{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0001","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[-12,-2,-3,1,-1,-1],\"x\":-2,\"y\":-3}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([-12, -2, -3, 1, -1, -1], -2, -3, -10)","explanation_zh":"現代橋梁核對=([-12, -2, -3, 1, -1, -1], -2, -3, -10)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237001,"parameters":{"coefficients":[-12,-2,-3,1,-1,-1],"x":-2,"y":-3,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[-12,-2,-3,1,-1,-1],\"x\":-2,\"y\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0002","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[-11,-1,-2,1,0,-1],\"x\":-1,\"y\":-2}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([-11, -1, -2, 1, 0, -1], -1, -2, -9)","explanation_zh":"現代橋梁核對=([-11, -1, -2, 1, 0, -1], -1, -2, -9)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237002,"parameters":{"coefficients":[-11,-1,-2,1,0,-1],"x":-1,"y":-2,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[-11,-1,-2,1,0,-1],\"x\":-1,\"y\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0003","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[-10,0,-1,1,1,-1],\"x\":0,\"y\":-1}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([-10, 0, -1, 1, 1, -1], 0, -1, -10)","explanation_zh":"現代橋梁核對=([-10, 0, -1, 1, 1, -1], 0, -1, -10)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237003,"parameters":{"coefficients":[-10,0,-1,1,1,-1],"x":0,"y":-1,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[-10,0,-1,1,1,-1],\"x\":0,\"y\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0004","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[-9,1,0,1,-1,-1],\"x\":1,\"y\":0}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([-9, 1, 0, 1, -1, -1], 1, 0, -7)","explanation_zh":"現代橋梁核對=([-9, 1, 0, 1, -1, -1], 1, 0, -7)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237004,"parameters":{"coefficients":[-9,1,0,1,-1,-1],"x":1,"y":0,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[-9,1,0,1,-1,-1],\"x\":1,\"y\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0005","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[-8,2,1,1,0,-1],\"x\":2,\"y\":1}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([-8, 2, 1, 1, 0, -1], 2, 1, 0)","explanation_zh":"現代橋梁核對=([-8, 2, 1, 1, 0, -1], 2, 1, 0)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237005,"parameters":{"coefficients":[-8,2,1,1,0,-1],"x":2,"y":1,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[-8,2,1,1,0,-1],\"x\":2,\"y\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0006","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[-7,-2,2,1,1,-1],\"x\":-2,\"y\":2}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([-7, -2, 2, 1, 1, -1], -2, 2, -3)","explanation_zh":"現代橋梁核對=([-7, -2, 2, 1, 1, -1], -2, 2, -3)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237006,"parameters":{"coefficients":[-7,-2,2,1,1,-1],"x":-2,"y":2,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[-7,-2,2,1,1,-1],\"x\":-2,\"y\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0007","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[-6,-1,3,1,-1,-1],\"x\":-1,\"y\":3}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([-6, -1, 3, 1, -1, -1], -1, 3, -1)","explanation_zh":"現代橋梁核對=([-6, -1, 3, 1, -1, -1], -1, 3, -1)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237007,"parameters":{"coefficients":[-6,-1,3,1,-1,-1],"x":-1,"y":3,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[-6,-1,3,1,-1,-1],\"x\":-1,\"y\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0008","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[-5,0,-3,1,0,-1],\"x\":0,\"y\":-3}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([-5, 0, -3, 1, 0, -1], 0, -3, -5)","explanation_zh":"現代橋梁核對=([-5, 0, -3, 1, 0, -1], 0, -3, -5)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237008,"parameters":{"coefficients":[-5,0,-3,1,0,-1],"x":0,"y":-3,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[-5,0,-3,1,0,-1],\"x\":0,\"y\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0009","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[-4,1,-2,1,1,-1],\"x\":1,\"y\":-2}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([-4, 1, -2, 1, 1, -1], 1, -2, -4)","explanation_zh":"現代橋梁核對=([-4, 1, -2, 1, 1, -1], 1, -2, -4)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237009,"parameters":{"coefficients":[-4,1,-2,1,1,-1],"x":1,"y":-2,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[-4,1,-2,1,1,-1],\"x\":1,\"y\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0010","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[-3,2,-1,1,-1,-1],\"x\":2,\"y\":-1}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([-3, 2, -1, 1, -1, -1], 2, -1, 7)","explanation_zh":"現代橋梁核對=([-3, 2, -1, 1, -1, -1], 2, -1, 7)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237010,"parameters":{"coefficients":[-3,2,-1,1,-1,-1],"x":2,"y":-1,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[-3,2,-1,1,-1,-1],\"x\":2,\"y\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0011","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[-2,-2,0,1,0,-1],\"x\":-2,\"y\":0}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([-2, -2, 