36, 20, 32]；B平方邊=[6561, 3700, 5725]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076014,"parameters":{"A":[[0,0],[6,0],[2,4]],"B":[[3,-4],[84,-4],[31,-58]],"p":27,"q":2,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"729/4\",\"185/1\",\"5725/32\"],\"27/2\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0015","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[48,-4],[18,-34]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=15/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=15/1；A平方邊=[9, 5, 8]；B平方邊=[2025, 1125, 1800]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076015,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[48,-4],[18,-34]],"p":15,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"225/1\",\"225/1\",\"225/1\"],\"15/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0016","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[51,-4],[19,-36]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=17/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"否","explanation_zh":"指定倍率=17/1；A平方邊=[9, 5, 8]；B平方邊=[2304, 1280, 2048]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076016,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[51,-4],[19,-36]],"p":17,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"256/1\",\"256/1\",\"256/1\"],\"17/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0017","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[54,-4],[20,-38]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=17/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=17/1；A平方邊=[9, 5, 8]；B平方邊=[2601, 1445, 2312]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076017,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[54,-4],[20,-38]],"p":17,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"289/1\",\"289/1\",\"289/1\"],\"17/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0018","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[57,-4],[21,-40]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=19/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"否","explanation_zh":"指定倍率=19/1；A平方邊=[9, 5, 8]；B平方邊=[2916, 1620, 2592]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076018,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[57,-4],[21,-40]],"p":19,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"324/1\",\"324/1\",\"324/1\"],\"19/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0019","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[2,4]]、B=[[3,-4],[114,-4],[40,-78]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=37/2。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=37/2；A平方邊=[36, 20, 32]；B平方邊=[12321, 6845, 10952]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076019,"parameters":{"A":[[0,0],[6,0],[2,4]],"B":[[3,-4],[114,-4],[40,-78]],"p":37,"q":2,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"1369/4\",\"1369/4\",\"1369/4\"],\"37/2\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0020","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[63,-4],[23,-44]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=21/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"否","explanation_zh":"指定倍率=21/1；A平方邊=[9, 5, 8]；B平方邊=[3600, 2000, 3200]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076020,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[63,-4],[23,-44]],"p":21,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"400/1\",\"400/1\",\"400/1\"],\"21/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0021","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[66,-4],[25,-46]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=21/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"否","explanation_zh":"指定倍率=21/1；A平方邊=[9, 5, 8]；B平方邊=[3969, 2248, 3445]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076021,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[66,-4],[25,-46]],"p":21,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"441/1\",\"2248/5\",\"3445/8\"],\"21/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0022","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[69,-4],[25,-48]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=23/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"否","explanation_zh":"指定倍率=23/1；A平方邊=[9, 5, 8]；B平方邊=[4356, 2420, 3872]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076022,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[69,-4],[25,-48]],"p":23,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"484/1\",\"484/1\",\"484/1\"],\"23/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0023","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[72,-4],[26,-50]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=23/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=23/1；A平方邊=[9, 5, 8]；B平方邊=[4761, 2645, 4232]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076023,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[72,-4],[26,-50]],"p":23,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"529/1\",\"529/1\",\"529/1\"],\"23/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0024","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[2,4]]、B=[[3,-4],[144,-4],[50,-98]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=47/2。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=47/2；A平方邊=[36, 20, 32]；B平方邊=[19881, 11045, 17672]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076024,"parameters":{"A":[[0,0],[6,0],[2,4]],"B":[[3,-4],[144,-4],[50,-98]],"p":47,"q":2,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"2209/4\",\"2209/4\",\"2209/4\"],\"47/2\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0025","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"指定正倍率的標記相似見證","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],[1,2]]、B=[[3,-4],[78,-4],[28,-54]]，兩者非退化且明示對應同索引；指定正長度倍率 k=B/A=25/1。這個倍率是否符合全部三條對應邊？","answer":{"kind":"short_text","value":"是","explanation_zh":"指定倍率=25/1；A平方邊=[9, 5, 8]；B平方邊=[5625, 3125, 5000]。以平方邊長比較 B²q²=A²p²；本次見證的否定不是其他倍率的否定，也不變更標記對應。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["指定正倍率的標記相似見證"]},"variant":{"family_id":"qf-similarity-specified-scale","seed":202610076025,"parameters":{"A":[[0,0],[3,0],[1,2]],"B":[[3,-4],[78,-4],[28,-54]],"p":25,"q":1,"operation":"specified_similarity","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-specified-scale/{\"inputs\":[[\"625/1\",\"625/1\",\"625/1\"],\"25/1\"],\"operation\":\"specified_similarity\"}"}},"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-r06-similarity-0026","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=-12/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=-12/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076026,"parameters":{"p":-12,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"-12/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0027","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=-11/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=-11/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076027,"parameters":{"p":-11,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"-11/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0028","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=-10/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=-10/