{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0001","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[0]、第二階段B=[0]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[0, 0]]","explanation_zh":"全部有序基本結果=[[0, 0]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116001,"parameters":{"A":[0],"B":[0],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[0],[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-r06-sample-space-0002","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-1, 1]、第二階段B=[0, 2]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-1, 0], [-1, 2], [1, 0], [1, 2]]","explanation_zh":"全部有序基本結果=[[-1, 0], [-1, 2], [1, 0], [1, 2]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116002,"parameters":{"A":[-1,1],"B":[0,2],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-1,1],[0,2]]"}},"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-r06-sample-space-0003","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-2, 2]、第二階段B=[-1, 0, 3]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-2, -1], [-2, 0], [-2, 3], [2, -1], [2, 0], [2, 3]]","explanation_zh":"全部有序基本結果=[[-2, -1], [-2, 0], [-2, 3], [2, -1], [2, 0], [2, 3]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116003,"parameters":{"A":[-2,2],"B":[-1,0,3],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-2,2],[-1,0,3]]"}},"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-r06-sample-space-0004","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-3, 3]、第二階段B=[0, 4]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-3, 0], [-3, 4], [3, 0], [3, 4]]","explanation_zh":"全部有序基本結果=[[-3, 0], [-3, 4], [3, 0], [3, 4]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116004,"parameters":{"A":[-3,3],"B":[0,4],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-3,3],[0,4]]"}},"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-r06-sample-space-0005","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-4, 4]、第二階段B=[-1, 0, 5]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-4, -1], [-4, 0], [-4, 5], [4, -1], [4, 0], [4, 5]]","explanation_zh":"全部有序基本結果=[[-4, -1], [-4, 0], [-4, 5], [4, -1], [4, 0], [4, 5]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116005,"parameters":{"A":[-4,4],"B":[-1,0,5],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-4,4],[-1,0,5]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0006","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-5, 5]、第二階段B=[0, 6]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-5, 0], [-5, 6], [5, 0], [5, 6]]","explanation_zh":"全部有序基本結果=[[-5, 0], [-5, 6], [5, 0], [5, 6]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116006,"parameters":{"A":[-5,5],"B":[0,6],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-5,5],[0,6]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0007","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-6, 6]、第二階段B=[-1, 0, 7]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-6, -1], [-6, 0], [-6, 7], [6, -1], [6, 0], [6, 7]]","explanation_zh":"全部有序基本結果=[[-6, -1], [-6, 0], [-6, 7], [6, -1], [6, 0], [6, 7]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116007,"parameters":{"A":[-6,6],"B":[-1,0,7],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-6,6],[-1,0,7]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0008","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-7, 7]、第二階段B=[0, 8]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-7, 0], [-7, 8], [7, 0], [7, 8]]","explanation_zh":"全部有序基本結果=[[-7, 0], [-7, 8], [7, 0], [7, 8]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116008,"parameters":{"A":[-7,7],"B":[0,8],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-7,7],[0,8]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0009","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-8, 8]、第二階段B=[-1, 0, 9]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-8, -1], [-8, 0], [-8, 9], [8, -1], [8, 0], [8, 9]]","explanation_zh":"全部有序基本結果=[[-8, -1], [-8, 0], [-8, 9], [8, -1], [8, 0], [8, 9]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116009,"parameters":{"A":[-8,8],"B":[-1,0,9],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-8,8],[-1,0,9]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0010","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-9, 9]、第二階段B=[0, 10]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-9, 0], [-9, 10], [9, 0], [9, 10]]","explanation_zh":"全部有序基本結果=[[-9, 0], [-9, 10], [9, 0], [9, 10]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116010,"parameters":{"A":[-9,9],"B":[0,10],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-9,9],[0,10]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0011","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-10, 10]、第二階段B=[-1, 0, 11]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-10, -1], [-10, 0], [-10, 11], [10, -1], [10, 0], [10, 11]]","explanation_zh":"全部有序基本結果=[[-10, -1], [-10, 0], [-10, 11], [10, -1], [10, 0], [10, 11]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116011,"parameters":{"A":[-10,10],"B":[-1,0,11],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-10,10],[-1,0,11]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0012","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-11, 11]、第二階段B=[0, 12]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-11, 0], [-11, 12], [11, 0], [11, 12]]","explanation_zh":"全部有序基本結果=[[-11, 0], [-11, 12], [11, 0], [11, 12]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116012,"parameters":{"A":[-11,11],"B":[0,12],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-11,11],[0,12]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0013","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-12, 12]、第二階段B=[-1, 0, 13]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-12, -1], [-12, 0], [-12, 13], [12, -1], [12, 0], [12, 13]]","explanation_zh":"全部有序基本結果=[[-12, -1], [-12, 0], [-12, 13], [12, -1], [12, 0], [12, 13]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116013,"parameters":{"A":[-12,12],"B":[-1,0,13],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-12,12],[-1,0,13]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0014","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-13, 13]、第二階段B=[0, 14]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-13, 0], [-13, 14], [13, 0], [13, 14]]","explanation_zh":"全部有序基本結果=[[-13, 0], [-13, 14], [13, 0], [13, 