{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0001","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 0/1 與 0/1，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"=","explanation_zh":"交叉乘積=0,0。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061001,"parameters":{"p":0,"q":1,"r":0,"s":1,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"0/1\",\"0/1\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0002","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 -2/3 與 -9/2，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":">","explanation_zh":"交叉乘積=-4,-27。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061002,"parameters":{"p":-2,"q":3,"r":-9,"s":2,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-2/3\",\"-9/2\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0003","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 3/4 與 -8/3，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":">","explanation_zh":"交叉乘積=9,-32。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061003,"parameters":{"p":3,"q":4,"r":-8,"s":3,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"3/4\",\"-8/3\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0004","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 -4/5 與 -5/4，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":">","explanation_zh":"交叉乘積=-16,-25。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061004,"parameters":{"p":-4,"q":5,"r":-5,"s":4,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-4/5\",\"-5/4\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0005","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 5/6 與 -6/1，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":">","explanation_zh":"交叉乘積=5,-36。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061005,"parameters":{"p":5,"q":6,"r":-6,"s":1,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"5/6\",\"-6/1\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0006","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 -6/2 與 -5/2，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"<","explanation_zh":"交叉乘積=-12,-10。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061006,"parameters":{"p":-6,"q":2,"r":-5,"s":2,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-3/1\",\"-5/2\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0007","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 7/3 與 7/3，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"=","explanation_zh":"交叉乘積=21,21。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061007,"parameters":{"p":7,"q":3,"r":7,"s":3,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"7/3\",\"7/3\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0008","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 -8/4 與 -3/4，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"<","explanation_zh":"交叉乘積=-32,-12。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061008,"parameters":{"p":-8,"q":4,"r":-3,"s":4,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-2/1\",\"-3/4\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0010","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 -10/6 與 -11/2，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":">","explanation_zh":"交叉乘積=-20,-66。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061010,"parameters":{"p":-10,"q":6,"r":-11,"s":2,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-5/3\",\"-11/2\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0011","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 11/2 與 0/3，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":">","explanation_zh":"交叉乘積=33,0。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061011,"parameters":{"p":11,"q":2,"r":0,"s":3,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"11/2\",\"0/1\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0012","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 -12/3 與 1/4，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"<","explanation_zh":"交叉乘積=-48,3。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061012,"parameters":{"p":-12,"q":3,"r":1,"s":4,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-4/1\",\"1/4\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0013","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 13/4 與 13/4，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"=","explanation_zh":"交叉乘積=52,52。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061013,"parameters":{"p":13,"q":4,"r":13,"s":4,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"13/4\",\"13/4\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0014","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 -14/5 與 3/2，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"<","explanation_zh":"交叉乘積=-28,15。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061014,"parameters":{"p":-14,"q":5,"r":3,"s":2,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-14/5\",\"3/2\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0015","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 15/6 與 4/3，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":">","explanation_zh":"交叉乘積=45,24。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061015,"parameters":{"p":15,"q":6,"r":4,"s":3,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"5/2\",\"4/3\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0016","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 -16/2 與 -17/4，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"<","explanation_zh":"交叉乘積=-64,-34。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061016,"parameters":{"p":-16,"q":2,"r":-17,"s":4,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-8/1\",\"-17/4\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0017","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 17/3 與 6/1，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"<","explanation_zh":"交叉乘積=17,18。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061017,"parameters":{"p":17,"q":3,"r":6,"s":1,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"17/3\",\"6/1\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0018","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 -18/4 與 7/2，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"<","explanation_zh":"交叉乘積=-36,28。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061018,"parameters":{"p":-18,"q":4,"r":7,"s":2,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-9/2\",\"7/2\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0019","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 19/5 與 19/5，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"=","explanation_zh":"交叉乘積=95,95。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061019,"parameters":{"p":19,"q":5,"r":19,"s":5,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"19/5\",\"19/5\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0020","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 -20/6 與 9/4，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"<","explanation_zh":"交叉乘積=-80,54。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061020,"parameters":{"p":-20,"q":6,"r":9,"s":4,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-10/3\",\"9/4\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0021","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 21/2 與 10/1，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":">","explanation_zh":"交叉乘積=21,20。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061021,"parameters":{"p":21,"q":2,"r":10,"s":1,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"21/2\",\"10/1\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0022","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 -22/3 與 -23/2，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":">","explanation_zh":"交叉乘積=-44,-69。