0, 1, 0, -1], -2, 0, 6)","explanation_zh":"現代橋梁核對=([-2, -2, 0, 1, 0, -1], -2, 0, 6)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237011,"parameters":{"coefficients":[-2,-2,0,1,0,-1],"x":-2,"y":0,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[-2,-2,0,1,0,-1],\"x\":-2,\"y\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0012","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[-1,-1,1,1,1,-1],\"x\":-1,\"y\":1}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([-1, -1, 1, 1, 1, -1], -1, 1, 0)","explanation_zh":"現代橋梁核對=([-1, -1, 1, 1, 1, -1], -1, 1, 0)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237012,"parameters":{"coefficients":[-1,-1,1,1,1,-1],"x":-1,"y":1,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[-1,-1,1,1,1,-1],\"x\":-1,\"y\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0013","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[0,0,2,1,-1,-1],\"x\":0,\"y\":2}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 2, 1, -1, -1], 0, 2, 0)","explanation_zh":"現代橋梁核對=([0, 0, 2, 1, -1, -1], 0, 2, 0)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237013,"parameters":{"coefficients":[0,0,2,1,-1,-1],"x":0,"y":2,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[0,0,2,1,-1,-1],\"x\":0,\"y\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0014","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[1,1,3,1,0,-1],\"x\":1,\"y\":3}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 3, 1, 0, -1], 1, 3, 3)","explanation_zh":"現代橋梁核對=([1, 1, 3, 1, 0, -1], 1, 3, 3)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237014,"parameters":{"coefficients":[1,1,3,1,0,-1],"x":1,"y":3,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[1,1,3,1,0,-1],\"x\":1,\"y\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0015","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[2,2,-3,1,1,-1],\"x\":2,\"y\":-3}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([2, 2, -3, 1, 1, -1], 2, -3, 4)","explanation_zh":"現代橋梁核對=([2, 2, -3, 1, 1, -1], 2, -3, 4)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237015,"parameters":{"coefficients":[2,2,-3,1,1,-1],"x":2,"y":-3,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[2,2,-3,1,1,-1],\"x\":2,\"y\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0016","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[3,-2,-2,1,-1,-1],\"x\":-2,\"y\":-2}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([3, -2, -2, 1, -1, -1], -2, -2, 7)","explanation_zh":"現代橋梁核對=([3, -2, -2, 1, -1, -1], -2, -2, 7)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237016,"parameters":{"coefficients":[3,-2,-2,1,-1,-1],"x":-2,"y":-2,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[3,-2,-2,1,-1,-1],\"x\":-2,\"y\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0017","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[4,-1,-1,1,0,-1],\"x\":-1,\"y\":-1}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([4, -1, -1, 1, 0, -1], -1, -1, 6)","explanation_zh":"現代橋梁核對=([4, -1, -1, 1, 0, -1], -1, -1, 6)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237017,"parameters":{"coefficients":[4,-1,-1,1,0,-1],"x":-1,"y":-1,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[4,-1,-1,1,0,-1],\"x\":-1,\"y\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0018","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[5,0,0,1,1,-1],\"x\":0,\"y\":0}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([5, 0, 0, 1, 1, -1], 0, 0, 5)","explanation_zh":"現代橋梁核對=([5, 0, 0, 1, 1, -1], 0, 0, 5)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237018,"parameters":{"coefficients":[5,0,0,1,1,-1],"x":0,"y":0,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[5,0,0,1,1,-1],\"x\":0,\"y\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0019","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[6,1,1,1,-1,-1],\"x\":1,\"y\":1}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([6, 1, 1, 1, -1, -1], 1, 1, 7)","explanation_zh":"現代橋梁核對=([6, 1, 1, 1, -1, -1], 1, 1, 7)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237019,"parameters":{"coefficients":[6,1,1,1,-1,-1],"x":1,"y":1,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[6,1,1,1,-1,-1],\"x\":1,\"y\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0020","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[7,2,2,1,0,-1],\"x\":2,\"y\":2}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([7, 2, 2, 1, 0, -1], 2, 2, 15)","explanation_zh":"現代橋梁核對=([7, 2, 2, 1, 0, -1], 2, 2, 15)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237020,"parameters":{"coefficients":[7,2,2,1,0,-1],"x":2,"y":2,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[7,2,2,1,0,-1],\"x\":2,\"y\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0021","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[8,-2,3,1,1,-1],\"x\":-2,\"y\":3}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([8, -2, 3, 1, 1, -1], -2, 3, 10)","explanation_zh":"現代橋梁核對=([8, -2, 