{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0001","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=1°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(89, 90)","explanation_zh":"直角銳角補足=(89, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125001,"parameters":{"alpha":1,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/1"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0002","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=89°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(1, 90)","explanation_zh":"直角銳角補足=(1, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125002,"parameters":{"alpha":89,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/89"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0003","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=45°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(45, 90)","explanation_zh":"直角銳角補足=(45, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125003,"parameters":{"alpha":45,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/45"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0004","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=5°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(85, 90)","explanation_zh":"直角銳角補足=(85, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125004,"parameters":{"alpha":5,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/5"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0005","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=6°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(84, 90)","explanation_zh":"直角銳角補足=(84, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125005,"parameters":{"alpha":6,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/6"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0006","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=7°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(83, 90)","explanation_zh":"直角銳角補足=(83, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125006,"parameters":{"alpha":7,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/7"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0007","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=8°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(82, 90)","explanation_zh":"直角銳角補足=(82, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125007,"parameters":{"alpha":8,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/8"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0008","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=9°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(81, 90)","explanation_zh":"直角銳角補足=(81, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125008,"parameters":{"alpha":9,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/9"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0009","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=10°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(80, 90)","explanation_zh":"直角銳角補足=(80, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125009,"parameters":{"alpha":10,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/10"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0010","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=11°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(79, 90)","explanation_zh":"直角銳角補足=(79, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125010,"parameters":{"alpha":11,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/11"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0011","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=12°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(78, 90)","explanation_zh":"直角銳角補足=(78, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125011,"parameters":{"alpha":12,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/12"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0012","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=13°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(77, 90)","explanation_zh":"直角銳角補足=(77, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125012,"parameters":{"alpha":13,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/13"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0013","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=14°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(76, 90)","explanation_zh":"直角銳角補足=(76, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125013,"parameters":{"alpha":14,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/14"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0014","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=15°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(75, 90)","explanation_zh":"直角銳角補足=(75, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125014,"parameters":{"alpha":15,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/15"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0015","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=16°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(74, 90)","explanation_zh":"直角銳角補足=(74, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125015,"parameters":{"alpha":16,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/16"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0016","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=17°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(73, 90)","explanation_zh":"直角銳角補足=(73, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125016,"parameters":{"alpha":17,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/17"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0017","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=18°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(72, 90)","explanation_zh":"直角銳角補足=(72, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125017,"parameters":{"alpha":18,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/18"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0018","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=19°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(71, 90)","explanation_zh":"直角銳角補足=(71, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125018,"parameters":{"alpha":19,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/19"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0019","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=20°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(70, 90)","explanation_zh":"直角銳角補足=(70, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125019,"parameters":{"alpha":20,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/20"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0020","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=21°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(69, 90)","explanation_zh":"直角銳角補足=(69, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125020,"parameters":{"alpha":21,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/21"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0021","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=22°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(68, 90)","explanation_zh":"直角銳角補足=(68, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125021,"parameters":{"alpha":22,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/22"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0022","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=23°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(67, 90)","explanation_zh":"直角銳角補足=(67, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125022,"parameters":{"alpha":23,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/23"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0023","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=24°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(66, 90)","explanation_zh":"直角銳角補足=(66, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125023,"parameters":{"alpha":24,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/24"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0024","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=25°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(65, 90)","explanation_zh":"直角銳角補足=(65, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125024,"parameters":{"alpha":25,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/25"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0025","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"精確直角協議的銳角補足","stem_zh":"精確角度協議；度數，假設非退化平面三角形的γ=90°、α=26°。