14]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116014,"parameters":{"A":[-13,13],"B":[0,14],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-13,13],[0,14]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0015","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-14, 14]、第二階段B=[-1, 0, 15]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-14, -1], [-14, 0], [-14, 15], [14, -1], [14, 0], [14, 15]]","explanation_zh":"全部有序基本結果=[[-14, -1], [-14, 0], [-14, 15], [14, -1], [14, 0], [14, 15]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116015,"parameters":{"A":[-14,14],"B":[-1,0,15],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-14,14],[-1,0,15]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0016","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-15, 15]、第二階段B=[0, 16]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-15, 0], [-15, 16], [15, 0], [15, 16]]","explanation_zh":"全部有序基本結果=[[-15, 0], [-15, 16], [15, 0], [15, 16]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116016,"parameters":{"A":[-15,15],"B":[0,16],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-15,15],[0,16]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0017","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-16, 16]、第二階段B=[-1, 0, 17]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-16, -1], [-16, 0], [-16, 17], [16, -1], [16, 0], [16, 17]]","explanation_zh":"全部有序基本結果=[[-16, -1], [-16, 0], [-16, 17], [16, -1], [16, 0], [16, 17]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116017,"parameters":{"A":[-16,16],"B":[-1,0,17],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-16,16],[-1,0,17]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0018","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-17, 17]、第二階段B=[0, 18]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-17, 0], [-17, 18], [17, 0], [17, 18]]","explanation_zh":"全部有序基本結果=[[-17, 0], [-17, 18], [17, 0], [17, 18]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116018,"parameters":{"A":[-17,17],"B":[0,18],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-17,17],[0,18]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0019","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-18, 18]、第二階段B=[-1, 0, 19]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-18, -1], [-18, 0], [-18, 19], [18, -1], [18, 0], [18, 19]]","explanation_zh":"全部有序基本結果=[[-18, -1], [-18, 0], [-18, 19], [18, -1], [18, 0], [18, 19]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116019,"parameters":{"A":[-18,18],"B":[-1,0,19],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-18,18],[-1,0,19]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0020","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-19, 19]、第二階段B=[0, 20]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-19, 0], [-19, 20], [19, 0], [19, 20]]","explanation_zh":"全部有序基本結果=[[-19, 0], [-19, 20], [19, 0], [19, 20]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116020,"parameters":{"A":[-19,19],"B":[0,20],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-19,19],[0,20]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0021","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-20, 20]、第二階段B=[-1, 0, 21]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-20, -1], [-20, 0], [-20, 21], [20, -1], [20, 0], [20, 21]]","explanation_zh":"全部有序基本結果=[[-20, -1], [-20, 0], [-20, 21], [20, -1], [20, 0], [20, 21]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116021,"parameters":{"A":[-20,20],"B":[-1,0,21],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-20,20],[-1,0,21]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0022","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-21, 21]、第二階段B=[0, 22]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-21, 0], [-21, 22], [21, 0], [21, 22]]","explanation_zh":"全部有序基本結果=[[-21, 0], [-21, 22], [21, 0], [21, 22]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116022,"parameters":{"A":[-21,21],"B":[0,22],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-21,21],[0,22]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0023","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-22, 22]、第二階段B=[-1, 0, 23]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-22, -1], [-22, 0], [-22, 23], [22, -1], [22, 0], [22, 23]]","explanation_zh":"全部有序基本結果=[[-22, -1], [-22, 0], [-22, 23], [22, -1], [22, 0], [22, 23]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116023,"parameters":{"A":[-22,22],"B":[-1,0,23],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-22,22],[-1,0,23]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0024","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-23, 23]、第二階段B=[0, 24]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-23, 0], [-23, 24], [23, 0], [23, 24]]","explanation_zh":"全部有序基本結果=[[-23, 0], [-23, 24], [23, 0], [23, 24]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116024,"parameters":{"A":[-23,23],"B":[0,24],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-23,23],[0,24]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0025","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"兩階段全部有序基本結果","stem_zh":"基本可能結果協定：第一階段A=[-24, 24]、第二階段B=[-1, 0, 25]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。","answer":{"kind":"expression","value":"[[-24, -1], [-24, 0], [-24, 25], [24, -1], [24, 0], [24, 25]]","explanation_zh":"全部有序基本結果=[[-24, -1], [-24, 0], [-24, 25], [24, -1], [24, 0], [24, 25]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["兩階段全部有序基本結果"]},"variant":{"family_id":"qf-density11-sample-ordered-product","seed":202610116025,"parameters":{"A":[-24,24],"B":[-1,0,25],"operation":"density11_sample_ordered_product","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-ordered-product/[[-24,24],[-1,0,25]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0026","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,0}，記錄表=[0]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([0], [[0]])","explanation_zh":"記錄像與原結果纖維=([0], [[0]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116026,"parameters":{"n":1,"recording":[0],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[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-r06-sample-space-0027","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[2, 1, 2, 1]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([1, 2], [[1, 3], [0, 2]])","explanation_zh":"記錄像與原結果纖維=([1, 2], [[1, 3], [0, 