{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0001","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=0x+(-3)，有序環境x=[0/1, -1/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-3/1, -3/1)","explanation_zh":"雙環境求值=(-3/1, -3/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113001,"parameters":{"a":0,"b":-3,"inputs":[[0,3],[-1,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[\"constant\",-3]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0002","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=-1x+(-6)，有序環境x=[1/3, -1/1]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-19/3, -5/1)","explanation_zh":"雙環境求值=(-19/3, -5/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113002,"parameters":{"a":-1,"b":-6,"inputs":[[1,3],[-2,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[-1,-6,[\"1/3\",\"-1/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0003","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=2x+(-5)，有序環境x=[2/3, -3/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-11/3, -8/1)","explanation_zh":"雙環境求值=(-11/3, -8/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113003,"parameters":{"a":2,"b":-5,"inputs":[[2,3],[-3,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[2,-5,[\"2/3\",\"-3/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0004","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=-3x+(-4)，有序環境x=[1/1, -2/1]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-7/1, 2/1)","explanation_zh":"雙環境求值=(-7/1, 2/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113004,"parameters":{"a":-3,"b":-4,"inputs":[[3,3],[-4,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[-3,-4,[\"1/1\",\"-2/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0005","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=4x+(-3)，有序環境x=[4/3, -5/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(7/3, -13/1)","explanation_zh":"雙環境求值=(7/3, -13/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113005,"parameters":{"a":4,"b":-3,"inputs":[[4,3],[-5,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[4,-3,[\"4/3\",\"-5/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0006","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=-5x+(-2)，有序環境x=[5/3, -3/1]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-31/3, 13/1)","explanation_zh":"雙環境求值=(-31/3, 13/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113006,"parameters":{"a":-5,"b":-2,"inputs":[[5,3],[-6,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[-5,-2,[\"5/3\",\"-3/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0007","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=6x+(-1)，有序環境x=[2/1, -7/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(11/1, -22/1)","explanation_zh":"雙環境求值=(11/1, -22/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113007,"parameters":{"a":6,"b":-1,"inputs":[[6,3],[-7,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[6,-1,[\"2/1\",\"-7/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0008","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=-7x+(0)，有序環境x=[7/3, -4/1]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-49/3, 28/1)","explanation_zh":"雙環境求值=(-49/3, 28/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113008,"parameters":{"a":-7,"b":0,"inputs":[[7,3],[-8,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[-7,0,[\"7/3\",\"-4/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0009","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=8x+(1)，有序環境x=[8/3, -9/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(67/3, -35/1)","explanation_zh":"雙環境求值=(67/3, -35/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113009,"parameters":{"a":8,"b":1,"inputs":[[8,3],[-9,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[8,1,[\"8/3\",\"-9/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0010","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=-9x+(2)，有序環境x=[3/1, -5/1]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-25/1, 47/1)","explanation_zh":"雙環境求值=(-25/1, 47/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113010,"parameters":{"a":-9,"b":2,"inputs":[[9,3],[-10,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[-9,2,[\"3/1\",\"-5/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0011","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=10x+(3)，有序環境x=[10/3, -11/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(109/3, -52/1)","explanation_zh":"雙環境求值=(109/3, -52/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113011,"parameters":{"a":10,"b":3,"inputs":[[10,3],[-11,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[10,3,[\"10/3\",\"-11/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0012","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=-11x+(4)，有序環境x=[11/3, -6/1]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-109/3, 70/1)","explanation_zh":"雙環境求值=(-109/3, 70/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113012,"parameters":{"a":-11,"b":4,"inputs":[[11,3],[-12,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[-11,4,[\"11/3\",\"-6/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0013","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=12x+(5)，有序環境x=[4/1, -13/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(53/1, -73/1)","explanation_zh":"雙環境求值=(53/1, -73/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113013,"parameters":{"a":12,"b":5,"inputs":[[12,3],[-13,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[12,5,[\"4/1\",\"-13/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0014","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=-13x+(6)，有序環境x=[13/3, -7/1]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-151/3, 