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061022,"parameters":{"p":-22,"q":3,"r":-23,"s":2,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-22/3\",\"-23/2\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0023","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 23/4 與 12/3，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":">","explanation_zh":"交叉乘積=69,48。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061023,"parameters":{"p":23,"q":4,"r":12,"s":3,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"23/4\",\"4/1\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0024","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 -24/5 與 13/4，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"<","explanation_zh":"交叉乘積=-96,65。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061024,"parameters":{"p":-24,"q":5,"r":13,"s":4,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-24/5\",\"13/4\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0025","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"正分母有理數的精確順序","stem_zh":"依實數順序，比較 25/6 與 25/6，分母明示為正整數；回答 <、= 或 >。","answer":{"kind":"short_text","value":"=","explanation_zh":"交叉乘積=150,150。正分母交叉相乘保留順序，以精確整數乘積比較，不靠小數外觀。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母有理數的精確順序"]},"variant":{"family_id":"qf-order-rational-comparison","seed":202610061025,"parameters":{"p":25,"q":6,"r":25,"s":6,"operation":"rational_comparison","semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"25/6\",\"25/6\"],\"operation\":\"rational_comparison\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0026","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {0}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(0, 0)","explanation_zh":"極值=(0, 0)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061026,"parameters":{"values":[0],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"0\",\"0\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0027","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-1, 0, 3}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-1, 3)","explanation_zh":"極值=(-1, 3)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061027,"parameters":{"values":[-1,0,3],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-1\",\"3\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0028","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-2, 0, 4}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-2, 4)","explanation_zh":"極值=(-2, 4)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061028,"parameters":{"values":[-2,0,4],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-2\",\"4\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0029","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-3, 0, 5}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-3, 5)","explanation_zh":"極值=(-3, 5)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061029,"parameters":{"values":[-3,0,5],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-3\",\"5\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0030","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-7, -6, -4}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-7, -4)","explanation_zh":"極值=(-7, -4)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061030,"parameters":{"values":[-7,-6,-4],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-7\",\"-4\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0031","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-5, 0, 7}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-5, 7)","explanation_zh":"極值=(-5, 7)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061031,"parameters":{"values":[-5,0,7],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-5\",\"7\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0032","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-6, 0, 8}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-6, 8)","explanation_zh":"極值=(-6, 8)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061032,"parameters":{"values":[-6,0,8],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-6\",\"8\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0033","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-7, 0, 9}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-7, 9)","explanation_zh":"極值=(-7, 9)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061033,"parameters":{"values":[-7,0,9],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-7\",\"9\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0034","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-11, -10, -8}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-11, -8)","explanation_zh":"極值=(-11, -8)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061034,"parameters":{"values":[-11,-10,-8],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-11\",\"-8\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0035","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-9, 0, 11}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-9, 11)","explanation_zh":"極值=(-9, 11)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061035,"parameters":{"values":[-9,0,11],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-9\",\"11\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0036","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-10, 0, 12}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-10, 12)","explanation_zh":"極值=(-10, 12)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061036,"parameters":{"values":[-10,0,12],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-10\",\"12\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0037","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-11, 0, 13}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-11, 13)","explanation_zh":"極值=(-11, 13)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061037,"parameters":{"values":[-11,0,13],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-11\",\"13\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0038","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-15, -14, -12}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-15, -12)","explanation_zh":"極值=(-15, -12)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061038,"parameters":{"values":[-15,-14,-12],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-15\",\"-12\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0039","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-13, 0, 15}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-13, 15)","explanation_zh":"極值=(-13, 15)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061039,"parameters":{"values":[-13,0,15],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-13\",\"15\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0040","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-14, 0, 16}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-14, 16)","explanation_zh":"極值=(-14, 16)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061040,"parameters":{"values":[-14,0,16],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-14\",\"16\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0041","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-15, 0, 17}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-15, 17)","explanation_zh":"極值=(-15, 