{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0001","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=0、b=-5且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(0/1, 否, 未定義, 未定義)","explanation_zh":"正向比與反向比資格=(0/1, 否, 未定義, 未定義)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152001,"parameters":{"a":0,"b":-5,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"0/1\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0002","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=1、b=-2且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(-1/2, 是, -2/1, 1/1)","explanation_zh":"正向比與反向比資格=(-1/2, 是, -2/1, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152002,"parameters":{"a":1,"b":-2,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"-1/2\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0003","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=1、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(1/3, 是, 3/1, 1/1)","explanation_zh":"正向比與反向比資格=(1/3, 是, 3/1, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152003,"parameters":{"a":1,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"1/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0004","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=2、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(2/3, 是, 3/2, 1/1)","explanation_zh":"正向比與反向比資格=(2/3, 是, 3/2, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152004,"parameters":{"a":2,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"2/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0005","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=3、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(1/1, 是, 1/1, 1/1)","explanation_zh":"正向比與反向比資格=(1/1, 是, 1/1, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152005,"parameters":{"a":3,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"1/1\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0006","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=4、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(4/3, 是, 3/4, 1/1)","explanation_zh":"正向比與反向比資格=(4/3, 是, 3/4, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152006,"parameters":{"a":4,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"4/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0007","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=5、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(5/3, 是, 3/5, 1/1)","explanation_zh":"正向比與反向比資格=(5/3, 是, 3/5, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152007,"parameters":{"a":5,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"5/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0008","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=6、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(2/1, 是, 1/2, 1/1)","explanation_zh":"正向比與反向比資格=(2/1, 是, 1/2, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152008,"parameters":{"a":6,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0009","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=7、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(7/3, 是, 3/7, 1/1)","explanation_zh":"正向比與反向比資格=(7/3, 是, 3/7, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152009,"parameters":{"a":7,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"7/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0010","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=8、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(8/3, 是, 3/8, 1/1)","explanation_zh":"正向比與反向比資格=(8/3, 是, 3/8, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152010,"parameters":{"a":8,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"8/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0011","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=9、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(3/1, 是, 1/3, 1/1)","explanation_zh":"正向比與反向比資格=(3/1, 是, 1/3, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152011,"parameters":{"a":9,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0012","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=10、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(10/3, 是, 3/10, 1/1)","explanation_zh":"正向比與反向比資格=(10/3, 是, 3/10, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152012,"parameters":{"a":10,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"10/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0013","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=11、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(11/3, 是, 3/11, 1/1)","explanation_zh":"正向比與反向比資格=(11/3, 是, 3/11, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152013,"parameters":{"a":11,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"11/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0014","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=12、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(4/1, 是, 1/4, 1/1)","explanation_zh":"正向比與反向比資格=(4/1, 是, 1/4, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152014,"parameters":{"a":12,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"4/1\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0015","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=13、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(13/3, 是, 3/13, 1/1)","explanation_zh":"正向比與反向比資格=(13/3, 是, 3/13, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152015,"parameters":{"a":13,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"13/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0016","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=14、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(14/3, 