97/1)","explanation_zh":"雙環境求值=(-151/3, 97/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113014,"parameters":{"a":-13,"b":6,"inputs":[[13,3],[-14,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[-13,6,[\"13/3\",\"-7/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0015","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=14x+(7)，有序環境x=[14/3, -15/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(217/3, -98/1)","explanation_zh":"雙環境求值=(217/3, -98/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113015,"parameters":{"a":14,"b":7,"inputs":[[14,3],[-15,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[14,7,[\"14/3\",\"-15/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0016","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=-15x+(8)，有序環境x=[5/1, -8/1]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-67/1, 128/1)","explanation_zh":"雙環境求值=(-67/1, 128/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113016,"parameters":{"a":-15,"b":8,"inputs":[[15,3],[-16,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[-15,8,[\"5/1\",\"-8/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0017","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=16x+(9)，有序環境x=[16/3, -17/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(283/3, -127/1)","explanation_zh":"雙環境求值=(283/3, -127/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113017,"parameters":{"a":16,"b":9,"inputs":[[16,3],[-17,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[16,9,[\"16/3\",\"-17/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0018","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=-17x+(10)，有序環境x=[17/3, -9/1]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-259/3, 163/1)","explanation_zh":"雙環境求值=(-259/3, 163/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113018,"parameters":{"a":-17,"b":10,"inputs":[[17,3],[-18,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[-17,10,[\"17/3\",\"-9/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0019","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=18x+(11)，有序環境x=[6/1, -19/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(119/1, -160/1)","explanation_zh":"雙環境求值=(119/1, -160/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113019,"parameters":{"a":18,"b":11,"inputs":[[18,3],[-19,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[18,11,[\"6/1\",\"-19/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0020","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=-19x+(12)，有序環境x=[19/3, -10/1]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-325/3, 202/1)","explanation_zh":"雙環境求值=(-325/3, 202/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113020,"parameters":{"a":-19,"b":12,"inputs":[[19,3],[-20,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[-19,12,[\"19/3\",\"-10/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0021","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=20x+(13)，有序環境x=[20/3, -21/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(439/3, -197/1)","explanation_zh":"雙環境求值=(439/3, -197/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113021,"parameters":{"a":20,"b":13,"inputs":[[20,3],[-21,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[20,13,[\"20/3\",\"-21/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0022","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=-21x+(14)，有序環境x=[7/1, -11/1]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-133/1, 245/1)","explanation_zh":"雙環境求值=(-133/1, 245/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113022,"parameters":{"a":-21,"b":14,"inputs":[[21,3],[-22,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[-21,14,[\"7/1\",\"-11/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0023","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=22x+(15)，有序環境x=[22/3, -23/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(529/3, -238/1)","explanation_zh":"雙環境求值=(529/3, -238/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113023,"parameters":{"a":22,"b":15,"inputs":[[22,3],[-23,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[22,15,[\"22/3\",\"-23/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0024","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=-23x+(16)，有序環境x=[23/3, -12/1]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(-481/3, 292/1)","explanation_zh":"雙環境求值=(-481/3, 292/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113024,"parameters":{"a":-23,"b":16,"inputs":[[23,3],[-24,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[-23,16,[\"23/3\",\"-12/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0025","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"同一表達式在兩環境的值","stem_zh":"有理數Q；表達式非方程式，E(x)=24x+(17)，有序環境x=[8/1, -25/2]。依序求兩個E值，均寫最簡分數。","answer":{"kind":"expression","value":"(209/1, -283/1)","explanation_zh":"雙環境求值=(209/1, -283/1)。分別把兩個環境代入同一式；常數式不受x影響，求值不是求解方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["同一表達式在兩環境的值"]},"variant":{"family_id":"qf-density11-expression-two-env-values","seed":202610113025,"parameters":{"a":24,"b":17,"inputs":[[24,3],[-25,2]],"operation":"density11_expression_two_env_values","domain":"typed_Q_affine_expression_slice","semantic_template":"qf-density11-expression-two-env-values/[24,17,[\"8/1\",\"-25/2\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0026","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=0x+(0)y，x=1、y=2。