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076028,"parameters":{"p":-10,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"-10/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0029","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=-9/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=-9/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076029,"parameters":{"p":-9,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"-9/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0030","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=-8/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=-8/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076030,"parameters":{"p":-8,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"-8/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0031","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=-7/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=-7/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076031,"parameters":{"p":-7,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"-7/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0032","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=-6/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=-6/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076032,"parameters":{"p":-6,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"-6/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0033","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=-5/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=-5/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076033,"parameters":{"p":-5,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"-5/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0034","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=-4/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=-4/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076034,"parameters":{"p":-4,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"-4/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0035","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=-3/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=-3/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076035,"parameters":{"p":-3,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"-3/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0036","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=-2/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=-2/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076036,"parameters":{"p":-2,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"-2/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0037","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=-1/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=-1/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076037,"parameters":{"p":-1,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"-1/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0038","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=0/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選倍率=0/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076038,"parameters":{"p":0,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"0/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0039","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=1/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選倍率=1/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076039,"parameters":{"p":1,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"1/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0040","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=2/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選倍率=2/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076040,"parameters":{"p":2,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"2/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0041","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=3/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選倍率=3/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076041,"parameters":{"p":3,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"3/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0042","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=4/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選倍率=4/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076042,"parameters":{"p":4,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"4/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0043","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=5/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選倍率=5/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076043,"parameters":{"p":5,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"5/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0044","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=6/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選倍率=6/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076044,"parameters":{"p":6,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"6/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0045","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=7/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選倍率=7/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076045,"parameters":{"p":7,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"7/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0046","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=8/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選倍率=8/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076046,"parameters":{"p":8,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"8/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0047","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=9/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選倍率=9/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076047,"parameters":{"p":9,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"9/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0048","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=10/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選倍率=10/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076048,"parameters":{"p":10,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"10/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0049","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=11/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選倍率=11/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076049,"parameters":{"p":11,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"11/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0050","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"候選長度倍率的正性資格","stem_zh":"等單位正交座標系，兩軸採同一長度單位。明示正分母 q=1，候選 k=12/1 是否具非退化相似所需的正長度倍率資格？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選倍率=12/1。分母先合法，分子須正；零或負候選沒有此正倍率資格，不改成有向縮放係數。