2]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116027,"parameters":{"n":4,"recording":[2,1,2,1],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[2,1,2,1]"}},"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-r06-sample-space-0028","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-2, 0, -2, 2]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-2, 0, 2], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-2, 0, 2], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116028,"parameters":{"n":4,"recording":[-2,0,-2,2],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-2,0,-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-r06-sample-space-0029","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-3, 0, -3, 3]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-3, 0, 3], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-3, 0, 3], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116029,"parameters":{"n":4,"recording":[-3,0,-3,3],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-3,0,-3,3]"}},"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-r06-sample-space-0030","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-4, 0, -4, 4]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-4, 0, 4], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-4, 0, 4], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116030,"parameters":{"n":4,"recording":[-4,0,-4,4],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-4,0,-4,4]"}},"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-r06-sample-space-0031","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-5, 0, -5, 5]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-5, 0, 5], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-5, 0, 5], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116031,"parameters":{"n":4,"recording":[-5,0,-5,5],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-5,0,-5,5]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0032","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-6, 0, -6, 6]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-6, 0, 6], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-6, 0, 6], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116032,"parameters":{"n":4,"recording":[-6,0,-6,6],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-6,0,-6,6]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0033","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-7, 0, -7, 7]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-7, 0, 7], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-7, 0, 7], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116033,"parameters":{"n":4,"recording":[-7,0,-7,7],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-7,0,-7,7]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0034","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-8, 0, -8, 8]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-8, 0, 8], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-8, 0, 8], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116034,"parameters":{"n":4,"recording":[-8,0,-8,8],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-8,0,-8,8]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0035","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-9, 0, -9, 9]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-9, 0, 9], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-9, 0, 9], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116035,"parameters":{"n":4,"recording":[-9,0,-9,9],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-9,0,-9,9]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0036","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-10, 0, -10, 10]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-10, 0, 10], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-10, 0, 10], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116036,"parameters":{"n":4,"recording":[-10,0,-10,10],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-10,0,-10,10]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0037","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-11, 0, -11, 11]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-11, 0, 11], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-11, 0, 11], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116037,"parameters":{"n":4,"recording":[-11,0,-11,11],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-11,0,-11,11]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0038","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-12, 0, -12, 12]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-12, 0, 12], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-12, 0, 12], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116038,"parameters":{"n":4,"recording":[-12,0,-12,12],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-12,0,-12,12]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0039","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-13, 0, -13, 13]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-13, 0, 13], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-13, 0, 13], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116039,"parameters":{"n":4,"recording":[-13,0,-13,13],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-13,0,-13,13]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0040","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-14, 0, -14, 14]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-14, 0, 14], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-14, 0, 14], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116040,"parameters":{"n":4,"recording":[-14,0,-14,14],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-14,0,-14,14]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0041","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-15, 0, -15, 15]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-15, 0, 15], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-15, 0, 15], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116041,"parameters":{"n":4,"recording":[-15,0,-15,15],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-15,0,-15,15]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0042","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-16, 0, -16, 16]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-16, 0, 16], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-16, 0, 16], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116042,"parameters":{"n":4,"recording":[-16,0,-16,16],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-16,0,-16,16]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0043","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-17, 0, -17, 17]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-17, 0, 17], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-17, 0, 17], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116043,"parameters":{"n":4,"recording":[-17,0,-17,17],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-17,0,-17,17]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0044","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-18, 0, -18, 18]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-18, 0, 18], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-18, 0, 18], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116044,"parameters":{"n":4,"recording":[-18,0,-18,18],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-18,0,-18,18]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0045","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-19, 0, -19, 19]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-19, 0, 19], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-19, 0, 19], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116045,"parameters":{"n":4,"recording":[-19,0,-19,19],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-19,0,-19,19]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0046","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-20, 0, -20, 20]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-20, 0, 20], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-20, 0, 20], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116046,"parameters":{"n":4,"recording":[-20,0,-20,20],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-20,0,-20,20]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0047","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-21, 0, -21, 21]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-21, 0, 21], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-21, 0, 21], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116047,"parameters":{"n":4,"recording":[-21,0,-21,21],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-21,0,-21,21]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0048","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-22, 0, -22, 22]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-22, 0, 22], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-22, 0, 22], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116048,"parameters":{"n":4,"recording":[-22,0,-22,22],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-22,0,-22,22]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0049","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-23, 0, -23, 23]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-23, 0, 23], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-23, 0, 23], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116049,"parameters":{"n":4,"recording":[-23,0,-23,23],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-23,0,-23,23]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0050","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"記錄像與對齊的原結果纖維","stem_zh":"基本可能結果S={0,…,3}，記錄表=[-24, 0, -24, 24]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。","answer":{"kind":"expression","value":"([-24, 0, 24], [[0, 2], [1], [3]])","explanation_zh":"記錄像與原結果纖維=([-24, 0, 24], [[0, 2], [1], [3]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["記錄像與對齊的原結果纖維"]},"variant":{"family_id":"qf-density11-sample-recording-image","seed":202610116050,"parameters":{"n":4,"recording":[-24,0,-24,24],"operation":"density11_sample_recording_image","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-recording-image/[-24,0,-24,24]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0051","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,0}；待核原列=[0]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([], [])","explanation_zh":"清單漏列與域外項=([], [])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116051,"parameters":{"n":1,"candidates":[0],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0052","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,0}；待核原列=[]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([0], [])","explanation_zh":"清單漏列與域外項=([0], [])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116052,"parameters":{"n":1,"candidates":[],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[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-r06-sample-space-0053","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,2}；待核原列=[0, 1, 2, 100]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([], [100])","explanation_zh":"清單漏列與域外項=([], [100])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116053,"parameters":{"n":3,"candidates":[0,1,2,100],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[],[100]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0054","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,3}；待核原列=[0, 1, 2, -4]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([3], [-4])","explanation_zh":"清單漏列與域外項=([3], [-4])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116054,"parameters":{"n":4,"candidates":[0,1,2,-4],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[3],[-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-r06-sample-space-0055","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,4}；待核原列=[0, 1, 2, 3, -5]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([4], [-5])","explanation_zh":"清單漏列與域外項=([4], [-5])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116055,"parameters":{"n":5,"candidates":[0,1,2,3,-5],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[4],[-5]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0056","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,5}；待核原列=[0, 1, 2, 3, 4, -6]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([5], [-6])","explanation_zh":"清單漏列與域外項=([5], [-6])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116056,"parameters":{"n":6,"candidates":[0,1,2,3,4,-6],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[5],[-6]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0057","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,6}；待核原列=[0, 1, 2, 3, 4, 