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(0, 0)","explanation_zh":"同時交換有序值=(0, 0)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113026,"parameters":{"a":0,"b":0,"x":1,"y":2,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[\"zero_pair\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0027","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=2x+(2)y，x=-1、y=3。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(4, 4)","explanation_zh":"同時交換有序值=(4, 4)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113027,"parameters":{"a":2,"b":2,"x":-1,"y":3,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[\"equal_coefficients\",\"2\",\"2\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0028","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=1x+(-2)y，x=3、y=3。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-3, -3)","explanation_zh":"同時交換有序值=(-3, -3)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113028,"parameters":{"a":1,"b":-2,"x":3,"y":3,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[\"equal_environment\",\"-3\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0029","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=4x+(-3)y，x=1、y=6。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-14, 21)","explanation_zh":"同時交換有序值=(-14, 21)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113029,"parameters":{"a":4,"b":-3,"x":1,"y":6,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-3,4,6,1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0030","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=5x+(-4)y，x=2、y=7。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-18, 27)","explanation_zh":"同時交換有序值=(-18, 27)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113030,"parameters":{"a":5,"b":-4,"x":2,"y":7,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-4,5,7,2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0031","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=6x+(-5)y，x=-2、y=8。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-52, 58)","explanation_zh":"同時交換有序值=(-52, 58)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113031,"parameters":{"a":6,"b":-5,"x":-2,"y":8,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-5,6,8,-2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0032","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=7x+(-6)y，x=-1、y=9。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-61, 69)","explanation_zh":"同時交換有序值=(-61, 69)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113032,"parameters":{"a":7,"b":-6,"x":-1,"y":9,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-6,7,9,-1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0033","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=8x+(-7)y，x=0、y=10。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-70, 80)","explanation_zh":"同時交換有序值=(-70, 80)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113033,"parameters":{"a":8,"b":-7,"x":0,"y":10,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-7,8,10,0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0034","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=9x+(-8)y，x=1、y=11。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-79, 91)","explanation_zh":"同時交換有序值=(-79, 91)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113034,"parameters":{"a":9,"b":-8,"x":1,"y":11,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-8,9,11,1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0035","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=10x+(-9)y，x=2、y=12。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-88, 102)","explanation_zh":"同時交換有序值=(-88, 102)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113035,"parameters":{"a":10,"b":-9,"x":2,"y":12,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-9,10,12,2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0036","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=11x+(-10)y，x=-2、y=13。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-152, 163)","explanation_zh":"同時交換有序值=(-152, 163)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113036,"parameters":{"a":11,"b":-10,"x":-2,"y":13,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-10,11,13,-2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0037","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=12x+(-11)y，x=-1、y=14。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-166, 179)","explanation_zh":"同時交換有序值=(-166, 179)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113037,"parameters":{"a":12,"b":-11,"x":-1,"y":14,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-11,12,14,-1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0038","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=13x+(-12)y，x=0、y=15。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-180, 195)","explanation_zh":"同時交換有序值=(-180, 195)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113038,"parameters":{"a":13,"b":-12,"x":0,"y":15,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-12,13,15,0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0039","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=14x+(-13)y，x=1、y=16。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-194, 211)","explanation_zh":"同時交換有序值=(-194, 211)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113039,"parameters":{"a":14,"b":-13,"x":1,"y":16,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-13,14,16,1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0040","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=15x+(-14)y，x=2、y=17。