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選長度倍率的正性資格"]},"variant":{"family_id":"qf-similarity-positive-ratio","seed":202610076050,"parameters":{"p":12,"q":1,"operation":"positive_scale_ratio","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-positive-ratio/{\"inputs\":[\"12/1\"],\"operation\":\"positive_scale_ratio\"}"}},"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-r06-similarity-0051","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=2>0，對應長度倍率 k=1/1>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"2/1","explanation_zh":"縮放平方邊長=2/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076051,"parameters":{"side_squared":2,"p":1,"q":1,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"2\",\"1/1\"],\"operation\":\"scaled_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-r06-similarity-0052","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=5>0，對應長度倍率 k=2/2>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"5/1","explanation_zh":"縮放平方邊長=5/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076052,"parameters":{"side_squared":5,"p":2,"q":2,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"5\",\"1/1\"],\"operation\":\"scaled_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-r06-similarity-0053","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=10>0，對應長度倍率 k=3/3>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"10/1","explanation_zh":"縮放平方邊長=10/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076053,"parameters":{"side_squared":10,"p":3,"q":3,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"10\",\"1/1\"],\"operation\":\"scaled_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-r06-similarity-0054","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=17>0，對應長度倍率 k=4/1>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"272/1","explanation_zh":"縮放平方邊長=272/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076054,"parameters":{"side_squared":17,"p":4,"q":1,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"17\",\"4/1\"],\"operation\":\"scaled_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-r06-similarity-0055","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=26>0，對應長度倍率 k=5/2>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"325/2","explanation_zh":"縮放平方邊長=325/2。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076055,"parameters":{"side_squared":26,"p":5,"q":2,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"26\",\"5/2\"],\"operation\":\"scaled_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-r06-similarity-0056","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=37>0，對應長度倍率 k=1/3>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"37/9","explanation_zh":"縮放平方邊長=37/9。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076056,"parameters":{"side_squared":37,"p":1,"q":3,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"37\",\"1/3\"],\"operation\":\"scaled_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-r06-similarity-0057","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=50>0，對應長度倍率 k=2/1>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"200/1","explanation_zh":"縮放平方邊長=200/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076057,"parameters":{"side_squared":50,"p":2,"q":1,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"50\",\"2/1\"],\"operation\":\"scaled_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-r06-similarity-0058","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=65>0，對應長度倍率 k=3/2>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"585/4","explanation_zh":"縮放平方邊長=585/4。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076058,"parameters":{"side_squared":65,"p":3,"q":2,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"65\",\"3/2\"],\"operation\":\"scaled_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-r06-similarity-0059","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=82>0，對應長度倍率 k=4/3>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"1312/9","explanation_zh":"縮放平方邊長=1312/9。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076059,"parameters":{"side_squared":82,"p":4,"q":3,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"82\",\"4/3\"],\"operation\":\"scaled_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-r06-similarity-0060","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=101>0，對應長度倍率 k=5/1>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"2525/1","explanation_zh":"縮放平方邊長=2525/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076060,"parameters":{"side_squared":101,"p":5,"q":1,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"101\",\"5/1\"],\"operation\":\"scaled_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-r06-similarity-0061","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=122>0，對應長度倍率 k=1/2>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"61/2","explanation_zh":"縮放平方邊長=61/2。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076061,"parameters":{"side_squared":122,"p":1,"q":2,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"122\",\"1/2\"],\"operation\":\"scaled_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-r06-similarity-0062","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=145>0，對應長度倍率 k=2/3>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"580/9","explanation_zh":"縮放平方邊長=580/9。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076062,"parameters":{"side_squared":145,"p":2,"q":3,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"145\",\"2/3\"],\"operation\":\"scaled_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-r06-similarity-0063","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=170>0，對應長度倍率 k=3/1>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"1530/1","explanation_zh":"縮放平方邊長=1530/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076063,"parameters":{"side_squared":170,"p":3,"q":1,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"170\",\"3/1\"],\"operation\":\"scaled_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-r06-similarity-0064","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=197>0，對應長度倍率 k=4/2>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"788/1","explanation_zh":"縮放平方邊長=788/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076064,"parameters":{"side_squared":197,"p":4,"q":2,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"197\",\"2/1\"],\"operation\":\"scaled_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-r06-similarity-0065","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=226>0，對應長度倍率 k=5/3>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"5650/9","explanation_zh":"縮放平方邊長=5650/9。