17)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061041,"parameters":{"values":[-15,0,17],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-15\",\"17\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0042","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-19, -18, -16}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-19, -16)","explanation_zh":"極值=(-19, -16)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061042,"parameters":{"values":[-19,-18,-16],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-19\",\"-16\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0043","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-17, 0, 19}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-17, 19)","explanation_zh":"極值=(-17, 19)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061043,"parameters":{"values":[-17,0,19],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-17\",\"19\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0044","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-18, 0, 20}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-18, 20)","explanation_zh":"極值=(-18, 20)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061044,"parameters":{"values":[-18,0,20],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-18\",\"20\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0045","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-19, 0, 21}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-19, 21)","explanation_zh":"極值=(-19, 21)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061045,"parameters":{"values":[-19,0,21],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-19\",\"21\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0046","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-23, -22, -20}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-23, -20)","explanation_zh":"極值=(-23, -20)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061046,"parameters":{"values":[-23,-22,-20],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-23\",\"-20\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0047","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-21, 0, 23}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-21, 23)","explanation_zh":"極值=(-21, 23)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061047,"parameters":{"values":[-21,0,23],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-21\",\"23\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0048","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-22, 0, 24}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-22, 24)","explanation_zh":"極值=(-22, 24)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061048,"parameters":{"values":[-22,0,24],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-22\",\"24\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0049","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-23, 0, 25}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-23, 25)","explanation_zh":"極值=(-23, 25)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061049,"parameters":{"values":[-23,0,25],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-23\",\"25\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0050","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"有限實數集合的最小與最大值","stem_zh":"依實數順序，明示非空有限整數集合 {-27, -26, -24}，求 (最小值, 最大值)。","answer":{"kind":"expression","value":"(-27, -24)","explanation_zh":"極值=(-27, -24)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限實數集合的最小與最大值"]},"variant":{"family_id":"qf-order-finite-extrema","seed":202610061050,"parameters":{"values":[-27,-26,-24],"operation":"finite_extrema","semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-27\",\"-24\"],\"operation\":\"finite_extrema\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0051","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 0/1 是否屬於閉區間 [0,0]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[0,0]；值=0/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061051,"parameters":{"p":0,"q":1,"lower":0,"upper":0,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"0/1\",\"0\",\"0\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0052","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 6/2 是否屬於閉區間 [-1,3]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-1,3]；值=3/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061052,"parameters":{"p":6,"q":2,"lower":-1,"upper":3,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"3/1\",\"-1\",\"3\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0053","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 -7/3 是否屬於閉區間 [-2,4]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"否","explanation_zh":"閉區間[-2,4]；值=-7/3。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061053,"parameters":{"p":-7,"q":3,"lower":-2,"upper":4,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-7/3\",\"-2\",\"4\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0054","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 21/4 是否屬於閉區間 [-3,5]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"否","explanation_zh":"閉區間[-3,5]；值=21/4。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061054,"parameters":{"p":21,"q":4,"lower":-3,"upper":5,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"21/4\",\"-3\",\"5\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0055","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 1/1 是否屬於閉區間 [-4,6]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-4,6]；值=1/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061055,"parameters":{"p":1,"q":1,"lower":-4,"upper":6,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"1/1\",\"-4\",\"6\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0056","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 -10/2 是否屬於閉區間 [-5,7]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-5,7]；值=-5/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061056,"parameters":{"p":-10,"q":2,"lower":-5,"upper":7,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-5/1\",\"-5\",\"7\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0057","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 24/3 是否屬於閉區間 [-6,8]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-6,8]；值=8/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061057,"parameters":{"p":24,"q":3,"lower":-6,"upper":8,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"8/1\",\"-6\",\"8\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0058","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 -29/4 是否屬於閉區間 [-7,9]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"否","explanation_zh":"閉區間[-7,9]；值=-29/4。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061058,"parameters":{"p":-29,"q":4,"lower":-7,"upper":9,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-29/4\",\"-7\",\"9\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0059","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 11/1 是否屬於閉區間 [-8,10]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"否","explanation_zh":"閉區間[-8,10]；值=11/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061059,"parameters":{"p":11,"q":1,"lower":-8,"upper":10,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"11/1\",\"-8\",\"10\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0060","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 1/2 是否屬於閉區間 [-9,11]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-9,11]；值=1/2。