{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0001","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(0)=∅、Fin(0)=∅、Fin(0)=∅，完整f:n→m表=[]、g:m→k表=[]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([0, 0, 0], [], [])","explanation_zh":"完整合成型別與求值路徑=([0, 0, 0], [], [])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154001,"parameters":{"n":0,"m":0,"k":0,"f":[],"g":[],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[0,0,0,[],[]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0002","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[0, 0, 0]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 0, 3], [1, 0, 3], [2, 0, 3]], [3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 0, 3], [1, 0, 3], [2, 0, 3]], [3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154002,"parameters":{"n":3,"m":3,"k":4,"f":[0,0,0],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[0,0,0],[3,3,3]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0003","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[1, 0, 0]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 1, 1], [1, 0, 3], [2, 0, 3]], [1, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 1, 1], [1, 0, 3], [2, 0, 3]], [1, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154003,"parameters":{"n":3,"m":3,"k":4,"f":[1,0,0],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[1,0,0],[1,3,3]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0004","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[2, 0, 0]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 2, 0], [1, 0, 3], [2, 0, 3]], [0, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 2, 0], [1, 0, 3], [2, 0, 3]], [0, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154004,"parameters":{"n":3,"m":3,"k":4,"f":[2,0,0],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[2,0,0],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0005","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[0, 1, 0]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 0, 3], [1, 1, 1], [2, 0, 3]], [1, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 0, 3], [1, 1, 1], [2, 0, 3]], [1, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154005,"parameters":{"n":3,"m":3,"k":4,"f":[0,1,0],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[0,1,0],[3,1,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0006","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[1, 1, 0]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 1, 1], [1, 1, 1], [2, 0, 3]], [1, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 1, 1], [1, 1, 1], [2, 0, 3]], [1, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154006,"parameters":{"n":3,"m":3,"k":4,"f":[1,1,0],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[1,1,0],[1,1,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0007","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[2, 1, 0]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 2, 0], [1, 1, 1], [2, 0, 3]], [0, 1, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 2, 0], [1, 1, 1], [2, 0, 3]], [0, 1, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154007,"parameters":{"n":3,"m":3,"k":4,"f":[2,1,0],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[2,1,0],[0,1,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0008","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[0, 2, 0]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 0, 3], [1, 2, 0], [2, 0, 3]], [0, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 0, 3], [1, 2, 0], [2, 0, 3]], [0, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154008,"parameters":{"n":3,"m":3,"k":4,"f":[0,2,0],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[0,2,0],[3,0,3]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0009","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[1, 2, 0]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 1, 1], [1, 2, 0], [2, 0, 3]], [0, 1, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 1, 1], [1, 2, 0], [2, 0, 3]], [0, 1, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154009,"parameters":{"n":3,"m":3,"k":4,"f":[1,2,0],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[1,2,0],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0010","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[2, 2, 0]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 2, 0], [1, 2, 0], [2, 0, 3]], [0, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 2, 0], [1, 2, 0], [2, 0, 3]], [0, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154010,"parameters":{"n":3,"m":3,"k":4,"f":[2,2,0],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[2,2,0],[0,0,3]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0011","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[0, 0, 1]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 0, 3], [1, 0, 3], [2, 1, 1]], [1, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 0, 3], [1, 0, 3], [2, 1, 1]], [1, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154011,"parameters":{"n":3,"m":3,"k":4,"f":[0,0,1],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[0,0,1],[3,3,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0012","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[1, 0, 1]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 1, 1], [1, 0, 3], [2, 1, 1]], [1, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 1, 1], [1, 0, 3], [2, 1, 1]], [1, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154012,"parameters":{"n":3,"m":3,"k":4,"f":[1,0,1],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[1,0,1],[1,3,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0013","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[2, 0, 1]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 2, 0], [1, 0, 3], [2, 1, 1]], [0, 1, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 2, 0], [1, 0, 3], [2, 1, 1]], [0, 1, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154013,"parameters":{"n":3,"m":3,"k":4,"f":[2,0,1],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[2,0,1],[0,3,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0014","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[0, 1, 1]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 0, 3], [1, 1, 1], [2, 1, 1]], [1, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 0, 3], [1, 1, 1], [2, 1, 1]], [1, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154014,"parameters":{"n":3,"m":3,"k":4,"f":[0,1,1],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[0,1,1],[3,1,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0015","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[1, 