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076065,"parameters":{"side_squared":226,"p":5,"q":3,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"226\",\"5/3\"],\"operation\":\"scaled_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-r06-similarity-0066","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=257>0，對應長度倍率 k=1/1>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"257/1","explanation_zh":"縮放平方邊長=257/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076066,"parameters":{"side_squared":257,"p":1,"q":1,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"257\",\"1/1\"],\"operation\":\"scaled_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-r06-similarity-0067","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=290>0，對應長度倍率 k=2/2>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"290/1","explanation_zh":"縮放平方邊長=290/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076067,"parameters":{"side_squared":290,"p":2,"q":2,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"290\",\"1/1\"],\"operation\":\"scaled_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-r06-similarity-0068","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=325>0，對應長度倍率 k=3/3>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"325/1","explanation_zh":"縮放平方邊長=325/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076068,"parameters":{"side_squared":325,"p":3,"q":3,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"325\",\"1/1\"],\"operation\":\"scaled_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-r06-similarity-0069","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=362>0，對應長度倍率 k=4/1>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"5792/1","explanation_zh":"縮放平方邊長=5792/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076069,"parameters":{"side_squared":362,"p":4,"q":1,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"362\",\"4/1\"],\"operation\":\"scaled_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-r06-similarity-0070","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=401>0，對應長度倍率 k=5/2>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"10025/4","explanation_zh":"縮放平方邊長=10025/4。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076070,"parameters":{"side_squared":401,"p":5,"q":2,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"401\",\"5/2\"],\"operation\":\"scaled_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-r06-similarity-0071","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=442>0，對應長度倍率 k=1/3>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"442/9","explanation_zh":"縮放平方邊長=442/9。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076071,"parameters":{"side_squared":442,"p":1,"q":3,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"442\",\"1/3\"],\"operation\":\"scaled_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-r06-similarity-0072","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=485>0，對應長度倍率 k=2/1>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"1940/1","explanation_zh":"縮放平方邊長=1940/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076072,"parameters":{"side_squared":485,"p":2,"q":1,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"485\",\"2/1\"],\"operation\":\"scaled_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-r06-similarity-0073","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=530>0，對應長度倍率 k=3/2>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"2385/2","explanation_zh":"縮放平方邊長=2385/2。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076073,"parameters":{"side_squared":530,"p":3,"q":2,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"530\",\"3/2\"],\"operation\":\"scaled_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-r06-similarity-0074","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=577>0，對應長度倍率 k=4/3>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"9232/9","explanation_zh":"縮放平方邊長=9232/9。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076074,"parameters":{"side_squared":577,"p":4,"q":3,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"577\",\"4/3\"],\"operation\":\"scaled_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-r06-similarity-0075","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"正倍率下的平方邊長","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已知非退化三角形某邊平方長度 s=626>0，對應長度倍率 k=5/1>0。求縮放後平方邊長，採最簡正分母 p/q。","answer":{"kind":"expression","value":"15650/1","explanation_zh":"縮放平方邊長=15650/1。平方長度乘 k²，不是乘 k；只對已知正數量精確換算。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正倍率下的平方邊長"]},"variant":{"family_id":"qf-similarity-scaled-squared-side","seed":202610076075,"parameters":{"side_squared":626,"p":5,"q":1,"operation":"scaled_squared_side","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-squared-side/{\"inputs\":[\"626\",\"5/1\"],\"operation\":\"scaled_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-r06-similarity-0076","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 1/2>0 平方單位，對應長度倍率 k=1/1>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"1/2","explanation_zh":"條件面積=1/2。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076076,"parameters":{"area_n":1,"area_d":2,"p":1,"q":1,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"1/2\",\"1/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0077","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 3/2>0 平方單位，對應長度倍率 k=2/2>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"3/2","explanation_zh":"條件面積=3/2。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076077,"parameters":{"area_n":3,"area_d":2,"p":2,"q":2,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"3/2\",\"1/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0078","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 5/2>0 平方單位，對應長度倍率 k=3/3>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"5/2","explanation_zh":"條件面積=5/2。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076078,"parameters":{"area_n":5,"area_d":2,"p":3,"q":3,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"5/2\",\"1/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0079","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 7/2>0 平方單位，對應長度倍率 k=4/1>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"56/1","explanation_zh":"條件面積=56/1。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076079,"parameters":{"area_n":7,"area_d":2,"p":4,"q":1,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"7/2\",\"4/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0080","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 9/2>0 平方單位，對應長度倍率 k=1/2>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"9/8","explanation_zh":"條件面積=9/8。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076080,"parameters":{"area_n":9,"area_d":2,"p":1,"q":2,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"9/2\",\"1/2\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0081","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 11/2>0 平方單位，對應長度倍率 k=2/3>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"22/9","explanation_zh":"條件面積=22/9。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076081,"parameters":{"area_n":11,"area_d":2,"p":2,"q":3,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"11/2\",\"2/3\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0082","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 13/2>0 平方單位，對應長度倍率 k=3/1>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"117/2","explanation_zh":"條件面積=117/2。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076082,"parameters":{"area_n":13,"area_d":2,"p":3,"q":1,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"13/2\",\"3/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0083","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 15/2>0 平方單位，對應長度倍率 k=4/2>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"30/1","explanation_zh":"條件面積=30/1。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076083,"parameters":{"area_n":15,"area_d":2,"p":4,"q":2,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"15/2\",\"2/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0084","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 17/2>0 平方單位，對應長度倍率 k=1/3>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"17/18","explanation_zh":"條件面積=17/18。