5, -7]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([6], [-7])","explanation_zh":"清單漏列與域外項=([6], [-7])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116057,"parameters":{"n":7,"candidates":[0,1,2,3,4,5,-7],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[6],[-7]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0058","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,7}；待核原列=[0, 1, 2, 3, 4, 5, 6, -8]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([7], [-8])","explanation_zh":"清單漏列與域外項=([7], [-8])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116058,"parameters":{"n":8,"candidates":[0,1,2,3,4,5,6,-8],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[7],[-8]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0059","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,0}；待核原列=[-9]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([0], [-9])","explanation_zh":"清單漏列與域外項=([0], [-9])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116059,"parameters":{"n":1,"candidates":[-9],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[0],[-9]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0060","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,1}；待核原列=[0, -10]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([1], [-10])","explanation_zh":"清單漏列與域外項=([1], [-10])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116060,"parameters":{"n":2,"candidates":[0,-10],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[1],[-10]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0061","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,2}；待核原列=[0, 2, -11]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([1], [-11])","explanation_zh":"清單漏列與域外項=([1], [-11])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116061,"parameters":{"n":3,"candidates":[0,2,-11],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[1],[-11]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0062","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,3}；待核原列=[0, 1, 2, -12]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([3], [-12])","explanation_zh":"清單漏列與域外項=([3], [-12])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116062,"parameters":{"n":4,"candidates":[0,1,2,-12],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[3],[-12]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0063","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,4}；待核原列=[0, 1, 3, 4, -13]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([2], [-13])","explanation_zh":"清單漏列與域外項=([2], [-13])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116063,"parameters":{"n":5,"candidates":[0,1,3,4,-13],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[2],[-13]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0064","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,5}；待核原列=[0, 2, 3, 4, 5, -14]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([1], [-14])","explanation_zh":"清單漏列與域外項=([1], [-14])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116064,"parameters":{"n":6,"candidates":[0,2,3,4,5,-14],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[1],[-14]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0065","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,6}；待核原列=[1, 2, 3, 4, 5, 6, -15]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([0], [-15])","explanation_zh":"清單漏列與域外項=([0], [-15])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116065,"parameters":{"n":7,"candidates":[1,2,3,4,5,6,-15],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[0],[-15]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0066","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,7}；待核原列=[0, 1, 2, 3, 4, 5, 6, -16]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([7], [-16])","explanation_zh":"清單漏列與域外項=([7], [-16])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116066,"parameters":{"n":8,"candidates":[0,1,2,3,4,5,6,-16],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[7],[-16]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0067","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,0}；待核原列=[-17]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([0], [-17])","explanation_zh":"清單漏列與域外項=([0], [-17])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116067,"parameters":{"n":1,"candidates":[-17],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[0],[-17]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0068","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,1}；待核原列=[0, -18]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([1], [-18])","explanation_zh":"清單漏列與域外項=([1], [-18])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116068,"parameters":{"n":2,"candidates":[0,-18],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[1],[-18]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0069","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,2}；待核原列=[1, 2, -19]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([0], [-19])","explanation_zh":"清單漏列與域外項=([0], [-19])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116069,"parameters":{"n":3,"candidates":[1,2,-19],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[0],[-19]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0070","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,3}；待核原列=[0, 1, 2, -20]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([3], [-20])","explanation_zh":"清單漏列與域外項=([3], [-20])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116070,"parameters":{"n":4,"candidates":[0,1,2,-20],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[3],[-20]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0071","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,4}；待核原列=[1, 2, 3, 4, -21]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([0], [-21])","explanation_zh":"清單漏列與域外項=([0], [-21])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116071,"parameters":{"n":5,"candidates":[1,2,3,4,-21],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[0],[-21]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0072","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,5}；待核原列=[0, 1, 2, 4, 5, -22]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([3], [-22])","explanation_zh":"清單漏列與域外項=([3], [-22])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116072,"parameters":{"n":6,"candidates":[0,1,2,4,5,-22],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[3],[-22]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0073","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,6}；待核原列=[0, 