1, 1]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 1, 1], [1, 1, 1], [2, 1, 1]], [1])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 1, 1], [1, 1, 1], [2, 1, 1]], [1])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154015,"parameters":{"n":3,"m":3,"k":4,"f":[1,1,1],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[1,1,1],[1,1,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0016","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[2, 1, 1]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 2, 0], [1, 1, 1], [2, 1, 1]], [0, 1])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 2, 0], [1, 1, 1], [2, 1, 1]], [0, 1])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154016,"parameters":{"n":3,"m":3,"k":4,"f":[2,1,1],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[2,1,1],[0,1,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0017","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[0, 2, 1]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 0, 3], [1, 2, 0], [2, 1, 1]], [0, 1, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 0, 3], [1, 2, 0], [2, 1, 1]], [0, 1, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154017,"parameters":{"n":3,"m":3,"k":4,"f":[0,2,1],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[0,2,1],[3,0,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0018","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[1, 2, 1]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 1, 1], [1, 2, 0], [2, 1, 1]], [0, 1])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 1, 1], [1, 2, 0], [2, 1, 1]], [0, 1])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154018,"parameters":{"n":3,"m":3,"k":4,"f":[1,2,1],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[1,2,1],[1,0,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0019","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[2, 2, 1]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 2, 0], [1, 2, 0], [2, 1, 1]], [0, 1])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 2, 0], [1, 2, 0], [2, 1, 1]], [0, 1])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154019,"parameters":{"n":3,"m":3,"k":4,"f":[2,2,1],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[2,2,1],[0,0,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0020","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[0, 0, 2]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 0, 3], [1, 0, 3], [2, 2, 0]], [0, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 0, 3], [1, 0, 3], [2, 2, 0]], [0, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154020,"parameters":{"n":3,"m":3,"k":4,"f":[0,0,2],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[0,0,2],[3,3,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0021","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[1, 0, 2]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 1, 1], [1, 0, 3], [2, 2, 0]], [0, 1, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 1, 1], [1, 0, 3], [2, 2, 0]], [0, 1, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154021,"parameters":{"n":3,"m":3,"k":4,"f":[1,0,2],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[1,0,2],[1,3,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0022","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[2, 0, 2]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 2, 0], [1, 0, 3], [2, 2, 0]], [0, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 2, 0], [1, 0, 3], [2, 2, 0]], [0, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154022,"parameters":{"n":3,"m":3,"k":4,"f":[2,0,2],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[2,0,2],[0,3,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0023","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[0, 1, 2]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 0, 3], [1, 1, 1], [2, 2, 0]], [0, 1, 3])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 0, 3], [1, 1, 1], [2, 2, 0]], [0, 1, 3])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154023,"parameters":{"n":3,"m":3,"k":4,"f":[0,1,2],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[0,1,2],[3,1,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0024","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[1, 1, 2]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 1, 1], [1, 1, 1], [2, 2, 0]], [0, 1])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 1, 1], [1, 1, 1], [2, 2, 0]], [0, 1])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154024,"parameters":{"n":3,"m":3,"k":4,"f":[1,1,2],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[1,1,2],[1,1,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0025","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"完整兩表合成路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]，完整f:n→m表=[2, 1, 2]、g:m→k表=[3, 1, 0]。求 ([n,m,k], 每個[x,f(x),g(f(x))]路徑, 合成值域)。未使用格仍須合型。","answer":{"kind":"expression","value":"([3, 3, 4], [[0, 2, 0], [1, 1, 1], [2, 2, 0]], [0, 1])","explanation_zh":"完整合成型別與求值路徑=([3, 3, 4], [[0, 2, 0], [1, 1, 1], [2, 2, 0]], [0, 1])。依序查f再查g，全來源列保留中間值，最後輸出去重。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整兩表合成路徑"]},"variant":{"family_id":"qf-density15-composition-compatible-path-table","seed":202610154025,"parameters":{"n":3,"m":3,"k":4,"f":[2,1,2],"g":[3,1,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_compatible_path_table","semantic_template":"qf-density15-composition-compatible-path-table/[3,3,4,[2,1,2],[0,1,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0026","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(0)=∅、Fin(0)=∅、Fin(0)=∅。完整f表=[]，g的原序dom=[]，與dom原序配對g值=[]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([0, 0, 0], [], [], [], [])","explanation_zh":"中間域限制與允許合成=([0, 0, 0], [], [], [], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154026,"parameters":{"n":0,"m":0,"k":0,"f":[],"dom":[],"g":[],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[0,0,0,[],[]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0027","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[0, 1, 2]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([3, 3, 3], [0, 2], [0, 2], [2, 1], [1])","explanation_zh":"中間域限制與允許合成=([3, 3, 3], [0, 2], [0, 2], [2, 1], [1])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154027,"parameters":{"n":3,"m":3,"k":3,"f":[0,1,2],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[3,3,3,[0,2],[[0,2],[2,1]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0028","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(0)=∅。