是, 3/14, 1/1)","explanation_zh":"正向比與反向比資格=(14/3, 是, 3/14, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152016,"parameters":{"a":14,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"14/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0017","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=15、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(5/1, 是, 1/5, 1/1)","explanation_zh":"正向比與反向比資格=(5/1, 是, 1/5, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152017,"parameters":{"a":15,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"5/1\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0018","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=16、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(16/3, 是, 3/16, 1/1)","explanation_zh":"正向比與反向比資格=(16/3, 是, 3/16, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152018,"parameters":{"a":16,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"16/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0019","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=17、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(17/3, 是, 3/17, 1/1)","explanation_zh":"正向比與反向比資格=(17/3, 是, 3/17, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152019,"parameters":{"a":17,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"17/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0020","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=18、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(6/1, 是, 1/6, 1/1)","explanation_zh":"正向比與反向比資格=(6/1, 是, 1/6, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152020,"parameters":{"a":18,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"6/1\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0021","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=19、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(19/3, 是, 3/19, 1/1)","explanation_zh":"正向比與反向比資格=(19/3, 是, 3/19, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152021,"parameters":{"a":19,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"19/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0022","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=20、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(20/3, 是, 3/20, 1/1)","explanation_zh":"正向比與反向比資格=(20/3, 是, 3/20, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152022,"parameters":{"a":20,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"20/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0023","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=21、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(7/1, 是, 1/7, 1/1)","explanation_zh":"正向比與反向比資格=(7/1, 是, 1/7, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152023,"parameters":{"a":21,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"7/1\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0024","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=22、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(22/3, 是, 3/22, 1/1)","explanation_zh":"正向比與反向比資格=(22/3, 是, 3/22, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152024,"parameters":{"a":22,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"22/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0025","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比與反向資格","stem_zh":"Q數值比協議。a=23、b=3且b≠0。求 (a/b, 反向資格, b/a或未定義, 前後乘積或未定義)。","answer":{"kind":"expression","value":"(23/3, 是, 3/23, 1/1)","explanation_zh":"正向比與反向比資格=(23/3, 是, 3/23, 1/1)。反向比另核a非零，不由合法正向比略過反向後項。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數值比與反向資格"]},"variant":{"family_id":"qf-density15-ratio-forward-reverse","seed":202610152025,"parameters":{"a":23,"b":3,"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_forward_reverse","semantic_template":"qf-density15-ratio-forward-reverse/\"23/3\""}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0026","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(1)/(1)、完整三點(x,y)=[[0, 0], [1, 1], [2, 2]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 0/1, 0/1], [是, 是, 是], [未定義, 1/1, 1/1])","explanation_zh":"完整三點比例律與殘差=([0/1, 0/1, 0/1], [是, 是, 是], [未定義, 1/1, 1/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152026,"parameters":{"k":[1,1],"pairs":[[0,0],[1,1],[2,2]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"0/1\",\"1/1\"],[\"0/1\",\"1/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0027","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(1)/(1)、完整三點(x,y)=[[0, 1], [1, 1], [2, 2]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([1/1, 0/1, 0/1], [否, 是, 是], [未定義, 1/1, 1/1])","explanation_zh":"完整三點比例律與殘差=([1/1, 0/1, 0/1], [否, 是, 是], [未定義, 1/1, 1/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152027,"parameters":{"k":[1,1],"pairs":[[0,1],[1,1],[2,2]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"1/1\",\"undefined\"],[\"0/1\",\"1/1\"],[\"0/1\",\"1/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0028","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(-10)/(2)、完整三點(x,y)=[[0, 0], [1, 2], [2, -1]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 7/1, 9/1], [是, 否, 否], [未定義, 2/1, -1/2])","explanation_zh":"完整三點比例律與殘差=([0/1, 7/1, 9/1], [是, 否, 否], [未定義, 2/1, -1/2])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152028,"parameters":{"k":[-10,2],"pairs":[[0,0],[1,2],[2,-1]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"7/1\",\"2/1\"],[\"9/1\",\"-1/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0029","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(-9)/(2)、完整三點(x,y)=[[0, 0], [1, 3], [2, -2]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 