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-208, 227)","explanation_zh":"同時交換有序值=(-208, 227)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113040,"parameters":{"a":15,"b":-14,"x":2,"y":17,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-14,15,17,2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0041","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=16x+(-15)y，x=-2、y=18。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-302, 318)","explanation_zh":"同時交換有序值=(-302, 318)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113041,"parameters":{"a":16,"b":-15,"x":-2,"y":18,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-15,16,18,-2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0042","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=17x+(-16)y，x=-1、y=19。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-321, 339)","explanation_zh":"同時交換有序值=(-321, 339)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113042,"parameters":{"a":17,"b":-16,"x":-1,"y":19,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-16,17,19,-1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0043","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=18x+(-17)y，x=0、y=20。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-340, 360)","explanation_zh":"同時交換有序值=(-340, 360)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113043,"parameters":{"a":18,"b":-17,"x":0,"y":20,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-17,18,20,0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0044","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=19x+(-18)y，x=1、y=21。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-359, 381)","explanation_zh":"同時交換有序值=(-359, 381)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113044,"parameters":{"a":19,"b":-18,"x":1,"y":21,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-18,19,21,1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0045","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=20x+(-19)y，x=2、y=22。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-378, 402)","explanation_zh":"同時交換有序值=(-378, 402)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113045,"parameters":{"a":20,"b":-19,"x":2,"y":22,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-19,20,22,2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0046","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=21x+(-20)y，x=-2、y=23。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-502, 523)","explanation_zh":"同時交換有序值=(-502, 523)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113046,"parameters":{"a":21,"b":-20,"x":-2,"y":23,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-20,21,23,-2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0047","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=22x+(-21)y，x=-1、y=24。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-526, 549)","explanation_zh":"同時交換有序值=(-526, 549)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113047,"parameters":{"a":22,"b":-21,"x":-1,"y":24,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-21,22,24,-1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0048","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=23x+(-22)y，x=0、y=25。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-550, 575)","explanation_zh":"同時交換有序值=(-550, 575)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113048,"parameters":{"a":23,"b":-22,"x":0,"y":25,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-22,23,25,0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0049","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=24x+(-23)y，x=1、y=26。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-574, 601)","explanation_zh":"同時交換有序值=(-574, 601)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113049,"parameters":{"a":24,"b":-23,"x":1,"y":26,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-23,24,26,1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0050","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"兩變數同時交換的有序值","stem_zh":"有理數Q；表達式非方程式，E(x,y)=25x+(-24)y，x=2、y=27。以同時代換交換x與y，依序求原值與交換值的整數對。","answer":{"kind":"expression","value":"(-598, 627)","explanation_zh":"同時交換有序值=(-598, 627)。兩個新環境同時從原環境取得，不逐步覆寫；先後代換不能冒充同時交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩變數同時交換的有序值"]},"variant":{"family_id":"qf-density11-expression-simultaneous-swap","seed":202610113050,"parameters":{"a":25,"b":-24,"x":2,"y":27,"operation":"density11_expression_simultaneous_swap","domain":"typed_Q_two_variable_slice","semantic_template":"qf-density11-expression-simultaneous-swap/[-24,25,27,2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0051","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=0，內層局部x=0詞法遮蔽外層，c=1。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(1, 1)","explanation_zh":"外層與遮蔽內層值=(1, 1)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113051,"parameters":{"outer":0,"inner":0,"c":1,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[0,0,1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0052","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=3，內層局部x=-2詞法遮蔽外層，c=4。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(7, 2)","explanation_zh":"外層與遮蔽內層值=(7, 2)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113052,"parameters":{"outer":3,"inner":-2,"c":4,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[3,-2,4]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0053","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=-10，內層局部x=-1詞法遮蔽外層，c=0。