完整f表=[0, 1, 2]，g的原序dom=[]，與dom原序配對g值=[]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([3, 3, 0], [], [], [], [0, 1, 2])","explanation_zh":"中間域限制與允許合成=([3, 3, 0], [], [], [], [0, 1, 2])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154028,"parameters":{"n":3,"m":3,"k":0,"f":[0,1,2],"dom":[],"g":[],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[3,3,0,[],[]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0029","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[0, 0, 0, 0, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 2, 2, 2, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 2, 2, 2, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154029,"parameters":{"n":5,"m":3,"k":3,"f":[0,0,0,0,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,2],[1,2],[2,2],[3,2],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0030","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[2, 0, 0, 0, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 2, 2, 2, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 2, 2, 2, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154030,"parameters":{"n":5,"m":3,"k":3,"f":[2,0,0,0,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,1],[1,2],[2,2],[3,2],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0031","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[0, 2, 0, 0, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 1, 2, 2, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 1, 2, 2, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154031,"parameters":{"n":5,"m":3,"k":3,"f":[0,2,0,0,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,2],[1,1],[2,2],[3,2],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0032","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[2, 2, 0, 0, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 1, 2, 2, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 1, 2, 2, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154032,"parameters":{"n":5,"m":3,"k":3,"f":[2,2,0,0,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,1],[1,1],[2,2],[3,2],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0033","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[0, 0, 2, 0, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 2, 1, 2, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 2, 1, 2, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154033,"parameters":{"n":5,"m":3,"k":3,"f":[0,0,2,0,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,2],[1,2],[2,1],[3,2],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0034","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[2, 0, 2, 0, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 2, 1, 2, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 2, 1, 2, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154034,"parameters":{"n":5,"m":3,"k":3,"f":[2,0,2,0,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,1],[1,2],[2,1],[3,2],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0035","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[0, 2, 2, 0, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 1, 1, 2, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 1, 1, 2, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154035,"parameters":{"n":5,"m":3,"k":3,"f":[0,2,2,0,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,2],[1,1],[2,1],[3,2],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0036","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[2, 2, 2, 0, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 1, 1, 2, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 1, 1, 2, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154036,"parameters":{"n":5,"m":3,"k":3,"f":[2,2,2,0,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,1],[1,1],[2,1],[3,2],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0037","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[0, 0, 0, 2, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 2, 2, 1, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 2, 2, 1, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154037,"parameters":{"n":5,"m":3,"k":3,"f":[0,0,0,2,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,2],[1,2],[2,2],[3,1],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0038","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[2, 0, 0, 2, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 2, 2, 1, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 2, 2, 1, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154038,"parameters":{"n":5,"m":3,"k":3,"f":[2,0,0,2,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,1],[1,2],[2,2],[3,1],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0039","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[0, 2, 0, 2, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 1, 2, 1, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 1, 2, 1, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154039,"parameters":{"n":5,"m":3,"k":3,"f":[0,2,0,2,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,2],[1,1],[2,2],[3,1],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0040","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[2, 2, 0, 2, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 1, 2, 1, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 1, 2, 1, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154040,"parameters":{"n":5,"m":3,"k":3,"f":[2,2,0,2,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,1],[1,1],[2,2],[3,1],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0041","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[0, 0, 2, 2, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 2, 1, 1, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 2, 1, 1, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154041,"parameters":{"n":5,"m":3,"k":3,"f":[0,0,2,2,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,2],[1,2],[2,1],[3,1],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0042","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[2, 0, 2, 2, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 2, 1, 1, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 2, 1, 1, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154042,"parameters":{"n":5,"m":3,"k":3,"f":[2,0,2,2,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,1],[1,2],[2,1],[3,1],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0043","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[0, 