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061060,"parameters":{"p":1,"q":2,"lower":-9,"upper":11,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"1/2\",\"-9\",\"11\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0061","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 -30/3 是否屬於閉區間 [-10,12]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-10,12]；值=-10/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061061,"parameters":{"p":-30,"q":3,"lower":-10,"upper":12,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-10/1\",\"-10\",\"12\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0062","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 52/4 是否屬於閉區間 [-11,13]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-11,13]；值=13/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061062,"parameters":{"p":52,"q":4,"lower":-11,"upper":13,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"13/1\",\"-11\",\"13\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0063","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 -13/1 是否屬於閉區間 [-12,14]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"否","explanation_zh":"閉區間[-12,14]；值=-13/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061063,"parameters":{"p":-13,"q":1,"lower":-12,"upper":14,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-13/1\",\"-12\",\"14\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0064","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 31/2 是否屬於閉區間 [-13,15]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"否","explanation_zh":"閉區間[-13,15]；值=31/2。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061064,"parameters":{"p":31,"q":2,"lower":-13,"upper":15,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"31/2\",\"-13\",\"15\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0065","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 1/3 是否屬於閉區間 [-14,16]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-14,16]；值=1/3。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061065,"parameters":{"p":1,"q":3,"lower":-14,"upper":16,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"1/3\",\"-14\",\"16\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0066","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 -60/4 是否屬於閉區間 [-15,17]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-15,17]；值=-15/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061066,"parameters":{"p":-60,"q":4,"lower":-15,"upper":17,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-15/1\",\"-15\",\"17\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0067","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 18/1 是否屬於閉區間 [-16,18]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-16,18]；值=18/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061067,"parameters":{"p":18,"q":1,"lower":-16,"upper":18,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"18/1\",\"-16\",\"18\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0068","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 -35/2 是否屬於閉區間 [-17,19]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"否","explanation_zh":"閉區間[-17,19]；值=-35/2。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061068,"parameters":{"p":-35,"q":2,"lower":-17,"upper":19,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-35/2\",\"-17\",\"19\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0069","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 61/3 是否屬於閉區間 [-18,20]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"否","explanation_zh":"閉區間[-18,20]；值=61/3。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061069,"parameters":{"p":61,"q":3,"lower":-18,"upper":20,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"61/3\",\"-18\",\"20\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0070","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 1/4 是否屬於閉區間 [-19,21]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-19,21]；值=1/4。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061070,"parameters":{"p":1,"q":4,"lower":-19,"upper":21,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"1/4\",\"-19\",\"21\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0071","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 -20/1 是否屬於閉區間 [-20,22]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-20,22]；值=-20/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061071,"parameters":{"p":-20,"q":1,"lower":-20,"upper":22,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-20/1\",\"-20\",\"22\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0072","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 46/2 是否屬於閉區間 [-21,23]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-21,23]；值=23/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061072,"parameters":{"p":46,"q":2,"lower":-21,"upper":23,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"23/1\",\"-21\",\"23\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0073","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 -67/3 是否屬於閉區間 [-22,24]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"否","explanation_zh":"閉區間[-22,24]；值=-67/3。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061073,"parameters":{"p":-67,"q":3,"lower":-22,"upper":24,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-67/3\",\"-22\",\"24\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0074","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 101/4 是否屬於閉區間 [-23,25]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"否","explanation_zh":"閉區間[-23,25]；值=101/4。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061074,"parameters":{"p":101,"q":4,"lower":-23,"upper":25,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"101/4\",\"-23\",\"25\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0075","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"閉區間的含端點判定","stem_zh":"依實數順序，正分母有理數 1/1 是否屬於閉區間 [-24,26]？閉區間包含兩端點，允許單點區間。","answer":{"kind":"short_text","value":"是","explanation_zh":"閉區間[-24,26]；值=1/1。將兩個非嚴格不等式同乘正分母，兩側都成立才屬於；端點相等仍按閉區間慣例判定。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間的含端點判定"]},"variant":{"family_id":"qf-order-closed-interval","seed":202610061075,"parameters":{"p":1,"q":1,"lower":-24,"upper":26,"operation":"closed_interval","semantic_template":"qf-order-closed-interval/{\"inputs\":[\"1/1\",\"-24\",\"26\"],\"operation\":\"closed_interval\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0076","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (0)+(-12) 與 (0)+(-12)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"=","explanation_zh":"共同平移後=(-12, -12)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061076,"parameters":{"a":0,"b":0,"c":-12,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"0\",\"0\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0077","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-3)+(-11) 與 (2)+(-11)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"<","explanation_zh":"共同平移後=(-14, -9)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061077,"parameters":{"a":-3,"b":2,"c":-11,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-3\",\"2\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0078","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-4)+(-10) 與 (-8)+(-10)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":">","explanation_zh":"共同平移後=(-14, -18)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061078,"parameters":{"a":-4,"b":-8,"c":-10,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-4\",\"-8\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0079","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-5)+(-9) 與 (-5)+(-9)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"=","explanation_zh":"共同平移後=(-14, -14)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061079,"parameters":{"a":-5,"b":-5,"c":-9,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-5\",\"-5\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0080","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-6)+(-8) 與 (5)+(-8)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"<","explanation_zh":"共同平移後=(-14, -3)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061080,"parameters":{"a":-6,"b":5,"c":-8,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-6\",\"5\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0081","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-7)+(-7) 