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(-10, -1)","explanation_zh":"外層與遮蔽內層值=(-10, -1)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113053,"parameters":{"outer":-10,"inner":-1,"c":0,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[-10,-1,0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0054","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=-9，內層局部x=-2詞法遮蔽外層，c=1。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(-8, -1)","explanation_zh":"外層與遮蔽內層值=(-8, -1)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113054,"parameters":{"outer":-9,"inner":-2,"c":1,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[-9,-2,1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0055","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=-8，內層局部x=-3詞法遮蔽外層，c=-2。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(-10, -5)","explanation_zh":"外層與遮蔽內層值=(-10, -5)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113055,"parameters":{"outer":-8,"inner":-3,"c":-2,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[-8,-3,-2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0056","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=-7，內層局部x=-4詞法遮蔽外層，c=-1。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(-8, -5)","explanation_zh":"外層與遮蔽內層值=(-8, -5)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113056,"parameters":{"outer":-7,"inner":-4,"c":-1,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[-7,-4,-1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0057","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=-6，內層局部x=-5詞法遮蔽外層，c=0。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(-6, -5)","explanation_zh":"外層與遮蔽內層值=(-6, -5)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113057,"parameters":{"outer":-6,"inner":-5,"c":0,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[-6,-5,0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0058","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=-5，內層局部x=-6詞法遮蔽外層，c=1。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(-4, -5)","explanation_zh":"外層與遮蔽內層值=(-4, -5)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113058,"parameters":{"outer":-5,"inner":-6,"c":1,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[-5,-6,1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0059","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=-4，內層局部x=-7詞法遮蔽外層，c=-2。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(-6, -9)","explanation_zh":"外層與遮蔽內層值=(-6, -9)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113059,"parameters":{"outer":-4,"inner":-7,"c":-2,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[-4,-7,-2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0060","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=-3，內層局部x=-8詞法遮蔽外層，c=-1。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(-4, -9)","explanation_zh":"外層與遮蔽內層值=(-4, -9)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113060,"parameters":{"outer":-3,"inner":-8,"c":-1,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[-3,-8,-1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0061","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=-2，內層局部x=-9詞法遮蔽外層，c=0。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(-2, -9)","explanation_zh":"外層與遮蔽內層值=(-2, -9)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113061,"parameters":{"outer":-2,"inner":-9,"c":0,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[-2,-9,0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0062","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=-1，內層局部x=-10詞法遮蔽外層，c=1。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(0, -9)","explanation_zh":"外層與遮蔽內層值=(0, -9)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113062,"parameters":{"outer":-1,"inner":-10,"c":1,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[-1,-10,1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0063","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=0，內層局部x=-11詞法遮蔽外層，c=-2。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(-2, -13)","explanation_zh":"外層與遮蔽內層值=(-2, -13)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113063,"parameters":{"outer":0,"inner":-11,"c":-2,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[0,-11,-2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0064","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=1，內層局部x=-12詞法遮蔽外層，c=-1。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(0, -13)","explanation_zh":"外層與遮蔽內層值=(0, -13)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113064,"parameters":{"outer":1,"inner":-12,"c":-1,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[1,-12,-1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0065","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=2，內層局部x=-13詞法遮蔽外層，c=0。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(2, -13)","explanation_zh":"外層與遮蔽內層值=(2, -13)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113065,"parameters":{"outer":2,"inner":-13,"c":0,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[2,-13,0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0066","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=3，內層局部x=-14詞法遮蔽外層，c=1。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(4, -13)","explanation_zh":"外層與遮蔽內層值=(4, -13)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113066,"parameters":{"outer":3,"inner":-14,"c":1,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[3,-14,1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0067","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=4，內層局部x=-15詞法遮蔽外層，c=-2。