依序求 (β度數, α+β度數)。","answer":{"kind":"expression","value":"(64, 90)","explanation_zh":"直角銳角補足=(64, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["精確直角協議的銳角補足"]},"variant":{"family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125025,"parameters":{"alpha":26,"angle_unit":"degrees","operation":"density12_right_triangle_angle_remainder","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-angle-remainder/26"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0026","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[90, 90, 0]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(否, 否, 0)","explanation_zh":"角度條件資格與和缺陷=(否, 否, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125026,"parameters":{"angles":[90,90,0],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[0,90,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0027","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[60, 60, 60]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(是, 否, 0)","explanation_zh":"角度條件資格與和缺陷=(是, 否, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125027,"parameters":{"angles":[60,60,60],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[60,60,60]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0028","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[90, 30, 60]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(是, 是, 0)","explanation_zh":"角度條件資格與和缺陷=(是, 是, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125028,"parameters":{"angles":[90,30,60],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[30,60,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0029","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[-1, 90, 91]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(否, 否, 0)","explanation_zh":"角度條件資格與和缺陷=(否, 否, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125029,"parameters":{"angles":[-1,90,91],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[-1,90,91]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0030","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[90, 45, 46]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(否, 否, 1)","explanation_zh":"角度條件資格與和缺陷=(否, 否, 1)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125030,"parameters":{"angles":[90,45,46],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[45,46,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0031","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[0, 0, 180]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(否, 否, 0)","explanation_zh":"角度條件資格與和缺陷=(否, 否, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125031,"parameters":{"angles":[0,0,180],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[0,0,180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0032","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[90, 7, 83]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(是, 是, 0)","explanation_zh":"角度條件資格與和缺陷=(是, 是, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125032,"parameters":{"angles":[90,7,83],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[7,83,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0033","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[90, 8, 82]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(是, 是, 0)","explanation_zh":"角度條件資格與和缺陷=(是, 是, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125033,"parameters":{"angles":[90,8,82],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[8,82,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0034","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[90, 9, 81]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(是, 是, 0)","explanation_zh":"角度條件資格與和缺陷=(是, 是, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125034,"parameters":{"angles":[90,9,81],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[9,81,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0035","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[90, 10, 80]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(是, 是, 0)","explanation_zh":"角度條件資格與和缺陷=(是, 是, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125035,"parameters":{"angles":[90,10,80],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[10,80,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0036","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[90, 11, 79]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(是, 是, 0)","explanation_zh":"角度條件資格與和缺陷=(是, 是, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125036,"parameters":{"angles":[90,11,79],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[11,79,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0037","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[90, 12, 78]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(是, 是, 0)","explanation_zh":"角度條件資格與和缺陷=(是, 是, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125037,"parameters":{"angles":[90,12,78],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[12,78,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0048","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[90, 23, 67]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(是, 是, 0)","explanation_zh":"角度條件資格與和缺陷=(是, 是, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125048,"parameters":{"angles":[90,23,67],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[23,67,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0049","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[90, 24, 66]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(是, 是, 0)","explanation_zh":"角度條件資格與和缺陷=(是, 是, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125049,"parameters":{"angles":[90,24,66],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[24,66,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0050","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"候選角度資料的條件資格","stem_zh":"精確角度協議；度數，候選角度資料angles=[90, 25, 65]。依序答 (全為正且和180資格, 合資格且有90角資格, 角和−180有號缺陷)。","answer":{"kind":"expression","value":"(是, 是, 0)","explanation_zh":"角度條件資格與和缺陷=(是, 是, 0)。先核正角與精確和，再核90；不冒稱幾何構造，候選含零或負角也可待反駁，不使用容差。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選角度資料的條件資格"]},"variant":{"family_id":"qf-density12-right-triangle-validity-pair","seed":202610125050,"parameters":{"angles":[90,25,65],"angle_unit":"degrees","operation":"density12_right_triangle_validity_pair","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-validity-pair/[25,65,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0052","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[1, 90, 89]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(2, [1, 3], [1, 89])","explanation_zh":"直角索引與對邊端點=(2, [1, 3], [1, 89])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125052,"parameters":{"angles":[1,90,89],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[1,90,89]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0054","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[90, 4, 86]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(1, [2, 3], [4, 86])","explanation_zh":"直角索引與對邊端點=(1, [2, 3], [4, 86])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125054,"parameters":{"angles":[90,4,86],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[90,4,86]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0055","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[5, 90, 85]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(2, [1, 3], [5, 85])","explanation_zh":"直角索引與對邊端點=(2, [1, 3], [5, 85])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125055,"parameters":{"angles":[5,90,85],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[5,90,85]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0056","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[6, 84, 90]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(3, [1, 2], [6, 84])","explanation_zh":"直角索引與對邊端點=(3, [1, 2], [6, 84])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125056,"parameters":{"angles":[6,84,90],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[6,84,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0057","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[90, 7, 83]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(1, [2, 3], [7, 83])","explanation_zh":"直角索引與對邊端點=(1, [2, 3], [7, 83])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125057,"parameters":{"angles":[90,7,83],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[90,7,83]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0058","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[8, 