15/2, 7/1], [是, 否, 否], [未定義, 3/1, -1/1])","explanation_zh":"完整三點比例律與殘差=([0/1, 15/2, 7/1], [是, 否, 否], [未定義, 3/1, -1/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152029,"parameters":{"k":[-9,2],"pairs":[[0,0],[1,3],[2,-2]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"15/2\",\"3/1\"],[\"7/1\",\"-1/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0030","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(-8)/(2)、完整三點(x,y)=[[0, 0], [1, 4], [2, -3]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 8/1, 5/1], [是, 否, 否], [未定義, 4/1, -3/2])","explanation_zh":"完整三點比例律與殘差=([0/1, 8/1, 5/1], [是, 否, 否], [未定義, 4/1, -3/2])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152030,"parameters":{"k":[-8,2],"pairs":[[0,0],[1,4],[2,-3]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"8/1\",\"4/1\"],[\"5/1\",\"-3/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0031","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(-7)/(2)、完整三點(x,y)=[[0, 0], [1, 5], [2, -4]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 17/2, 3/1], [是, 否, 否], [未定義, 5/1, -2/1])","explanation_zh":"完整三點比例律與殘差=([0/1, 17/2, 3/1], [是, 否, 否], [未定義, 5/1, -2/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152031,"parameters":{"k":[-7,2],"pairs":[[0,0],[1,5],[2,-4]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"17/2\",\"5/1\"],[\"3/1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0032","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(-6)/(2)、完整三點(x,y)=[[0, 0], [1, 6], [2, -5]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 9/1, 1/1], [是, 否, 否], [未定義, 6/1, -5/2])","explanation_zh":"完整三點比例律與殘差=([0/1, 9/1, 1/1], [是, 否, 否], [未定義, 6/1, -5/2])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152032,"parameters":{"k":[-6,2],"pairs":[[0,0],[1,6],[2,-5]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"9/1\",\"6/1\"],[\"1/1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0033","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(-5)/(2)、完整三點(x,y)=[[0, 0], [1, 7], [2, -6]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 19/2, -1/1], [是, 否, 否], [未定義, 7/1, -3/1])","explanation_zh":"完整三點比例律與殘差=([0/1, 19/2, -1/1], [是, 否, 否], [未定義, 7/1, -3/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152033,"parameters":{"k":[-5,2],"pairs":[[0,0],[1,7],[2,-6]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"19/2\",\"7/1\"],[\"-1/1\",\"-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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0034","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(-4)/(2)、完整三點(x,y)=[[0, 0], [1, 8], [2, -7]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 10/1, -3/1], [是, 否, 否], [未定義, 8/1, -7/2])","explanation_zh":"完整三點比例律與殘差=([0/1, 10/1, -3/1], [是, 否, 否], [未定義, 8/1, -7/2])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152034,"parameters":{"k":[-4,2],"pairs":[[0,0],[1,8],[2,-7]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"10/1\",\"8/1\"],[\"-3/1\",\"-7/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0035","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(-3)/(2)、完整三點(x,y)=[[0, 0], [1, 9], [2, -8]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 21/2, -5/1], [是, 否, 否], [未定義, 9/1, -4/1])","explanation_zh":"完整三點比例律與殘差=([0/1, 21/2, -5/1], [是, 否, 否], [未定義, 9/1, -4/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152035,"parameters":{"k":[-3,2],"pairs":[[0,0],[1,9],[2,-8]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"21/2\",\"9/1\"],[\"-5/1\",\"-4/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0036","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(-2)/(2)、完整三點(x,y)=[[0, 0], [1, 10], [2, -9]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 11/1, -7/1], [是, 否, 否], [未定義, 10/1, -9/2])","explanation_zh":"完整三點比例律與殘差=([0/1, 11/1, -7/1], [是, 否, 否], [未定義, 10/1, -9/2])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152036,"parameters":{"k":[-2,2],"pairs":[[0,0],[1,10],[2,-9]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"11/1\",\"10/1\"],[\"-7/1\",\"-9/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0037","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(-1)/(2)、完整三點(x,y)=[[0, 0], [1, 11], [2, -10]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 23/2, -9/1], [是, 否, 否], [未定義, 11/1, -5/1])","explanation_zh":"完整三點比例律與殘差=([0/1, 23/2, -9/1], [是, 否, 否], [未定義, 11/1, -5/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152037,"parameters":{"k":[-1,2],"pairs":[[0,0],[1,11],[2,-10]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"23/2\",\"11/1\"],[\"-9/1\",\"-5/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0038","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(0)/(2)、完整三點(x,y)=[[0, 0], [1, 12], [2, -11]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 12/1, -11/1], [是, 否, 否], [未定義, 12/1, -11/2])","explanation_zh":"完整三點比例律與殘差=([0/1, 12/1, -11/1], [是, 否, 否], [未定義, 12/1, -11/2])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152038,"parameters":{"k":[0,2],"pairs":[[0,0],[1,12],[2,-11]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"12/1\",\"12/1\"],[\"-11/1\",\"-11/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0039","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(1)/(2)、完整三點(x,y)=[[0, 0], [1, 13], [2, -12]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 25/2, -13/1], [是, 否, 否], [未定義, 13/1, -6/1])","explanation_zh":"完整三點比例律與殘差=([0/1, 25/2, -13/1], [是, 否, 否], [未定義, 13/1, -6/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152039,"parameters":{"k":[1,2],"pairs":[[0,0],[1,13],[2,-12]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"25/2\",\"13/1\"],[\"-13/1\",\"-6/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0040","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(2)/(2)、完整三點(x,y)=[[0, 