2, 2, 2, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 1, 1, 1, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 1, 1, 1, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154043,"parameters":{"n":5,"m":3,"k":3,"f":[0,2,2,2,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,2],[1,1],[2,1],[3,1],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0044","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[2, 2, 2, 2, 0]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 1, 1, 1, 2], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 1, 1, 1, 2], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154044,"parameters":{"n":5,"m":3,"k":3,"f":[2,2,2,2,0],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,1],[1,1],[2,1],[3,1],[4,2]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0045","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[0, 0, 0, 0, 2]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 2, 2, 2, 1], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 2, 2, 2, 1], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154045,"parameters":{"n":5,"m":3,"k":3,"f":[0,0,0,0,2],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,2],[1,2],[2,2],[3,2],[4,1]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0046","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[2, 0, 0, 0, 2]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 2, 2, 2, 1], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 2, 2, 2, 1], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154046,"parameters":{"n":5,"m":3,"k":3,"f":[2,0,0,0,2],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,1],[1,2],[2,2],[3,2],[4,1]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0047","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[0, 2, 0, 0, 2]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 1, 2, 2, 1], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 1, 2, 2, 1], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154047,"parameters":{"n":5,"m":3,"k":3,"f":[0,2,0,0,2],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,2],[1,1],[2,2],[3,2],[4,1]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0048","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[2, 2, 0, 0, 2]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 1, 2, 2, 1], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 1, 2, 2, 1], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154048,"parameters":{"n":5,"m":3,"k":3,"f":[2,2,0,0,2],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,1],[1,1],[2,2],[3,2],[4,1]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0049","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[0, 0, 2, 0, 2]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 2, 1, 2, 1], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [2, 2, 1, 2, 1], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154049,"parameters":{"n":5,"m":3,"k":3,"f":[0,0,2,0,2],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,2],[1,2],[2,1],[3,2],[4,1]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0050","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限中間域的允許來源","stem_zh":"先f後g，明示中間域。Fin(5)=[0, 1, 2, 3, 4]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]。完整f表=[2, 0, 2, 0, 2]，g的原序dom=[2, 0]，與dom原序配對g值=[1, 2]。求 ([n,m,k], 排序dom, 允許來源, 對應輸出, 拒絕來源)，不改原dom/g配對。","answer":{"kind":"expression","value":"([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 2, 1, 2, 1], [])","explanation_zh":"中間域限制與允許合成=([5, 3, 3], [0, 2], [0, 1, 2, 3, 4], [1, 2, 1, 2, 1], [])。先以原序建立dom到g值的配對，僅在f輸出入域時求值；另排序呈現域。未入g域不求g值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["受限中間域的允許來源"]},"variant":{"family_id":"qf-density15-composition-restricted-table-domain","seed":202610154050,"parameters":{"n":5,"m":3,"k":3,"f":[2,0,2,0,2],"dom":[2,0],"g":[1,2],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_restricted_table_domain","semantic_template":"qf-density15-composition-restricted-table-domain/[5,3,3,[0,2],[[0,1],[1,2],[2,1],[3,2],[4,1]]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0051","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(1)x+(0)，g(x)=(1)x+(0)，有序輸入=[(0)/(1), (1)/(1), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([1, 0], [1, 0], [0/1, 1/1, -1/1], [0/1, 1/1, -1/1], 0)","explanation_zh":"兩序仿射合成與常數差=([1, 0], [1, 0], [0/1, 1/1, -1/1], [0/1, 1/1, -1/1], 0)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154051,"parameters":{"a":1,"b":0,"c":1,"d":0,"inputs":[[0,1],[1,1],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"1\",\"0\"],[\"1\",\"0\"],[\"0/1\",\"1/1\",\"-1/1\"],[\"0/1\",\"1/1\",\"-1/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0052","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(1)x+(1)，g(x)=(2)x+(0)，有序輸入=[(0)/(1), (1)/(1), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([2, 2], [2, 1], [2/1, 4/1, 0/1], [1/1, 3/1, -1/1], 1)","explanation_zh":"兩序仿射合成與常數差=([2, 2], [2, 1], [2/1, 4/1, 0/1], [1/1, 3/1, -1/1], 1)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154052,"parameters":{"a":1,"b":1,"c":2,"d":0,"inputs":[[0,1],[1,1],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"2\",\"2\"],[\"2\",\"1\"],[\"2/1\",\"4/1\",\"0/1\"],[\"1/1\",\"3/1\",\"-1/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0053","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(0)x+(1)，g(x)=(0)x+(2)，有序輸入=[(0)/(1), (1)/(1), (2)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([0, 2], [0, 1], [2/1, 2/1, 2/1], [1/1, 1/1, 1/1], 1)","explanation_zh":"兩序仿射合成與常數差=([0, 2], [0, 1], [2/1, 2/1, 2/1], [1/1, 1/1, 1/1], 1)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154053,"parameters":{"a":0,"b":1,"c":0,"d":2,"inputs":[[0,1],[1,1],[2,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"0\",\"2\"],[\"0\",\"1\"],[\"2/1\",\"2/1\",\"2/1\"],[\"1/1\",\"1/1\",\"1/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0054","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(2)x+(-1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-4, 3], [-4, 1], [3/1, 1/1, 7/1], [1/1, -1/1, 5/1], 2)","explanation_zh":"兩序仿射合成與常數差=([-4, 3], [-4, 1], [3/1, 1/1, 7/1], [1/1, -1/1, 5/1], 2)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154054,"parameters":{"a":2,"b":-1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-4\",\"3\"],[\"-4\",\"1\"],[\"3/1\",\"1/1\",\"7/1\"],[\"1/1\",\"-1/1\",\"5/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0055","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(3)x+(0)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-6, 