90, 82]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(2, [1, 3], [8, 82])","explanation_zh":"直角索引與對邊端點=(2, [1, 3], [8, 82])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125058,"parameters":{"angles":[8,90,82],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[8,90,82]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0059","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[9, 81, 90]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(3, [1, 2], [9, 81])","explanation_zh":"直角索引與對邊端點=(3, [1, 2], [9, 81])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125059,"parameters":{"angles":[9,81,90],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[9,81,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0060","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[90, 10, 80]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(1, [2, 3], [10, 80])","explanation_zh":"直角索引與對邊端點=(1, [2, 3], [10, 80])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125060,"parameters":{"angles":[90,10,80],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[90,10,80]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0061","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[11, 90, 79]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(2, [1, 3], [11, 79])","explanation_zh":"直角索引與對邊端點=(2, [1, 3], [11, 79])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125061,"parameters":{"angles":[11,90,79],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[11,90,79]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0062","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[12, 78, 90]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(3, [1, 2], [12, 78])","explanation_zh":"直角索引與對邊端點=(3, [1, 2], [12, 78])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125062,"parameters":{"angles":[12,78,90],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[12,78,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0063","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[90, 13, 77]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(1, [2, 3], [13, 77])","explanation_zh":"直角索引與對邊端點=(1, [2, 3], [13, 77])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125063,"parameters":{"angles":[90,13,77],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[90,13,77]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0064","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[14, 90, 76]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(2, [1, 3], [14, 76])","explanation_zh":"直角索引與對邊端點=(2, [1, 3], [14, 76])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125064,"parameters":{"angles":[14,90,76],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[14,90,76]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0065","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[15, 75, 90]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(3, [1, 2], [15, 75])","explanation_zh":"直角索引與對邊端點=(3, [1, 2], [15, 75])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125065,"parameters":{"angles":[15,75,90],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[15,75,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0066","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[90, 16, 74]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(1, [2, 3], [16, 74])","explanation_zh":"直角索引與對邊端點=(1, [2, 3], [16, 74])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125066,"parameters":{"angles":[90,16,74],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[90,16,74]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0067","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[17, 90, 73]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(2, [1, 3], [17, 73])","explanation_zh":"直角索引與對邊端點=(2, [1, 3], [17, 73])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125067,"parameters":{"angles":[17,90,73],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[17,90,73]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0068","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[18, 72, 90]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(3, [1, 2], [18, 72])","explanation_zh":"直角索引與對邊端點=(3, [1, 2], [18, 72])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125068,"parameters":{"angles":[18,72,90],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[18,72,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0069","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[90, 19, 71]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(1, [2, 3], [19, 71])","explanation_zh":"直角索引與對邊端點=(1, [2, 3], [19, 71])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125069,"parameters":{"angles":[90,19,71],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[90,19,71]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0070","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[20, 90, 70]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(2, [1, 3], [20, 70])","explanation_zh":"直角索引與對邊端點=(2, [1, 3], [20, 70])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125070,"parameters":{"angles":[20,90,70],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[20,90,70]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0071","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[21, 69, 90]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(3, [1, 2], [21, 69])","explanation_zh":"直角索引與對邊端點=(3, [1, 2], [21, 69])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125071,"parameters":{"angles":[21,69,90],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[21,69,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0072","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[90, 22, 68]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(1, [2, 3], [22, 68])","explanation_zh":"直角索引與對邊端點=(1, [2, 3], [22, 68])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125072,"parameters":{"angles":[90,22,68],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[90,22,68]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0073","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[23, 90, 67]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(2, [1, 3], [23, 67])","explanation_zh":"直角索引與對邊端點=(2, [1, 3], [23, 67])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125073,"parameters":{"angles":[23,90,67],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[23,90,67]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0074","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[24, 66, 90]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(3, [1, 2], [24, 66])","explanation_zh":"直角索引與對邊端點=(3, [1, 2], [24, 66])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125074,"parameters":{"angles":[24,66,90],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[24,66,90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0075","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"標記直角索引與對邊端點","stem_zh":"精確角度協議；度數，頂點索引1、2、3依序有angles=[90, 25, 65]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。","answer":{"kind":"expression","value":"(1, [2, 3], [25, 65])","explanation_zh":"直角索引與對邊端點=(1, [2, 3], [25, 65])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["標記直角索引與對邊端點"]},"variant":{"family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125075,"parameters":{"angles":[90,25,65],"angle_unit":"degrees","operation":"density12_right_triangle_marked_vertices","domain":"exact_integer_angle_protocol","semantic_template":"qf-density12-right-triangle-marked-vertices/[90,25,65]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0076","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(1/2)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(90/1, 是)","explanation_zh":"π倍角度數與直角資格=(90/1, 是)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125076,"parameters":{"pi_n":1,"pi_d":2,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"1/2\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0077","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(5/2)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(450/1, 否)","explanation_zh":"π倍角度數與直角資格=(450/1, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125077,"parameters":{"pi_n":5,"pi_d":2,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"5/2\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0078","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(0/1)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(0/1, 