0], [1, 14], [2, -13]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 13/1, -15/1], [是, 否, 否], [未定義, 14/1, -13/2])","explanation_zh":"完整三點比例律與殘差=([0/1, 13/1, -15/1], [是, 否, 否], [未定義, 14/1, -13/2])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152040,"parameters":{"k":[2,2],"pairs":[[0,0],[1,14],[2,-13]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"13/1\",\"14/1\"],[\"-15/1\",\"-13/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0041","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(3)/(2)、完整三點(x,y)=[[0, 0], [1, 15], [2, -14]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 27/2, -17/1], [是, 否, 否], [未定義, 15/1, -7/1])","explanation_zh":"完整三點比例律與殘差=([0/1, 27/2, -17/1], [是, 否, 否], [未定義, 15/1, -7/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152041,"parameters":{"k":[3,2],"pairs":[[0,0],[1,15],[2,-14]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"27/2\",\"15/1\"],[\"-17/1\",\"-7/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0042","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(4)/(2)、完整三點(x,y)=[[0, 0], [1, 16], [2, -15]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 14/1, -19/1], [是, 否, 否], [未定義, 16/1, -15/2])","explanation_zh":"完整三點比例律與殘差=([0/1, 14/1, -19/1], [是, 否, 否], [未定義, 16/1, -15/2])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152042,"parameters":{"k":[4,2],"pairs":[[0,0],[1,16],[2,-15]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"14/1\",\"16/1\"],[\"-19/1\",\"-15/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0043","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(5)/(2)、完整三點(x,y)=[[0, 0], [1, 17], [2, -16]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 29/2, -21/1], [是, 否, 否], [未定義, 17/1, -8/1])","explanation_zh":"完整三點比例律與殘差=([0/1, 29/2, -21/1], [是, 否, 否], [未定義, 17/1, -8/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152043,"parameters":{"k":[5,2],"pairs":[[0,0],[1,17],[2,-16]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"29/2\",\"17/1\"],[\"-21/1\",\"-8/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0044","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(6)/(2)、完整三點(x,y)=[[0, 0], [1, 18], [2, -17]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 15/1, -23/1], [是, 否, 否], [未定義, 18/1, -17/2])","explanation_zh":"完整三點比例律與殘差=([0/1, 15/1, -23/1], [是, 否, 否], [未定義, 18/1, -17/2])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152044,"parameters":{"k":[6,2],"pairs":[[0,0],[1,18],[2,-17]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"15/1\",\"18/1\"],[\"-23/1\",\"-17/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0045","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(7)/(2)、完整三點(x,y)=[[0, 0], [1, 19], [2, -18]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 31/2, -25/1], [是, 否, 否], [未定義, 19/1, -9/1])","explanation_zh":"完整三點比例律與殘差=([0/1, 31/2, -25/1], [是, 否, 否], [未定義, 19/1, -9/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152045,"parameters":{"k":[7,2],"pairs":[[0,0],[1,19],[2,-18]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"31/2\",\"19/1\"],[\"-25/1\",\"-9/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0046","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(8)/(2)、完整三點(x,y)=[[0, 0], [1, 20], [2, -19]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 16/1, -27/1], [是, 否, 否], [未定義, 20/1, -19/2])","explanation_zh":"完整三點比例律與殘差=([0/1, 16/1, -27/1], [是, 否, 否], [未定義, 20/1, -19/2])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152046,"parameters":{"k":[8,2],"pairs":[[0,0],[1,20],[2,-19]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"16/1\",\"20/1\"],[\"-27/1\",\"-19/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0047","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(9)/(2)、完整三點(x,y)=[[0, 0], [1, 21], [2, -20]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 33/2, -29/1], [是, 否, 否], [未定義, 21/1, -10/1])","explanation_zh":"完整三點比例律與殘差=([0/1, 33/2, -29/1], [是, 否, 否], [未定義, 21/1, -10/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152047,"parameters":{"k":[9,2],"pairs":[[0,0],[1,21],[2,-20]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"33/2\",\"21/1\"],[\"-29/1\",\"-10/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0048","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(10)/(2)、完整三點(x,y)=[[0, 0], [1, 22], [2, -21]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 17/1, -31/1], [是, 否, 否], [未定義, 22/1, -21/2])","explanation_zh":"完整三點比例律與殘差=([0/1, 17/1, -31/1], [是, 否, 否], [未定義, 22/1, -21/2])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152048,"parameters":{"k":[10,2],"pairs":[[0,0],[1,22],[2,-21]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"17/1\",\"22/1\"],[\"-31/1\",\"-21/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0049","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(11)/(2)、完整三點(x,y)=[[0, 0], [1, 23], [2, -22]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 35/2, -33/1], [是, 否, 否], [未定義, 23/1, -11/1])","explanation_zh":"完整三點比例律與殘差=([0/1, 35/2, -33/1], [是, 否, 否], [未定義, 23/1, -11/1])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152049,"parameters":{"k":[11,2],"pairs":[[0,0],[1,23],[2,-22]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"35/2\",\"23/1\"],[\"-33/1\",\"-11/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0050","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"三點同參數比例核對","stem_zh":"Q數值比協議。給定k=(12)/(2)、完整三點(x,y)=[[0, 0], [1, 24], [2, -23]]。