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(2, -17)","explanation_zh":"外層與遮蔽內層值=(2, -17)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113067,"parameters":{"outer":4,"inner":-15,"c":-2,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[4,-15,-2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0068","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=5，內層局部x=-16詞法遮蔽外層，c=-1。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(4, -17)","explanation_zh":"外層與遮蔽內層值=(4, -17)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113068,"parameters":{"outer":5,"inner":-16,"c":-1,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[5,-16,-1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0069","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=6，內層局部x=-17詞法遮蔽外層，c=0。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(6, -17)","explanation_zh":"外層與遮蔽內層值=(6, -17)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113069,"parameters":{"outer":6,"inner":-17,"c":0,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[6,-17,0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0070","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=7，內層局部x=-18詞法遮蔽外層，c=1。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(8, -17)","explanation_zh":"外層與遮蔽內層值=(8, -17)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113070,"parameters":{"outer":7,"inner":-18,"c":1,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[7,-18,1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0071","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=8，內層局部x=-19詞法遮蔽外層，c=-2。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(6, -21)","explanation_zh":"外層與遮蔽內層值=(6, -21)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113071,"parameters":{"outer":8,"inner":-19,"c":-2,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[8,-19,-2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0072","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=9，內層局部x=-20詞法遮蔽外層，c=-1。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(8, -21)","explanation_zh":"外層與遮蔽內層值=(8, -21)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113072,"parameters":{"outer":9,"inner":-20,"c":-1,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[9,-20,-1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0073","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=10，內層局部x=-21詞法遮蔽外層，c=0。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(10, -21)","explanation_zh":"外層與遮蔽內層值=(10, -21)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113073,"parameters":{"outer":10,"inner":-21,"c":0,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[10,-21,0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0074","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=11，內層局部x=-22詞法遮蔽外層，c=1。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(12, -21)","explanation_zh":"外層與遮蔽內層值=(12, -21)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113074,"parameters":{"outer":11,"inner":-22,"c":1,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[11,-22,1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0075","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"詞法遮蔽的內外層值","stem_zh":"有理數Q；表達式非方程式。外層x=12，內層局部x=-23詞法遮蔽外層，c=-2。依序求外層及內層x+c的整數值。","answer":{"kind":"expression","value":"(10, -25)","explanation_zh":"外層與遮蔽內層值=(10, -25)。各層用自己的綁定後加c；內層不改外層，局部遮蔽不是外層賦值更新。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["詞法遮蔽的內外層值"]},"variant":{"family_id":"qf-density11-expression-local-shadow-pair","seed":202610113075,"parameters":{"outer":12,"inner":-23,"c":-2,"binding_mode":"lexical_shadow_no_mutation","operation":"density11_expression_local_shadow_pair","domain":"typed_Q_scoped_binding_slice","semantic_template":"qf-density11-expression-local-shadow-pair/[12,-23,-2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0076","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=0/(x−(1))。原式定義域排除x=1；有序候選=[1/1, 2/1, 0/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 0/1, 0/1])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 0/1, 0/1])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113076,"parameters":{"a":0,"b":1,"candidates":[[1,1],[2,1],[0,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[\"zero_numerator\",[\"hole\",\"valid\",\"valid\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0077","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=5/(x−(-2))。原式定義域排除x=-2；有序候選=[-2/1, -2/1, -2/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 否, 否], [未定義, 未定義, 未定義])","explanation_zh":"定義域資格與求值=([否, 否, 否], [未定義, 未定義, 未定義])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113077,"parameters":{"a":5,"b":-2,"candidates":[[-2,1],[-2,1],[-2,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[\"all_holes\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0078","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=2/(x−(0))。原式定義域排除x=0；有序候選=[0/1, 1/1, -1/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 2/1, -2/1])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 2/1, -2/1])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113078,"parameters":{"a":2,"b":0,"candidates":[[0,1],[1,1],[-1,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[2,[\"0/1\",\"1/1\",\"-1/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0079","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=2/(x−(1))。