3, 1, 1, -1], -2, 3, 10)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237021,"parameters":{"coefficients":[8,-2,3,1,1,-1],"x":-2,"y":3,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[8,-2,3,1,1,-1],\"x\":-2,\"y\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0022","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[9,-1,-3,1,-1,-1],\"x\":-1,\"y\":-3}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([9, -1, -3, 1, -1, -1], -1, -3, 8)","explanation_zh":"現代橋梁核對=([9, -1, -3, 1, -1, -1], -1, -3, 8)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237022,"parameters":{"coefficients":[9,-1,-3,1,-1,-1],"x":-1,"y":-3,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[9,-1,-3,1,-1,-1],\"x\":-1,\"y\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0023","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[10,0,-2,1,0,-1],\"x\":0,\"y\":-2}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([10, 0, -2, 1, 0, -1], 0, -2, 10)","explanation_zh":"現代橋梁核對=([10, 0, -2, 1, 0, -1], 0, -2, 10)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237023,"parameters":{"coefficients":[10,0,-2,1,0,-1],"x":0,"y":-2,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[10,0,-2,1,0,-1],\"x\":0,\"y\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0024","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[11,1,-1,1,1,-1],\"x\":1,\"y\":-1}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([11, 1, -1, 1, 1, -1], 1, -1, 12)","explanation_zh":"現代橋梁核對=([11, 1, -1, 1, 1, -1], 1, -1, 12)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237024,"parameters":{"coefficients":[11,1,-1,1,1,-1],"x":1,"y":-1,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[11,1,-1,1,1,-1],\"x\":1,\"y\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0025","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-evaluate；資料={\"coefficients\":[12,2,0,1,-1,-1],\"x\":2,\"y\":0}。請依 [coefficients,x,y,value] 欄序回答。","answer":{"kind":"expression","value":"([12, 2, 0, 1, -1, -1], 2, 0, 20)","explanation_zh":"現代橋梁核對=([12, 2, 0, 1, -1, -1], 2, 0, 20)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-evaluate","seed":202610237025,"parameters":{"coefficients":[12,2,0,1,-1,-1],"x":2,"y":0,"domain":"Polynomial_R2_to_R_slice","operation":"multivar-evaluate","semantic_template":"qf-mod23-multivar-evaluate/{\"coefficients\":[12,2,0,1,-1,-1],\"x\":2,\"y\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0026","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-2,2,-1,3],\"point\":[-3,-2]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-2, 2, -1, 3], [-3, -2], 否)","explanation_zh":"現代橋梁核對=([-2, 2, -1, 3], [-3, -2], 否)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237026,"parameters":{"bounds":[-2,2,-1,3],"point":[-3,-2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-2,2,-1,3],\"point\":[-3,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0027","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-3,3,-2,4],\"point\":[-2,-1]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-3, 3, -2, 4], [-2, -1], 是)","explanation_zh":"現代橋梁核對=([-3, 3, -2, 4], [-2, -1], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237027,"parameters":{"bounds":[-3,3,-2,4],"point":[-2,-1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-3,3,-2,4],\"point\":[-2,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0028","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-4,4,-3,5],\"point\":[-1,0]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-4, 4, -3, 5], [-1, 0], 是)","explanation_zh":"現代橋梁核對=([-4, 4, -3, 5], [-1, 0], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237028,"parameters":{"bounds":[-4,4,-3,5],"point":[-1,0],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-4,4,-3,5],\"point\":[-1,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0029","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-5,5,-4,6],\"point\":[0,1]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-5, 5, -4, 6], [0, 1], 是)","explanation_zh":"現代橋梁核對=([-5, 5, -4, 6], [0, 1], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237029,"parameters":{"bounds":[-5,5,-4,6],"point":[0,1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-5,5,-4,6],\"point\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0030","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-6,6,-5,7],\"point\":[1,2]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-6, 6, -5, 7], [1, 2], 是)","explanation_zh":"現代橋梁核對=([-6, 6, -5, 7], [1, 2], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237030,"parameters":{"bounds":[-6,6,-5,7],"point":[1,2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-6,6,-5,7],\"point\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0031","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-7,7,-6,8],\"point\":[2,-2]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-7, 7, -6, 8], [2, -2], 是)","explanation_zh":"現代橋梁核對=([-7, 7, -6, 