依原序求 (y−kx三殘差, 同k資格三值, y/x三值或未定義)，x=0時仍核y是否為0。","answer":{"kind":"expression","value":"([0/1, 18/1, -35/1], [是, 否, 否], [未定義, 24/1, -23/2])","explanation_zh":"完整三點比例律與殘差=([0/1, 18/1, -35/1], [是, 否, 否], [未定義, 24/1, -23/2])。逐點算殘差；比值再分開核x非零。有限點不能推論所有輸入。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三點同參數比例核對"]},"variant":{"family_id":"qf-density15-ratio-complete-point-law","seed":202610152050,"parameters":{"k":[12,2],"pairs":[[0,0],[1,24],[2,-23]],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_complete_point_law","semantic_template":"qf-density15-ratio-complete-point-law/[[\"0/1\",\"undefined\"],[\"18/1\",\"24/1\"],[\"-35/1\",\"-23/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0051","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=1、b=1、總量T=(0)/(1)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(0/1, 0/1, 0/1, 0/1, 否, 未定義)","explanation_zh":"同單位比例分配與比資格=(0/1, 0/1, 0/1, 0/1, 否, 未定義)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152051,"parameters":{"a":1,"b":1,"total":[0,1],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"0/1\",\"0/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0052","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=1、b=3、總量T=(8)/(1)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(2/1, 6/1, 0/1, 0/1, 是, 1/3)","explanation_zh":"同單位比例分配與比資格=(2/1, 6/1, 0/1, 0/1, 是, 1/3)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152052,"parameters":{"a":1,"b":3,"total":[8,1],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"2/1\",\"6/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0053","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=3、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(3/2, 1/1, 0/1, 0/1, 是, 3/2)","explanation_zh":"同單位比例分配與比資格=(3/2, 1/1, 0/1, 0/1, 是, 3/2)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152053,"parameters":{"a":3,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"3/2\",\"1/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0054","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=4、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(5/3, 5/6, 0/1, 0/1, 是, 2/1)","explanation_zh":"同單位比例分配與比資格=(5/3, 5/6, 0/1, 0/1, 是, 2/1)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152054,"parameters":{"a":4,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"5/3\",\"5/6\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0055","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=5、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(25/14, 5/7, 0/1, 0/1, 是, 5/2)","explanation_zh":"同單位比例分配與比資格=(25/14, 5/7, 0/1, 0/1, 是, 5/2)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152055,"parameters":{"a":5,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"25/14\",\"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0056","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=6、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(15/8, 5/8, 0/1, 0/1, 是, 3/1)","explanation_zh":"同單位比例分配與比資格=(15/8, 5/8, 0/1, 0/1, 是, 3/1)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152056,"parameters":{"a":6,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"15/8\",\"5/8\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0057","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=7、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(35/18, 5/9, 0/1, 0/1, 是, 7/2)","explanation_zh":"同單位比例分配與比資格=(35/18, 5/9, 0/1, 0/1, 是, 7/2)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152057,"parameters":{"a":7,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"35/18\",\"5/9\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0058","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=8、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(2/1, 1/2, 0/1, 0/1, 是, 4/1)","explanation_zh":"同單位比例分配與比資格=(2/1, 1/2, 0/1, 0/1, 是, 4/1)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152058,"parameters":{"a":8,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"2/1\",\"1/2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0059","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=9、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(45/22, 5/11, 0/1, 0/1, 是, 9/2)","explanation_zh":"同單位比例分配與比資格=(45/22, 5/11, 0/1, 0/1, 是, 9/2)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152059,"parameters":{"a":9,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"45/22\",\"5/11\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0060","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=10、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(25/12, 5/12, 0/1, 0/1, 是, 5/1)","explanation_zh":"同單位比例分配與比資格=(25/12, 5/12, 0/1, 0/1, 是, 5/1)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152060,"parameters":{"a":10,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"25/12\",\"5/12\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0061","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=11、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(55/26, 5/13, 0/1, 0/1, 是, 11/2)","explanation_zh":"同單位比例分配與比資格=(55/26, 5/13, 0/1, 0/1, 是, 11/2)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152061,"parameters":{"a":11,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"55/26\",\"5/13\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0062","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=12、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(15/7, 5/14, 0/1, 0/1, 是, 6/1)","explanation_zh":"同單位比例分配與比資格=(15/7, 5/14, 0/1, 0/1, 是, 6/1)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152062,"parameters":{"a":12,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"15/7\",\"5/14\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0063","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=13、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(13/6, 