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076084,"parameters":{"area_n":17,"area_d":2,"p":1,"q":3,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"17/2\",\"1/3\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0085","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 19/2>0 平方單位，對應長度倍率 k=2/1>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"38/1","explanation_zh":"條件面積=38/1。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076085,"parameters":{"area_n":19,"area_d":2,"p":2,"q":1,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"19/2\",\"2/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0086","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 21/2>0 平方單位，對應長度倍率 k=3/2>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"189/8","explanation_zh":"條件面積=189/8。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076086,"parameters":{"area_n":21,"area_d":2,"p":3,"q":2,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"21/2\",\"3/2\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0087","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 23/2>0 平方單位，對應長度倍率 k=4/3>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"184/9","explanation_zh":"條件面積=184/9。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076087,"parameters":{"area_n":23,"area_d":2,"p":4,"q":3,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"23/2\",\"4/3\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0088","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 25/2>0 平方單位，對應長度倍率 k=1/1>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"25/2","explanation_zh":"條件面積=25/2。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076088,"parameters":{"area_n":25,"area_d":2,"p":1,"q":1,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"25/2\",\"1/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0089","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 27/2>0 平方單位，對應長度倍率 k=2/2>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"27/2","explanation_zh":"條件面積=27/2。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076089,"parameters":{"area_n":27,"area_d":2,"p":2,"q":2,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"27/2\",\"1/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0090","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 29/2>0 平方單位，對應長度倍率 k=3/3>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"29/2","explanation_zh":"條件面積=29/2。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076090,"parameters":{"area_n":29,"area_d":2,"p":3,"q":3,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"29/2\",\"1/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0091","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 31/2>0 平方單位，對應長度倍率 k=4/1>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"248/1","explanation_zh":"條件面積=248/1。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076091,"parameters":{"area_n":31,"area_d":2,"p":4,"q":1,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"31/2\",\"4/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0092","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 33/2>0 平方單位，對應長度倍率 k=1/2>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"33/8","explanation_zh":"條件面積=33/8。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076092,"parameters":{"area_n":33,"area_d":2,"p":1,"q":2,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"33/2\",\"1/2\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0093","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 35/2>0 平方單位，對應長度倍率 k=2/3>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"70/9","explanation_zh":"條件面積=70/9。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076093,"parameters":{"area_n":35,"area_d":2,"p":2,"q":3,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"35/2\",\"2/3\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0094","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 37/2>0 平方單位，對應長度倍率 k=3/1>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"333/2","explanation_zh":"條件面積=333/2。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076094,"parameters":{"area_n":37,"area_d":2,"p":3,"q":1,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"37/2\",\"3/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0095","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 39/2>0 平方單位，對應長度倍率 k=4/2>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"78/1","explanation_zh":"條件面積=78/1。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076095,"parameters":{"area_n":39,"area_d":2,"p":4,"q":2,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"39/2\",\"2/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0096","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 41/2>0 平方單位，對應長度倍率 k=1/3>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"41/18","explanation_zh":"條件面積=41/18。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076096,"parameters":{"area_n":41,"area_d":2,"p":1,"q":3,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"41/2\",\"1/3\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0097","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 43/2>0 平方單位，對應長度倍率 k=2/1>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"86/1","explanation_zh":"條件面積=86/1。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076097,"parameters":{"area_n":43,"area_d":2,"p":2,"q":1,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"43/2\",\"2/1\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0098","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 45/2>0 平方單位，對應長度倍率 k=3/2>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"405/8","explanation_zh":"條件面積=405/8。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076098,"parameters":{"area_n":45,"area_d":2,"p":3,"q":2,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"45/2\",\"3/2\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0099","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 47/2>0 平方單位，對應長度倍率 k=4/3>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"376/9","explanation_zh":"條件面積=376/9。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076099,"parameters":{"area_n":47,"area_d":2,"p":4,"q":3,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"47/2\",\"4/3\"],\"operation\":\"scaled_area\"}"}},"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-r06-similarity-0100","batch_id":"batch-20261006-advance-20261007-r06-similarity-foundations","language":"zh-Hant","source_mko_ids":["mko-similarity"],"title_zh":"已給正面積的條件縮放","stem_zh":"等單位正交座標系，兩軸採同一長度單位。已給某非退化三角形面積 49/2>0 平方單位，對應長度倍率 k=1/1>0。求縮放後條件面積，採最簡正分母分數。","answer":{"kind":"expression","value":"49/2","explanation_zh":"條件面積=49/2。給定面積乘 k²；不從座標另計三角形面積，不繼承矩形面積 Evidence，也不宣稱一般測度理論。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["已給正面積的條件縮放"]},"variant":{"family_id":"qf-similarity-scaled-area","seed":202610076100,"parameters":{"area_n":49,"area_d":2,"p":1,"q":1,"operation":"scaled_area","frame":"euclidean_orthonormal_equal_units","semantic_template":"qf-similarity-scaled-area/{\"inputs\":[\"49/2\",\"1/1\"],\"operation\":\"scaled_area\"}"}},"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"}}