1], [-6, 3], [1/1, -2/1, 7/1], [3/1, 0/1, 9/1], -2)","explanation_zh":"兩序仿射合成與常數差=([-6, 1], [-6, 3], [1/1, -2/1, 7/1], [3/1, 0/1, 9/1], -2)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154055,"parameters":{"a":3,"b":0,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-6\",\"1\"],[\"-6\",\"3\"],[\"1/1\",\"-2/1\",\"7/1\"],[\"3/1\",\"0/1\",\"9/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0056","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(4)x+(1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-8, -1], [-8, 5], [-1/1, -5/1, 7/1], [5/1, 1/1, 13/1], -6)","explanation_zh":"兩序仿射合成與常數差=([-8, -1], [-8, 5], [-1/1, -5/1, 7/1], [5/1, 1/1, 13/1], -6)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154056,"parameters":{"a":4,"b":1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-8\",\"-1\"],[\"-8\",\"5\"],[\"-1/1\",\"-5/1\",\"7/1\"],[\"5/1\",\"1/1\",\"13/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0057","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(5)x+(-1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-10, 3], [-10, 4], [3/1, -2/1, 13/1], [4/1, -1/1, 14/1], -1)","explanation_zh":"兩序仿射合成與常數差=([-10, 3], [-10, 4], [3/1, -2/1, 13/1], [4/1, -1/1, 14/1], -1)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154057,"parameters":{"a":5,"b":-1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-10\",\"3\"],[\"-10\",\"4\"],[\"3/1\",\"-2/1\",\"13/1\"],[\"4/1\",\"-1/1\",\"14/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0058","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(6)x+(0)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-12, 1], [-12, 6], [1/1, -5/1, 13/1], [6/1, 0/1, 18/1], -5)","explanation_zh":"兩序仿射合成與常數差=([-12, 1], [-12, 6], [1/1, -5/1, 13/1], [6/1, 0/1, 18/1], -5)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154058,"parameters":{"a":6,"b":0,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-12\",\"1\"],[\"-12\",\"6\"],[\"1/1\",\"-5/1\",\"13/1\"],[\"6/1\",\"0/1\",\"18/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0059","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(7)x+(1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-14, -1], [-14, 8], [-1/1, -8/1, 13/1], [8/1, 1/1, 22/1], -9)","explanation_zh":"兩序仿射合成與常數差=([-14, -1], [-14, 8], [-1/1, -8/1, 13/1], [8/1, 1/1, 22/1], -9)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154059,"parameters":{"a":7,"b":1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-14\",\"-1\"],[\"-14\",\"8\"],[\"-1/1\",\"-8/1\",\"13/1\"],[\"8/1\",\"1/1\",\"22/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0060","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(8)x+(-1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-16, 3], [-16, 7], [3/1, -5/1, 19/1], [7/1, -1/1, 23/1], -4)","explanation_zh":"兩序仿射合成與常數差=([-16, 3], [-16, 7], [3/1, -5/1, 19/1], [7/1, -1/1, 23/1], -4)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154060,"parameters":{"a":8,"b":-1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-16\",\"3\"],[\"-16\",\"7\"],[\"3/1\",\"-5/1\",\"19/1\"],[\"7/1\",\"-1/1\",\"23/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0061","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(9)x+(0)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-18, 1], [-18, 9], [1/1, -8/1, 19/1], [9/1, 0/1, 27/1], -8)","explanation_zh":"兩序仿射合成與常數差=([-18, 1], [-18, 9], [1/1, -8/1, 19/1], [9/1, 0/1, 27/1], -8)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154061,"parameters":{"a":9,"b":0,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-18\",\"1\"],[\"-18\",\"9\"],[\"1/1\",\"-8/1\",\"19/1\"],[\"9/1\",\"0/1\",\"27/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0062","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(10)x+(1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-20, -1], [-20, 11], [-1/1, -11/1, 19/1], [11/1, 1/1, 31/1], -12)","explanation_zh":"兩序仿射合成與常數差=([-20, -1], [-20, 11], [-1/1, -11/1, 19/1], [11/1, 1/1, 31/1], -12)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154062,"parameters":{"a":10,"b":1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-20\",\"-1\"],[\"-20\",\"11\"],[\"-1/1\",\"-11/1\",\"19/1\"],[\"11/1\",\"1/1\",\"31/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0063","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(11)x+(-1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-22, 3], [-22, 10], [3/1, -8/1, 25/1], [10/1, -1/1, 32/1], -7)","explanation_zh":"兩序仿射合成與常數差=([-22, 3], [-22, 10], [3/1, -8/1, 25/1], [10/1, -1/1, 32/1], -7)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154063,"parameters":{"a":11,"b":-1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-22\",\"3\"],[\"-22\",\"10\"],[\"3/1\",\"-8/1\",\"25/1\"],[\"10/1\",\"-1/1\",\"32/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0064","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(12)x+(0)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-24, 1], [-24, 12], [1/1, -11/1, 25/1], [12/1, 0/1, 36/1], -11)","explanation_zh":"兩序仿射合成與常數差=([-24, 1], [-24, 12], [1/1, -11/1, 25/1], [12/1, 0/1, 36/1], -11)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154064,"parameters":{"a":12,"b":0,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-24\",\"1\"],[\"-24\",\"12\"],[\"1/1\",\"-11/1\",\"25/1\"],[\"12/1\",\"0/1\",\"36/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0065","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(13)x+(1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-26, -1], [-26, 14], [-1/1, -14/1, 25/1], [14/1, 1/1, 40/1], -15)","explanation_zh":"兩序仿射合成與常數差=([-26, -1], [-26, 14], [-1/1, -14/1, 25/1], [14/1, 1/1, 40/1], -15)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154065,"parameters":{"a":13,"b":1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-26\",\"-1\"],[\"-26\",\"14\"],[\"-1/1\",\"-14/1\",\"25/1\"],[\"14/1\",\"1/1\",\"40/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0066","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(14)x+(-1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-28, 3], [-28, 13], [3/1, -11/1, 31/1], [13/1, -1/1, 41/1], -10)","explanation_zh":"兩序仿射合成與常數差=([-28, 3], [-28, 13], [3/1, -11/1, 31/1], [13/1, -1/1, 41/1], -10)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154066,"parameters":{"a":14,"b":-1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-28\",\"3\"],[\"-28\",\"13\"],[\"3/1\",\"-11/1\",\"31/1\"],[\"13/1\",\"-1/1\",\"41/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0067","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(15)x+(0)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-30, 