原式定義域排除x=1；有序候選=[1/1, 3/1, -4/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 1/1, -2/5])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 1/1, -2/5])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113079,"parameters":{"a":2,"b":1,"candidates":[[1,1],[6,2],[-4,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[2,[\"0/1\",\"2/1\",\"-5/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0080","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=3/(x−(2))。原式定義域排除x=2；有序候選=[2/1, 9/2, -4/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 6/5, -1/2])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 6/5, -1/2])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113080,"parameters":{"a":3,"b":2,"candidates":[[2,1],[9,2],[-4,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[3,[\"0/1\",\"5/2\",\"-6/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0081","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=4/(x−(-2))。原式定義域排除x=-2；有序候選=[-2/1, 1/1, -9/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 4/3, -4/7])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 4/3, -4/7])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113081,"parameters":{"a":4,"b":-2,"candidates":[[-2,1],[2,2],[-9,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[4,[\"0/1\",\"3/1\",\"-7/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0082","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=5/(x−(-1))。原式定義域排除x=-1；有序候選=[-1/1, 5/2, -9/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 10/7, -5/8])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 10/7, -5/8])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113082,"parameters":{"a":5,"b":-1,"candidates":[[-1,1],[5,2],[-9,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[5,[\"0/1\",\"7/2\",\"-8/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0083","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=6/(x−(0))。原式定義域排除x=0；有序候選=[0/1, 4/1, -9/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 3/2, -2/3])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 3/2, -2/3])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113083,"parameters":{"a":6,"b":0,"candidates":[[0,1],[8,2],[-9,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[6,[\"0/1\",\"4/1\",\"-9/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0084","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=7/(x−(1))。原式定義域排除x=1；有序候選=[1/1, 11/2, -9/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 14/9, -7/10])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 14/9, -7/10])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113084,"parameters":{"a":7,"b":1,"candidates":[[1,1],[11,2],[-9,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[7,[\"0/1\",\"9/2\",\"-10/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0085","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=8/(x−(2))。原式定義域排除x=2；有序候選=[2/1, 7/1, -9/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 8/5, -8/11])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 8/5, -8/11])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113085,"parameters":{"a":8,"b":2,"candidates":[[2,1],[14,2],[-9,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[8,[\"0/1\",\"5/1\",\"-11/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0086","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=9/(x−(-2))。原式定義域排除x=-2；有序候選=[-2/1, 7/2, -14/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 18/11, -3/4])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 18/11, -3/4])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113086,"parameters":{"a":9,"b":-2,"candidates":[[-2,1],[7,2],[-14,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[9,[\"0/1\",\"11/2\",\"-12/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0087","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=10/(x−(-1))。原式定義域排除x=-1；有序候選=[-1/1, 5/1, -14/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 5/3, -10/13])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 5/3, -10/13])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113087,"parameters":{"a":10,"b":-1,"candidates":[[-1,1],[10,2],[-14,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[10,[\"0/1\",\"6/1\",\"-13/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0088","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=11/(x−(0))。原式定義域排除x=0；有序候選=[0/1, 13/2, -14/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 22/13, -11/14])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 22/13, -11/14])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113088,"parameters":{"a":11,"b":0,"candidates":[[0,1],[13,2],[-14,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[11,[\"0/1\",\"13/2\",\"-14/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0089","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=12/(x−(1))。原式定義域排除x=1；有序候選=[1/1, 8/1, -14/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 12/7, -4/5])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 12/7, -4/5])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113089,"parameters":{"a":12,"b":1,"candidates":[[1,1],[16,2],[-14,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[12,[\"0/1\",\"7/1\",\"-15/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0090","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=13/(x−(2))。