否)","explanation_zh":"π倍角度數與直角資格=(0/1, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125078,"parameters":{"pi_n":0,"pi_d":1,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"0/1\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0079","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(-1/2)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(-90/1, 否)","explanation_zh":"π倍角度數與直角資格=(-90/1, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125079,"parameters":{"pi_n":-1,"pi_d":2,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"-1/2\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0080","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(1/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(180/7, 否)","explanation_zh":"π倍角度數與直角資格=(180/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125080,"parameters":{"pi_n":1,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"1/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0081","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(2/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(360/7, 否)","explanation_zh":"π倍角度數與直角資格=(360/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125081,"parameters":{"pi_n":2,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"2/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0082","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(3/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(540/7, 否)","explanation_zh":"π倍角度數與直角資格=(540/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125082,"parameters":{"pi_n":3,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"3/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0083","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(4/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(720/7, 否)","explanation_zh":"π倍角度數與直角資格=(720/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125083,"parameters":{"pi_n":4,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"4/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0084","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(5/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(900/7, 否)","explanation_zh":"π倍角度數與直角資格=(900/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125084,"parameters":{"pi_n":5,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"5/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0085","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(6/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(1080/7, 否)","explanation_zh":"π倍角度數與直角資格=(1080/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125085,"parameters":{"pi_n":6,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"6/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0086","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(7/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(180/1, 否)","explanation_zh":"π倍角度數與直角資格=(180/1, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125086,"parameters":{"pi_n":7,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"1/1\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0087","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(8/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(1440/7, 否)","explanation_zh":"π倍角度數與直角資格=(1440/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125087,"parameters":{"pi_n":8,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"8/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0088","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(9/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(1620/7, 否)","explanation_zh":"π倍角度數與直角資格=(1620/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125088,"parameters":{"pi_n":9,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"9/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0089","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(10/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(1800/7, 否)","explanation_zh":"π倍角度數與直角資格=(1800/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125089,"parameters":{"pi_n":10,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"10/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0090","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(11/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(1980/7, 否)","explanation_zh":"π倍角度數與直角資格=(1980/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125090,"parameters":{"pi_n":11,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"11/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0091","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(12/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(2160/7, 否)","explanation_zh":"π倍角度數與直角資格=(2160/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125091,"parameters":{"pi_n":12,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"12/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0092","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(13/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(2340/7, 否)","explanation_zh":"π倍角度數與直角資格=(2340/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125092,"parameters":{"pi_n":13,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"13/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0093","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(14/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(360/1, 否)","explanation_zh":"π倍角度數與直角資格=(360/1, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125093,"parameters":{"pi_n":14,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"2/1\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0094","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(15/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(2700/7, 否)","explanation_zh":"π倍角度數與直角資格=(2700/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125094,"parameters":{"pi_n":15,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"15/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0095","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(16/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(2880/7, 否)","explanation_zh":"π倍角度數與直角資格=(2880/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125095,"parameters":{"pi_n":16,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"16/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0096","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(17/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(3060/7, 否)","explanation_zh":"π倍角度數與直角資格=(3060/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125096,"parameters":{"pi_n":17,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"17/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0097","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(18/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(3240/7, 否)","explanation_zh":"π倍角度數與直角資格=(3240/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125097,"parameters":{"pi_n":18,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"18/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0098","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(19/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(3420/7, 否)","explanation_zh":"π倍角度數與直角資格=(3420/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125098,"parameters":{"pi_n":19,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"19/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0099","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(20/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(3600/7, 否)","explanation_zh":"π倍角度數與直角資格=(3600/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125099,"parameters":{"pi_n":20,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"20/7\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r05-right-triangle-0100","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","language":"zh-Hant","source_mko_ids":["mko-right-triangle"],"title_zh":"未取週期的π倍角資格","stem_zh":"精確角度協議；π倍數弧度候選θ=(21/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。","answer":{"kind":"expression","value":"(540/1, 否)","explanation_zh":"π倍角度數與直角資格=(540/1, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["未取週期的π倍角資格"]},"variant":{"family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125100,"parameters":{"pi_n":21,"pi_d":7,"angle_unit":"pi_radians","operation":"density12_right_triangle_pi_multiple","domain":"exact_pi_multiple_candidate","semantic_template":"qf-density12-right-triangle-pi-multiple/\"3/1\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}