1], [-30, 15], [1/1, -14/1, 31/1], [15/1, 0/1, 45/1], -14)","explanation_zh":"兩序仿射合成與常數差=([-30, 1], [-30, 15], [1/1, -14/1, 31/1], [15/1, 0/1, 45/1], -14)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154067,"parameters":{"a":15,"b":0,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-30\",\"1\"],[\"-30\",\"15\"],[\"1/1\",\"-14/1\",\"31/1\"],[\"15/1\",\"0/1\",\"45/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0068","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(16)x+(1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-32, -1], [-32, 17], [-1/1, -17/1, 31/1], [17/1, 1/1, 49/1], -18)","explanation_zh":"兩序仿射合成與常數差=([-32, -1], [-32, 17], [-1/1, -17/1, 31/1], [17/1, 1/1, 49/1], -18)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154068,"parameters":{"a":16,"b":1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-32\",\"-1\"],[\"-32\",\"17\"],[\"-1/1\",\"-17/1\",\"31/1\"],[\"17/1\",\"1/1\",\"49/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0069","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(17)x+(-1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-34, 3], [-34, 16], [3/1, -14/1, 37/1], [16/1, -1/1, 50/1], -13)","explanation_zh":"兩序仿射合成與常數差=([-34, 3], [-34, 16], [3/1, -14/1, 37/1], [16/1, -1/1, 50/1], -13)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154069,"parameters":{"a":17,"b":-1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-34\",\"3\"],[\"-34\",\"16\"],[\"3/1\",\"-14/1\",\"37/1\"],[\"16/1\",\"-1/1\",\"50/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0070","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(18)x+(0)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-36, 1], [-36, 18], [1/1, -17/1, 37/1], [18/1, 0/1, 54/1], -17)","explanation_zh":"兩序仿射合成與常數差=([-36, 1], [-36, 18], [1/1, -17/1, 37/1], [18/1, 0/1, 54/1], -17)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154070,"parameters":{"a":18,"b":0,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-36\",\"1\"],[\"-36\",\"18\"],[\"1/1\",\"-17/1\",\"37/1\"],[\"18/1\",\"0/1\",\"54/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0071","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(19)x+(1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-38, -1], [-38, 20], [-1/1, -20/1, 37/1], [20/1, 1/1, 58/1], -21)","explanation_zh":"兩序仿射合成與常數差=([-38, -1], [-38, 20], [-1/1, -20/1, 37/1], [20/1, 1/1, 58/1], -21)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154071,"parameters":{"a":19,"b":1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-38\",\"-1\"],[\"-38\",\"20\"],[\"-1/1\",\"-20/1\",\"37/1\"],[\"20/1\",\"1/1\",\"58/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0072","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(20)x+(-1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-40, 3], [-40, 19], [3/1, -17/1, 43/1], [19/1, -1/1, 59/1], -16)","explanation_zh":"兩序仿射合成與常數差=([-40, 3], [-40, 19], [3/1, -17/1, 43/1], [19/1, -1/1, 59/1], -16)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154072,"parameters":{"a":20,"b":-1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-40\",\"3\"],[\"-40\",\"19\"],[\"3/1\",\"-17/1\",\"43/1\"],[\"19/1\",\"-1/1\",\"59/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0073","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(21)x+(0)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-42, 1], [-42, 21], [1/1, -20/1, 43/1], [21/1, 0/1, 63/1], -20)","explanation_zh":"兩序仿射合成與常數差=([-42, 1], [-42, 21], [1/1, -20/1, 43/1], [21/1, 0/1, 63/1], -20)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154073,"parameters":{"a":21,"b":0,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-42\",\"1\"],[\"-42\",\"21\"],[\"1/1\",\"-20/1\",\"43/1\"],[\"21/1\",\"0/1\",\"63/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0074","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(22)x+(1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-44, -1], [-44, 23], [-1/1, -23/1, 43/1], [23/1, 1/1, 67/1], -24)","explanation_zh":"兩序仿射合成與常數差=([-44, -1], [-44, 23], [-1/1, -23/1, 43/1], [23/1, 1/1, 67/1], -24)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154074,"parameters":{"a":22,"b":1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-44\",\"-1\"],[\"-44\",\"23\"],[\"-1/1\",\"-23/1\",\"43/1\"],[\"23/1\",\"1/1\",\"67/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0075","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩序仿射合成的差","stem_zh":"先f後g，明示中間域。Q總函數f(x)=(23)x+(-1)，g(x)=(-2)x+(1)，有序輸入=[(0)/(1), (1)/(2), (-1)/(1)]。求 (g∘f的[一次係數,常數]順序, f∘g的[一次係數,常數]順序, 兩序各三個值, g∘f常數減f∘g常數)。","answer":{"kind":"expression","value":"([-46, 3], [-46, 22], [3/1, -20/1, 49/1], [22/1, -1/1, 68/1], -19)","explanation_zh":"兩序仿射合成與常數差=([-46, 3], [-46, 22], [3/1, -20/1, 49/1], [22/1, -1/1, 68/1], -19)。各序都作兩次代入，並用輸入0與1的值差取得一次係數；不互換求值順序。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩序仿射合成的差"]},"variant":{"family_id":"qf-density15-composition-noncommuting-affine","seed":202610154075,"parameters":{"a":23,"b":-1,"c":-2,"d":1,"inputs":[[0,1],[1,2],[-1,1]],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_noncommuting_affine","semantic_template":"qf-density15-composition-noncommuting-affine/[[\"-46\",\"3\"],[\"-46\",\"22\"],[\"3/1\",\"-20/1\",\"49/1\"],[\"22/1\",\"-1/1\",\"68/1\"]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0076","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(0)=∅、Fin(0)=∅、Fin(0)=∅、Fin(0)=∅。完整f=[]、g=[]、h=[]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([0, 0, 0, 0], [], [], [], 是)","explanation_zh":"三表括號兩路與型別路徑=([0, 0, 0, 0], [], [], [], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154076,"parameters":{"n":0,"m":0,"k":0,"l":0,"f":[],"g":[],"h":[],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[0,0,0,0,[],[],[]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0077","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[0, 0, 0]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [0, 0, 0], [0, 0, 0], [[0, 0, 2, 0], [1, 0, 2, 0], [2, 0, 2, 0]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [0, 0, 0], [0, 0, 0], [[0, 0, 2, 0], [1, 0, 2, 0], [2, 0, 2, 0]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154077,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[0,0,0],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[0,0,0],[2,2,2],[0,0,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0078","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[1, 0, 0]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [1, 0, 0], [1, 0, 