與 (-14)+(-7)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":">","explanation_zh":"共同平移後=(-14, -21)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061081,"parameters":{"a":-7,"b":-14,"c":-7,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-7\",\"-14\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0083","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-9)+(-5) 與 (8)+(-5)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"<","explanation_zh":"共同平移後=(-14, 3)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061083,"parameters":{"a":-9,"b":8,"c":-5,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-9\",\"8\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0084","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-10)+(-4) 與 (-20)+(-4)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":">","explanation_zh":"共同平移後=(-14, -24)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061084,"parameters":{"a":-10,"b":-20,"c":-4,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-10\",\"-20\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0085","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-11)+(-3) 與 (-11)+(-3)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"=","explanation_zh":"共同平移後=(-14, -14)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061085,"parameters":{"a":-11,"b":-11,"c":-3,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-11\",\"-11\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0086","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-12)+(-2) 與 (11)+(-2)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"<","explanation_zh":"共同平移後=(-14, 9)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061086,"parameters":{"a":-12,"b":11,"c":-2,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-12\",\"11\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0087","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-13)+(-1) 與 (-26)+(-1)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":">","explanation_zh":"共同平移後=(-14, -27)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061087,"parameters":{"a":-13,"b":-26,"c":-1,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-13\",\"-26\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0088","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-14)+(0) 與 (-14)+(0)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"=","explanation_zh":"共同平移後=(-14, -14)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061088,"parameters":{"a":-14,"b":-14,"c":0,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-14\",\"-14\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0089","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-15)+(1) 與 (14)+(1)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"<","explanation_zh":"共同平移後=(-14, 15)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061089,"parameters":{"a":-15,"b":14,"c":1,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-15\",\"14\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0090","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-16)+(2) 與 (-32)+(2)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":">","explanation_zh":"共同平移後=(-14, -30)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061090,"parameters":{"a":-16,"b":-32,"c":2,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-16\",\"-32\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0091","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-17)+(3) 與 (-17)+(3)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"=","explanation_zh":"共同平移後=(-14, -14)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061091,"parameters":{"a":-17,"b":-17,"c":3,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-17\",\"-17\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0092","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-18)+(4) 與 (17)+(4)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"<","explanation_zh":"共同平移後=(-14, 21)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061092,"parameters":{"a":-18,"b":17,"c":4,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-18\",\"17\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0093","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-19)+(5) 與 (-38)+(5)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":">","explanation_zh":"共同平移後=(-14, -33)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061093,"parameters":{"a":-19,"b":-38,"c":5,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-19\",\"-38\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0094","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-20)+(6) 與 (-20)+(6)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"=","explanation_zh":"共同平移後=(-14, -14)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061094,"parameters":{"a":-20,"b":-20,"c":6,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-20\",\"-20\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0095","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-21)+(7) 與 (20)+(7)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"<","explanation_zh":"共同平移後=(-14, 27)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061095,"parameters":{"a":-21,"b":20,"c":7,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-21\",\"20\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0096","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-22)+(8) 與 (-44)+(8)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":">","explanation_zh":"共同平移後=(-14, -36)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061096,"parameters":{"a":-22,"b":-44,"c":8,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-22\",\"-44\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0097","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-23)+(9) 與 (-23)+(9)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"=","explanation_zh":"共同平移後=(-14, -14)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061097,"parameters":{"a":-23,"b":-23,"c":9,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-23\",\"-23\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0098","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-24)+(10) 與 (23)+(10)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"<","explanation_zh":"共同平移後=(-14, 33)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061098,"parameters":{"a":-24,"b":23,"c":10,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-24\",\"23\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0099","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-25)+(11) 與 (-50)+(11)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":">","explanation_zh":"共同平移後=(-14, -39)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061099,"parameters":{"a":-25,"b":-50,"c":11,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-25\",\"-50\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r01-order-relation-0100","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-order-relation"],"title_zh":"共同加數後的順序","stem_zh":"依實數順序，比較 (-26)+(12) 與 (-26)+(12)，回答 <、= 或 >。兩數加同一個整數。","answer":{"kind":"short_text","value":"=","explanation_zh":"共同平移後=(-14, -14)。共同加數不改變兩數的順序；此題比較是精確有序實數運算，不泛化到其他偏序。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["共同加數後的順序"]},"variant":{"family_id":"qf-order-common-translation","seed":202610061100,"parameters":{"a":-26,"b":-26,"c":12,"operation":"common_translation","semantic_template":"qf-order-common-translation/{\"inputs\":[\"-26\",\"-26\"],\"operation\":\"common_translation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}