8], [2, -2], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237031,"parameters":{"bounds":[-7,7,-6,8],"point":[2,-2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-7,7,-6,8],\"point\":[2,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0032","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-8,8,-7,9],\"point\":[3,-1]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-8, 8, -7, 9], [3, -1], 是)","explanation_zh":"現代橋梁核對=([-8, 8, -7, 9], [3, -1], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237032,"parameters":{"bounds":[-8,8,-7,9],"point":[3,-1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-8,8,-7,9],\"point\":[3,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0033","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-9,9,-8,10],\"point\":[-3,0]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-9, 9, -8, 10], [-3, 0], 是)","explanation_zh":"現代橋梁核對=([-9, 9, -8, 10], [-3, 0], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237033,"parameters":{"bounds":[-9,9,-8,10],"point":[-3,0],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-9,9,-8,10],\"point\":[-3,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0034","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-10,10,-9,11],\"point\":[-2,1]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-10, 10, -9, 11], [-2, 1], 是)","explanation_zh":"現代橋梁核對=([-10, 10, -9, 11], [-2, 1], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237034,"parameters":{"bounds":[-10,10,-9,11],"point":[-2,1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-10,10,-9,11],\"point\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0035","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-11,11,-10,12],\"point\":[-1,2]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-11, 11, -10, 12], [-1, 2], 是)","explanation_zh":"現代橋梁核對=([-11, 11, -10, 12], [-1, 2], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237035,"parameters":{"bounds":[-11,11,-10,12],"point":[-1,2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-11,11,-10,12],\"point\":[-1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0036","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-12,12,-11,13],\"point\":[0,-2]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-12, 12, -11, 13], [0, -2], 是)","explanation_zh":"現代橋梁核對=([-12, 12, -11, 13], [0, -2], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237036,"parameters":{"bounds":[-12,12,-11,13],"point":[0,-2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-12,12,-11,13],\"point\":[0,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0037","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-13,13,-12,14],\"point\":[1,-1]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-13, 13, -12, 14], [1, -1], 是)","explanation_zh":"現代橋梁核對=([-13, 13, -12, 14], [1, -1], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237037,"parameters":{"bounds":[-13,13,-12,14],"point":[1,-1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-13,13,-12,14],\"point\":[1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0038","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-14,14,-13,15],\"point\":[2,0]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-14, 14, -13, 15], [2, 0], 是)","explanation_zh":"現代橋梁核對=([-14, 14, -13, 15], [2, 0], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237038,"parameters":{"bounds":[-14,14,-13,15],"point":[2,0],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-14,14,-13,15],\"point\":[2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0039","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-15,15,-14,16],\"point\":[3,1]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-15, 15, -14, 16], [3, 1], 是)","explanation_zh":"現代橋梁核對=([-15, 15, -14, 16], [3, 1], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237039,"parameters":{"bounds":[-15,15,-14,16],"point":[3,1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-15,15,-14,16],\"point\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0040","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-16,16,-15,17],\"point\":[-3,2]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-16, 16, -15, 17], [-3, 2], 是)","explanation_zh":"現代橋梁核對=([-16, 16, -15, 17], [-3, 2], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237040,"parameters":{"bounds":[-16,16,-15,17],"point":[-3,2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-16,16,-15,17],\"point\":[-3,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0041","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-17,17,-16,18],\"point\":[-2,-2]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-17, 17, -16, 18], [-2, -2], 是)","explanation_zh":"現代橋梁核對=([-17, 17, -16, 18], [-2, -2], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237041,"parameters":{"bounds":[-17,17,-16,18],"point":[-2,-2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-17,17,-16,18],\"point\":[-2,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0042","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-18,18,-17,19],\"point\":[-1,-1]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-18, 18, -17, 19], [-1, -1], 是)","explanation_zh":"現代橋梁核對=([-18, 18, -17, 