0], [[0, 1, 0, 1], [1, 0, 2, 0], [2, 0, 2, 0]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [1, 0, 0], [1, 0, 0], [[0, 1, 0, 1], [1, 0, 2, 0], [2, 0, 2, 0]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154078,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[1,0,0],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[1,0,0],[0,2,2],[1,0,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0079","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[2, 0, 0]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [3, 0, 0], [3, 0, 0], [[0, 2, 1, 3], [1, 0, 2, 0], [2, 0, 2, 0]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [3, 0, 0], [3, 0, 0], [[0, 2, 1, 3], [1, 0, 2, 0], [2, 0, 2, 0]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154079,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[2,0,0],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[2,0,0],[1,2,2],[3,0,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0080","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[0, 1, 0]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [0, 1, 0], [0, 1, 0], [[0, 0, 2, 0], [1, 1, 0, 1], [2, 0, 2, 0]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [0, 1, 0], [0, 1, 0], [[0, 0, 2, 0], [1, 1, 0, 1], [2, 0, 2, 0]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154080,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[0,1,0],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[0,1,0],[2,0,2],[0,1,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0081","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[1, 1, 0]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [1, 1, 0], [1, 1, 0], [[0, 1, 0, 1], [1, 1, 0, 1], [2, 0, 2, 0]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [1, 1, 0], [1, 1, 0], [[0, 1, 0, 1], [1, 1, 0, 1], [2, 0, 2, 0]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154081,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[1,1,0],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[1,1,0],[0,0,2],[1,1,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0082","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[2, 1, 0]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [3, 1, 0], [3, 1, 0], [[0, 2, 1, 3], [1, 1, 0, 1], [2, 0, 2, 0]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [3, 1, 0], [3, 1, 0], [[0, 2, 1, 3], [1, 1, 0, 1], [2, 0, 2, 0]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154082,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[2,1,0],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[2,1,0],[1,0,2],[3,1,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0083","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[0, 2, 0]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [0, 3, 0], [0, 3, 0], [[0, 0, 2, 0], [1, 2, 1, 3], [2, 0, 2, 0]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [0, 3, 0], [0, 3, 0], [[0, 0, 2, 0], [1, 2, 1, 3], [2, 0, 2, 0]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154083,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[0,2,0],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[0,2,0],[2,1,2],[0,3,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0084","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[1, 2, 0]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [1, 3, 0], [1, 3, 0], [[0, 1, 0, 1], [1, 2, 1, 3], [2, 0, 2, 0]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [1, 3, 0], [1, 3, 0], [[0, 1, 0, 1], [1, 2, 1, 3], [2, 0, 2, 0]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154084,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[1,2,0],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[1,2,0],[0,1,2],[1,3,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0085","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[2, 2, 0]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [3, 3, 0], [3, 3, 0], [[0, 2, 1, 3], [1, 2, 1, 3], [2, 0, 2, 0]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [3, 3, 0], [3, 3, 0], [[0, 2, 1, 3], [1, 2, 1, 3], [2, 0, 2, 0]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154085,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[2,2,0],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[2,2,0],[1,1,2],[3,3,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0086","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[0, 0, 1]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [0, 0, 1], [0, 0, 1], [[0, 0, 2, 0], [1, 0, 2, 0], [2, 1, 0, 1]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [0, 0, 1], [0, 0, 1], [[0, 0, 2, 0], [1, 0, 2, 0], [2, 1, 0, 1]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154086,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[0,0,1],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[0,0,1],[2,2,0],[0,0,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0087","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[1, 0, 1]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [1, 0, 1], [1, 0, 1], [[0, 1, 0, 1], [1, 0, 2, 0], [2, 1, 0, 1]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [1, 0, 1], [1, 0, 1], [[0, 1, 0, 1], [1, 0, 2, 0], [2, 1, 0, 1]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154087,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[1,0,1],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[1,0,1],[0,2,0],[1,0,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0088","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[2, 0, 1]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [3, 0, 1], [3, 0, 1], [[0, 2, 1, 3], [1, 0, 2, 0], [2, 1, 0, 1]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [3, 0, 1], [3, 0, 1], [[0, 2, 1, 3], [1, 0, 2, 0], [2, 1, 0, 1]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154088,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[2,0,1],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[2,0,1],[1,2,0],[3,0,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0089","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[0, 1, 1]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [0, 1, 1], [0, 1, 1], [[0, 0, 2, 0], [1, 1, 0, 1], [2, 1, 0, 1]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [0, 1, 1], [0, 1, 1], [[0, 0, 2, 0], [1, 1, 0, 1], [2, 1, 0, 1]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154089,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[0,1,1],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[0,1,1],[2,0,0],[0,1,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0090","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[1, 1, 