原式定義域排除x=2；有序候選=[2/1, 19/2, -14/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 26/15, -13/16])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 26/15, -13/16])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113090,"parameters":{"a":13,"b":2,"candidates":[[2,1],[19,2],[-14,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[13,[\"0/1\",\"15/2\",\"-16/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0091","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=14/(x−(-2))。原式定義域排除x=-2；有序候選=[-2/1, 6/1, -19/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 7/4, -14/17])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 7/4, -14/17])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113091,"parameters":{"a":14,"b":-2,"candidates":[[-2,1],[12,2],[-19,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[14,[\"0/1\",\"8/1\",\"-17/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0092","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=15/(x−(-1))。原式定義域排除x=-1；有序候選=[-1/1, 15/2, -19/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 30/17, -5/6])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 30/17, -5/6])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113092,"parameters":{"a":15,"b":-1,"candidates":[[-1,1],[15,2],[-19,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[15,[\"0/1\",\"17/2\",\"-18/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0093","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=16/(x−(0))。原式定義域排除x=0；有序候選=[0/1, 9/1, -19/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 16/9, -16/19])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 16/9, -16/19])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113093,"parameters":{"a":16,"b":0,"candidates":[[0,1],[18,2],[-19,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[16,[\"0/1\",\"9/1\",\"-19/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0094","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=17/(x−(1))。原式定義域排除x=1；有序候選=[1/1, 21/2, -19/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 34/19, -17/20])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 34/19, -17/20])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113094,"parameters":{"a":17,"b":1,"candidates":[[1,1],[21,2],[-19,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[17,[\"0/1\",\"19/2\",\"-20/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0095","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=18/(x−(2))。原式定義域排除x=2；有序候選=[2/1, 12/1, -19/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 9/5, -6/7])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 9/5, -6/7])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113095,"parameters":{"a":18,"b":2,"candidates":[[2,1],[24,2],[-19,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[18,[\"0/1\",\"10/1\",\"-21/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0096","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=19/(x−(-2))。原式定義域排除x=-2；有序候選=[-2/1, 17/2, -24/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 38/21, -19/22])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 38/21, -19/22])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113096,"parameters":{"a":19,"b":-2,"candidates":[[-2,1],[17,2],[-24,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[19,[\"0/1\",\"21/2\",\"-22/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0097","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=20/(x−(-1))。原式定義域排除x=-1；有序候選=[-1/1, 10/1, -24/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 20/11, -20/23])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 20/11, -20/23])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113097,"parameters":{"a":20,"b":-1,"candidates":[[-1,1],[20,2],[-24,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[20,[\"0/1\",\"11/1\",\"-23/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0098","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=21/(x−(0))。原式定義域排除x=0；有序候選=[0/1, 23/2, -24/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 42/23, -7/8])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 42/23, -7/8])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113098,"parameters":{"a":21,"b":0,"candidates":[[0,1],[23,2],[-24,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[21,[\"0/1\",\"23/2\",\"-24/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0099","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=22/(x−(1))。原式定義域排除x=1；有序候選=[1/1, 13/1, -24/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 11/6, -22/25])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 11/6, -22/25])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113099,"parameters":{"a":22,"b":1,"candidates":[[1,1],[26,2],[-24,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[22,[\"0/1\",\"12/1\",\"-25/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r03-variable-expression-0100","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"原式定義域資格與有序求值","stem_zh":"有理數Q；表達式非方程式，原式E(x)=23/(x−(2))。原式定義域排除x=2；有序候選=[2/1, 29/2, -24/1]。依序答 (三項合法資格列表, 三項E值列表)，排除點寫未定義。","answer":{"kind":"expression","value":"([否, 是, 是], [未定義, 46/25, -23/26])","explanation_zh":"定義域資格與求值=([否, 是, 是], [未定義, 46/25, -23/26])。先檢查原式排除點再求值；零分子也不能消除原分母為零的空洞，不擴張原式定義域。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["原式定義域資格與有序求值"]},"variant":{"family_id":"qf-density11-expression-domain-candidate","seed":202610113100,"parameters":{"a":23,"b":2,"candidates":[[2,1],[29,2],[-24,1]],"operation":"density11_expression_domain_candidate","domain":"Q_partial_rational_expression","semantic_template":"qf-density11-expression-domain-candidate/[23,[\"0/1\",\"25/2\",\"-26/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}