1/3, 0/1, 0/1, 是, 13/2)","explanation_zh":"同單位比例分配與比資格=(13/6, 1/3, 0/1, 0/1, 是, 13/2)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152063,"parameters":{"a":13,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"13/6\",\"1/3\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0064","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=14、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(35/16, 5/16, 0/1, 0/1, 是, 7/1)","explanation_zh":"同單位比例分配與比資格=(35/16, 5/16, 0/1, 0/1, 是, 7/1)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152064,"parameters":{"a":14,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"35/16\",\"5/16\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0065","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=15、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(75/34, 5/17, 0/1, 0/1, 是, 15/2)","explanation_zh":"同單位比例分配與比資格=(75/34, 5/17, 0/1, 0/1, 是, 15/2)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152065,"parameters":{"a":15,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"75/34\",\"5/17\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0066","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=16、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(20/9, 5/18, 0/1, 0/1, 是, 8/1)","explanation_zh":"同單位比例分配與比資格=(20/9, 5/18, 0/1, 0/1, 是, 8/1)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152066,"parameters":{"a":16,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"20/9\",\"5/18\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0067","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=17、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(85/38, 5/19, 0/1, 0/1, 是, 17/2)","explanation_zh":"同單位比例分配與比資格=(85/38, 5/19, 0/1, 0/1, 是, 17/2)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152067,"parameters":{"a":17,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"85/38\",\"5/19\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0068","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=18、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(9/4, 1/4, 0/1, 0/1, 是, 9/1)","explanation_zh":"同單位比例分配與比資格=(9/4, 1/4, 0/1, 0/1, 是, 9/1)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152068,"parameters":{"a":18,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"9/4\",\"1/4\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0069","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=19、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(95/42, 5/21, 0/1, 0/1, 是, 19/2)","explanation_zh":"同單位比例分配與比資格=(95/42, 5/21, 0/1, 0/1, 是, 19/2)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152069,"parameters":{"a":19,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"95/42\",\"5/21\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0070","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=20、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(25/11, 5/22, 0/1, 0/1, 是, 10/1)","explanation_zh":"同單位比例分配與比資格=(25/11, 5/22, 0/1, 0/1, 是, 10/1)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152070,"parameters":{"a":20,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"25/11\",\"5/22\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0071","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=21、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(105/46, 5/23, 0/1, 0/1, 是, 21/2)","explanation_zh":"同單位比例分配與比資格=(105/46, 5/23, 0/1, 0/1, 是, 21/2)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152071,"parameters":{"a":21,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"105/46\",\"5/23\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0072","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=22、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(55/24, 5/24, 0/1, 0/1, 是, 11/1)","explanation_zh":"同單位比例分配與比資格=(55/24, 5/24, 0/1, 0/1, 是, 11/1)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152072,"parameters":{"a":22,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"55/24\",\"5/24\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0073","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=23、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(23/10, 1/5, 0/1, 0/1, 是, 23/2)","explanation_zh":"同單位比例分配與比資格=(23/10, 1/5, 0/1, 0/1, 是, 23/2)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152073,"parameters":{"a":23,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"23/10\",\"1/5\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0074","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=24、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(30/13, 5/26, 0/1, 0/1, 是, 12/1)","explanation_zh":"同單位比例分配與比資格=(30/13, 5/26, 0/1, 0/1, 是, 12/1)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152074,"parameters":{"a":24,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"30/13\",\"5/26\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0075","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"同單位量的比例分配","stem_zh":"Q數值比協議。同單位有理量分配：正權重a=25、b=2、總量T=(5)/(2)。指定x=T*a/(a+b)，y=T*b/(a+b)。求 (x, y, x+y−T, bx−ay, 實際x:y合法資格, 比值或未定義)。","answer":{"kind":"expression","value":"(125/54, 5/27, 0/1, 0/1, 是, 25/2)","explanation_zh":"同單位比例分配與比資格=(125/54, 5/27, 0/1, 0/1, 是, 25/2)。先分出x，再由總量減x取得y並核兩種殘差；實際比另核y非零。零總量不證實0:0合法比。