1]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [1, 1, 1], [1, 1, 1], [[0, 1, 0, 1], [1, 1, 0, 1], [2, 1, 0, 1]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [1, 1, 1], [1, 1, 1], [[0, 1, 0, 1], [1, 1, 0, 1], [2, 1, 0, 1]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154090,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[1,1,1],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[1,1,1],[0,0,0],[1,1,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0091","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[2, 1, 1]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [3, 1, 1], [3, 1, 1], [[0, 2, 1, 3], [1, 1, 0, 1], [2, 1, 0, 1]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [3, 1, 1], [3, 1, 1], [[0, 2, 1, 3], [1, 1, 0, 1], [2, 1, 0, 1]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154091,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[2,1,1],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[2,1,1],[1,0,0],[3,1,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0092","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[0, 2, 1]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [0, 3, 1], [0, 3, 1], [[0, 0, 2, 0], [1, 2, 1, 3], [2, 1, 0, 1]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [0, 3, 1], [0, 3, 1], [[0, 0, 2, 0], [1, 2, 1, 3], [2, 1, 0, 1]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154092,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[0,2,1],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[0,2,1],[2,1,0],[0,3,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0093","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[1, 2, 1]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [1, 3, 1], [1, 3, 1], [[0, 1, 0, 1], [1, 2, 1, 3], [2, 1, 0, 1]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [1, 3, 1], [1, 3, 1], [[0, 1, 0, 1], [1, 2, 1, 3], [2, 1, 0, 1]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154093,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[1,2,1],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[1,2,1],[0,1,0],[1,3,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0094","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[2, 2, 1]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [3, 3, 1], [3, 3, 1], [[0, 2, 1, 3], [1, 2, 1, 3], [2, 1, 0, 1]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [3, 3, 1], [3, 3, 1], [[0, 2, 1, 3], [1, 2, 1, 3], [2, 1, 0, 1]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154094,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[2,2,1],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[2,2,1],[1,1,0],[3,3,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0095","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[0, 0, 2]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [0, 0, 3], [0, 0, 3], [[0, 0, 2, 0], [1, 0, 2, 0], [2, 2, 1, 3]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [0, 0, 3], [0, 0, 3], [[0, 0, 2, 0], [1, 0, 2, 0], [2, 2, 1, 3]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154095,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[0,0,2],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[0,0,2],[2,2,1],[0,0,3]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0096","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[1, 0, 2]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [1, 0, 3], [1, 0, 3], [[0, 1, 0, 1], [1, 0, 2, 0], [2, 2, 1, 3]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [1, 0, 3], [1, 0, 3], [[0, 1, 0, 1], [1, 0, 2, 0], [2, 2, 1, 3]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154096,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[1,0,2],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[1,0,2],[0,2,1],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0097","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[2, 0, 2]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [3, 0, 3], [3, 0, 3], [[0, 2, 1, 3], [1, 0, 2, 0], [2, 2, 1, 3]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [3, 0, 3], [3, 0, 3], [[0, 2, 1, 3], [1, 0, 2, 0], [2, 2, 1, 3]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154097,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[2,0,2],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[2,0,2],[1,2,1],[3,0,3]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0098","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[0, 1, 2]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [0, 1, 3], [0, 1, 3], [[0, 0, 2, 0], [1, 1, 0, 1], [2, 2, 1, 3]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [0, 1, 3], [0, 1, 3], [[0, 0, 2, 0], [1, 1, 0, 1], [2, 2, 1, 3]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154098,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[0,1,2],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[0,1,2],[2,0,1],[0,1,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0099","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[1, 1, 2]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [1, 1, 3], [1, 1, 3], [[0, 1, 0, 1], [1, 1, 0, 1], [2, 2, 1, 3]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [1, 1, 3], [1, 1, 3], [[0, 1, 0, 1], [1, 1, 0, 1], [2, 2, 1, 3]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154099,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[1,1,2],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[1,1,2],[0,0,1],[1,1,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r04-composition-0100","batch_id":"batch-20261011-advance-20261015-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"三表括號的兩條路徑","stem_zh":"先f後g，明示中間域。Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(3)=[0, 1, 2]、Fin(4)=[0, 1, 2, 3]。完整f=[2, 1, 2]、g=[2, 0, 1]、h=[1, 3, 0]。求 ([n,m,k,l], (h∘g)∘f全表, h∘(g∘f)全表, 每列[x,f(x),g(f(x)),h(g(f(x)))], 兩表相同資格)。","answer":{"kind":"expression","value":"([3, 3, 3, 4], [3, 1, 3], [3, 1, 3], [[0, 2, 1, 3], [1, 1, 0, 1], [2, 2, 1, 3]], 是)","explanation_zh":"三表括號兩路與型別路徑=([3, 3, 3, 4], [3, 1, 3], [3, 1, 3], [[0, 2, 1, 3], [1, 1, 0, 1], [2, 2, 1, 3]], 是)。先組h∘g與先組g∘f的兩路各查全表，再比較有限來源上的值。合成不當乘法或任意交換，有限路徑非全部函數等式形式證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["三表括號的兩條路徑"]},"variant":{"family_id":"qf-density15-composition-three-map-parentheses","seed":202610154100,"parameters":{"n":3,"m":3,"k":3,"l":4,"f":[2,1,2],"g":[2,0,1],"h":[1,3,0],"domain":"finite_explicit_composition_protocol","operation":"density15_composition_three_map_parentheses","semantic_template":"qf-density15-composition-three-map-parentheses/[3,3,3,4,[2,1,2],[1,0,1],[3,1,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}