2, 3, 4, 5, 6, -23]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([1], [-23])","explanation_zh":"清單漏列與域外項=([1], [-23])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116073,"parameters":{"n":7,"candidates":[0,2,3,4,5,6,-23],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[1],[-23]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0074","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,7}；待核原列=[0, 1, 2, 3, 4, 5, 6, -24]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([7], [-24])","explanation_zh":"清單漏列與域外項=([7], [-24])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116074,"parameters":{"n":8,"candidates":[0,1,2,3,4,5,6,-24],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[7],[-24]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0075","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果清單的漏列與域外項","stem_zh":"基本可能結果S={0,…,0}；待核原列=[-25]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。","answer":{"kind":"expression","value":"([0], [-25])","explanation_zh":"清單漏列與域外項=([0], [-25])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果清單的漏列與域外項"]},"variant":{"family_id":"qf-density11-sample-list-completeness-defects","seed":202610116075,"parameters":{"n":1,"candidates":[-25],"operation":"density11_sample_list_completeness_defects","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-list-completeness-defects/[[0],[-25]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0076","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,0}，事件E=[]⊆S；有序候選=[100, 101, 102]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([否, 否, 否], [否, 否, 否])","explanation_zh":"可能結果與事件資格=([否, 否, 否], [否, 否, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116076,"parameters":{"n":1,"E":[],"candidates":[100,101,102],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_space\",\"outside_space\",\"outside_space\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0077","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[1, 101, 102]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 否, 否], [是, 否, 否])","explanation_zh":"可能結果與事件資格=([是, 否, 否], [是, 否, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116077,"parameters":{"n":6,"E":[1,2,3],"candidates":[1,101,102],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"in_event\",\"outside_space\",\"outside_space\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0078","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[0, 4, 102]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 是, 否], [否, 否, 否])","explanation_zh":"可能結果與事件資格=([是, 是, 否], [否, 否, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116078,"parameters":{"n":6,"E":[1,2,3],"candidates":[0,4,102],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_event\",\"outside_event\",\"outside_space\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0079","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[1, 4, 102]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 是, 否], [是, 否, 否])","explanation_zh":"可能結果與事件資格=([是, 是, 否], [是, 否, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116079,"parameters":{"n":6,"E":[1,2,3],"candidates":[1,4,102],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"in_event\",\"outside_event\",\"outside_space\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0080","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[100, 2, 102]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([否, 是, 否], [否, 是, 否])","explanation_zh":"可能結果與事件資格=([否, 是, 否], [否, 是, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116080,"parameters":{"n":6,"E":[1,2,3],"candidates":[100,2,102],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_space\",\"in_event\",\"outside_space\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0081","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[0, 2, 102]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 是, 否], [否, 是, 否])","explanation_zh":"可能結果與事件資格=([是, 是, 否], [否, 是, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116081,"parameters":{"n":6,"E":[1,2,3],"candidates":[0,2,102],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_event\",\"in_event\",\"outside_space\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0082","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[1, 2, 102]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 是, 否], [是, 是, 否])","explanation_zh":"可能結果與事件資格=([是, 是, 否], [是, 是, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116082,"parameters":{"n":6,"E":[1,2,3],"candidates":[1,2,102],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"in_event\",\"in_event\",\"outside_space\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0083","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[100, 101, 5]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([否, 否, 是], [否, 否, 否])","explanation_zh":"可能結果與事件資格=([否, 否, 是], [否, 否, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116083,"parameters":{"n":6,"E":[1,2,3],"candidates":[100,101,5],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_space\",\"outside_space\",\"outside_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0084","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[0, 101, 5]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 否, 是], [否, 否, 否])","explanation_zh":"可能結果與事件資格=([是, 否, 是], [否, 否, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116084,"parameters":{"n":6,"E":[1,2,3],"candidates":[0,101,5],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_event\",\"outside_space\",\"outside_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0085","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[1, 101, 5]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 否, 是], [是, 否, 否])","explanation_zh":"可能結果與事件資格=([是, 否, 是], [是, 否, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116085,"parameters":{"n":6,"E":[1,2,3],"candidates":[1,101,5],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"in_event\",\"outside_space\",\"outside_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0086","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[100, 4, 5]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([否, 是, 是], [否, 否, 否])","explanation_zh":"可能結果與事件資格=([否, 是, 是], [否, 否, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116086,"parameters":{"n":6,"E":[1,2,3],"candidates":[100,4,5],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_space\",\"outside_event\",\"outside_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0087","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[0, 4, 5]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 是, 是], [否, 否, 否])","explanation_zh":"可能結果與事件資格=([是, 是, 是], [否, 否, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116087,"parameters":{"n":6,"E":[1,2,3],"candidates":[0,4,5],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_event\",\"outside_event\",\"outside_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r06-sample-space-0089","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[100, 2, 5]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([否, 是, 是], [否, 是, 否])","explanation_zh":"可能結果與事件資格=([否, 是, 是], [否, 是, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116089,"parameters":{"n":6,"E":[1,2,3],"candidates":[100,2,5],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_space\",\"in_event\",\"outside_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0090","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[0, 2, 5]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 是, 是], [否, 是, 否])","explanation_zh":"可能結果與事件資格=([是, 是, 是], [否, 是, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116090,"parameters":{"n":6,"E":[1,2,3],"candidates":[0,2,5],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_event\",\"in_event\",\"outside_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0091","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[1, 2, 5]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 是, 是], [是, 是, 否])","explanation_zh":"可能結果與事件資格=([是, 是, 是], [是, 是, 否])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116091,"parameters":{"n":6,"E":[1,2,3],"candidates":[1,2,5],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"in_event\",\"in_event\",\"outside_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0092","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[100, 101, 3]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([否, 否, 是], [否, 否, 是])","explanation_zh":"可能結果與事件資格=([否, 否, 是], [否, 否, 是])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116092,"parameters":{"n":6,"E":[1,2,3],"candidates":[100,101,3],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_space\",\"outside_space\",\"in_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0093","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[0, 101, 3]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 否, 是], [否, 否, 是])","explanation_zh":"可能結果與事件資格=([是, 否, 是], [否, 否, 是])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116093,"parameters":{"n":6,"E":[1,2,3],"candidates":[0,101,3],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_event\",\"outside_space\",\"in_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0094","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[1, 101, 3]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 否, 是], [是, 否, 是])","explanation_zh":"可能結果與事件資格=([是, 否, 是], [是, 否, 是])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116094,"parameters":{"n":6,"E":[1,2,3],"candidates":[1,101,3],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"in_event\",\"outside_space\",\"in_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0095","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[100, 4, 3]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([否, 是, 是], [否, 否, 是])","explanation_zh":"可能結果與事件資格=([否, 是, 是], [否, 否, 是])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116095,"parameters":{"n":6,"E":[1,2,3],"candidates":[100,4,3],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_space\",\"outside_event\",\"in_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0096","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[0, 4, 3]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 是, 是], [否, 否, 是])","explanation_zh":"可能結果與事件資格=([是, 是, 是], [否, 否, 是])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116096,"parameters":{"n":6,"E":[1,2,3],"candidates":[0,4,3],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_event\",\"outside_event\",\"in_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0097","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[1, 4, 3]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 是, 是], [是, 否, 是])","explanation_zh":"可能結果與事件資格=([是, 是, 是], [是, 否, 是])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116097,"parameters":{"n":6,"E":[1,2,3],"candidates":[1,4,3],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"in_event\",\"outside_event\",\"in_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0098","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[100, 2, 3]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([否, 是, 是], [否, 是, 是])","explanation_zh":"可能結果與事件資格=([否, 是, 是], [否, 是, 是])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116098,"parameters":{"n":6,"E":[1,2,3],"candidates":[100,2,3],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_space\",\"in_event\",\"in_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0099","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[0, 2, 3]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 是, 是], [否, 是, 是])","explanation_zh":"可能結果與事件資格=([是, 是, 是], [否, 是, 是])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116099,"parameters":{"n":6,"E":[1,2,3],"candidates":[0,2,3],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"outside_event\",\"in_event\",\"in_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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-r06-sample-space-0100","batch_id":"batch-20261008-advance-20261011-r06-sample-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"基本結果與事件的有序資格","stem_zh":"基本可能結果S={0,…,2}，事件E=[0, 1, 2]⊆S；有序候選=[0, 1, 2]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。","answer":{"kind":"expression","value":"([是, 是, 是], [是, 是, 是])","explanation_zh":"可能結果與事件資格=([是, 是, 是], [是, 是, 是])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["基本結果與事件的有序資格"]},"variant":{"family_id":"qf-density11-sample-outcome-event-masks","seed":202610116100,"parameters":{"n":3,"E":[0,1,2],"candidates":[0,1,2],"operation":"density11_sample_outcome_event_masks","domain":"finite_possible_outcome_protocol","semantic_template":"qf-density11-sample-outcome-event-masks/[\"in_event\",\"in_event\",\"in_event\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、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"}}