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["同單位量的比例分配"]},"variant":{"family_id":"qf-density15-ratio-proportional-partition","seed":202610152075,"parameters":{"a":25,"b":2,"total":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_proportional_partition","semantic_template":"qf-density15-ratio-proportional-partition/[\"125/54\",\"5/27\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0076","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=0、b=0、d=0、候選x=(0)/(1)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(否, 未定義, 0/1, 否)","explanation_zh":"候選比例後項資格與交乘=(否, 未定義, 0/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152076,"parameters":{"a":0,"b":0,"d":0,"x":[0,1],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[false,\"undefined\",\"0/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0077","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=1、b=0、d=2、候選x=(3)/(1)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(否, 未定義, 2/1, 否)","explanation_zh":"候選比例後項資格與交乘=(否, 未定義, 2/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152077,"parameters":{"a":1,"b":0,"d":2,"x":[3,1],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[false,\"undefined\",\"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0078","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=2、b=3、d=0、候選x=(1)/(3)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(否, 未定義, -1/1, 否)","explanation_zh":"候選比例後項資格與交乘=(否, 未定義, -1/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152078,"parameters":{"a":2,"b":3,"d":0,"x":[1,3],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[false,\"undefined\",\"-1/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0079","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=1、b=2、d=3、候選x=(3)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 3/2, 0/1, 是)","explanation_zh":"候選比例後項資格與交乘=(是, 3/2, 0/1, 是)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152079,"parameters":{"a":1,"b":2,"d":3,"x":[3,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"3/2\",\"0/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0080","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=-8、b=3、d=2、候選x=(5)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, -16/3, -47/2, 否)","explanation_zh":"候選比例後項資格與交乘=(是, -16/3, -47/2, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152080,"parameters":{"a":-8,"b":3,"d":2,"x":[5,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"-16/3\",\"-47/2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0081","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=-7、b=3、d=2、候選x=(6)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, -14/3, -23/1, 否)","explanation_zh":"候選比例後項資格與交乘=(是, -14/3, -23/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152081,"parameters":{"a":-7,"b":3,"d":2,"x":[6,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"-14/3\",\"-23/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0082","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=-6、b=3、d=2、候選x=(7)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, -4/1, -45/2, 否)","explanation_zh":"候選比例後項資格與交乘=(是, -4/1, -45/2, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152082,"parameters":{"a":-6,"b":3,"d":2,"x":[7,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"-4/1\",\"-45/2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0083","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=-5、b=3、d=2、候選x=(8)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, -10/3, -22/1, 否)","explanation_zh":"候選比例後項資格與交乘=(是, -10/3, -22/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152083,"parameters":{"a":-5,"b":3,"d":2,"x":[8,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"-10/3\",\"-22/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0084","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=-4、b=3、d=2、候選x=(9)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, -8/3, -43/2, 否)","explanation_zh":"候選比例後項資格與交乘=(是, -8/3, -43/2, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152084,"parameters":{"a":-4,"b":3,"d":2,"x":[9,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"-8/3\",\"-43/2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0085","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=-3、b=3、d=2、候選x=(10)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, -2/1, -21/1, 否)","explanation_zh":"候選比例後項資格與交乘=(是, -2/1, -21/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152085,"parameters":{"a":-3,"b":3,"d":2,"x":[10,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"-2/1\",\"-21/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0086","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=-2、b=3、d=2、候選x=(11)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, -4/3, -41/2, 否)","explanation_zh":"候選比例後項資格與交乘=(是, -4/3, -41/2, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152086,"parameters":{"a":-2,"b":3,"d":2,"x":[11,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"-4/3\",\"-41/2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0087","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=-1、b=3、d=2、候選x=(12)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, -2/3, -20/1, 否)","explanation_zh":"候選比例後項資格與交乘=(是, -2/3, -20/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152087,"parameters":{"a":-1,"b":3,"d":2,"x":[12,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"-2/3\",\"-20/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0088","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=0、b=3、d=2、候選x=(13)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 0/1, -39/2, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 0/1, -39/2, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152088,"parameters":{"a":0,"b":3,"d":2,"x":[13,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"0/1\",\"-39/2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0089","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=1、b=3、d=2、候選x=(14)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 2/3, -19/1, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 2/3, -19/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152089,"parameters":{"a":1,"b":3,"d":2,"x":[14,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"2/3\",\"-19/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0090","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=2、b=3、d=2、候選x=(15)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 4/3, -37/2, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 4/3, -37/2, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152090,"parameters":{"a":2,"b":3,"d":2,"x":[15,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"4/3\",\"-37/2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0091","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=3、b=3、d=2、候選x=(16)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 2/1, -18/1, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 2/1, -18/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152091,"parameters":{"a":3,"b":3,"d":2,"x":[16,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"2/1\",\"-18/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0092","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=4、b=3、d=2、候選x=(17)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 8/3, -35/2, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 8/3, -35/2, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152092,"parameters":{"a":4,"b":3,"d":2,"x":[17,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"8/3\",\"-35/2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0093","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=5、b=3、d=2、候選x=(18)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 10/3, -17/1, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 10/3, -17/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152093,"parameters":{"a":5,"b":3,"d":2,"x":[18,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"10/3\",\"-17/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0094","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=6、b=3、d=2、候選x=(19)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 4/1, -33/2, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 4/1, -33/2, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152094,"parameters":{"a":6,"b":3,"d":2,"x":[19,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"4/1\",\"-33/2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0095","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=7、b=3、d=2、候選x=(20)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 14/3, -16/1, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 14/3, -16/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152095,"parameters":{"a":7,"b":3,"d":2,"x":[20,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"14/3\",\"-16/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0096","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=8、b=3、d=2、候選x=(21)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 16/3, -31/2, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 16/3, -31/2, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152096,"parameters":{"a":8,"b":3,"d":2,"x":[21,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"16/3\",\"-31/2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0097","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=9、b=3、d=2、候選x=(22)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 6/1, -15/1, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 6/1, -15/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152097,"parameters":{"a":9,"b":3,"d":2,"x":[22,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"6/1\",\"-15/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0098","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=10、b=3、d=2、候選x=(23)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 20/3, -29/2, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 20/3, -29/2, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152098,"parameters":{"a":10,"b":3,"d":2,"x":[23,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"20/3\",\"-29/2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0099","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=11、b=3、d=2、候選x=(24)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 22/3, -14/1, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 22/3, -14/1, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152099,"parameters":{"a":11,"b":3,"d":2,"x":[24,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"22/3\",\"-14/1\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r02-ratio-proportion-0100","batch_id":"batch-20261011-advance-20261015-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"候選比例的後項與交乘","stem_zh":"Q數值比協議。待核候選a:b=x:d，a=12、b=3、d=2、候選x=(25)/(2)。求 (兩後項合法資格, 合法時解x*=ad/b或未定義, ad−b*x, 原比例成立資格)，候選後項未先假定合法。","answer":{"kind":"expression","value":"(是, 8/1, -27/2, 否)","explanation_zh":"候選比例後項資格與交乘=(是, 8/1, -27/2, 否)。先核b與d，交乘殘差和原比例資格分開；非法後項不被零殘差恢復。零後項不因交乘相等而合法，有限比例非因果或幾何相似證明。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選比例的後項與交乘"]},"variant":{"family_id":"qf-density15-ratio-missing-component-guard","seed":202610152100,"parameters":{"a":12,"b":3,"d":2,"x":[25,2],"domain":"finite_Q_numeric_ratio_protocol","operation":"density15_ratio_missing_component_guard","semantic_template":"qf-density15-ratio-missing-component-guard/[true,\"8/1\",\"-27/2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}