19], [-1, -1], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237042,"parameters":{"bounds":[-18,18,-17,19],"point":[-1,-1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-18,18,-17,19],\"point\":[-1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0043","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-19,19,-18,20],\"point\":[0,0]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-19, 19, -18, 20], [0, 0], 是)","explanation_zh":"現代橋梁核對=([-19, 19, -18, 20], [0, 0], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237043,"parameters":{"bounds":[-19,19,-18,20],"point":[0,0],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-19,19,-18,20],\"point\":[0,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0044","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-20,20,-19,21],\"point\":[1,1]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-20, 20, -19, 21], [1, 1], 是)","explanation_zh":"現代橋梁核對=([-20, 20, -19, 21], [1, 1], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237044,"parameters":{"bounds":[-20,20,-19,21],"point":[1,1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-20,20,-19,21],\"point\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0045","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-21,21,-20,22],\"point\":[2,2]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-21, 21, -20, 22], [2, 2], 是)","explanation_zh":"現代橋梁核對=([-21, 21, -20, 22], [2, 2], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237045,"parameters":{"bounds":[-21,21,-20,22],"point":[2,2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-21,21,-20,22],\"point\":[2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0046","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-22,22,-21,23],\"point\":[3,-2]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-22, 22, -21, 23], [3, -2], 是)","explanation_zh":"現代橋梁核對=([-22, 22, -21, 23], [3, -2], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237046,"parameters":{"bounds":[-22,22,-21,23],"point":[3,-2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-22,22,-21,23],\"point\":[3,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0047","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-23,23,-22,24],\"point\":[-3,-1]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-23, 23, -22, 24], [-3, -1], 是)","explanation_zh":"現代橋梁核對=([-23, 23, -22, 24], [-3, -1], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237047,"parameters":{"bounds":[-23,23,-22,24],"point":[-3,-1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-23,23,-22,24],\"point\":[-3,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0048","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-24,24,-23,25],\"point\":[-2,0]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-24, 24, -23, 25], [-2, 0], 是)","explanation_zh":"現代橋梁核對=([-24, 24, -23, 25], [-2, 0], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237048,"parameters":{"bounds":[-24,24,-23,25],"point":[-2,0],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-24,24,-23,25],\"point\":[-2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0049","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-25,25,-24,26],\"point\":[-1,1]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-25, 25, -24, 26], [-1, 1], 是)","explanation_zh":"現代橋梁核對=([-25, 25, -24, 26], [-1, 1], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237049,"parameters":{"bounds":[-25,25,-24,26],"point":[-1,1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-25,25,-24,26],\"point\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0050","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-rectangle-domain-audit；資料={\"bounds\":[-26,26,-25,27],\"point\":[0,2]}。請依 [bounds,point,in_domain] 欄序回答。","answer":{"kind":"expression","value":"([-26, 26, -25, 27], [0, 2], 是)","explanation_zh":"現代橋梁核對=([-26, 26, -25, 27], [0, 2], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-rectangle-domain-audit","seed":202610237050,"parameters":{"bounds":[-26,26,-25,27],"point":[0,2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-rectangle-domain-audit","semantic_template":"qf-mod23-multivar-rectangle-domain-audit/{\"bounds\":[-26,26,-25,27],\"point\":[0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0051","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[-12,-2,-3,1,-1,-1],\"y\":-2,\"xs\":[-1,0,-3]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([-12, -2, -3, 1, -1, -1], -2, [-3, -1, 0], [[-3, -1], [-1, -9], [0, -10]])","explanation_zh":"現代橋梁核對=([-12, -2, -3, 1, -1, -1], -2, [-3, -1, 0], [[-3, -1], [-1, -9], [0, -10]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237051,"parameters":{"coefficients":[-12,-2,-3,1,-1,-1],"y":-2,"xs":[-1,0,-3],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[-12,-2,-3,1,-1,-1],\"xs\":[-3,-1,0],\"y\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0052","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[-11,-1,-2,1,0,-1],\"y\":-1,\"xs\":[-1,0,-2]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([-11, -1, -2, 1, 0, -1], -1, [-2, -1, 0], [[-2, -4], [-1, -8], [0, -10]])","explanation_zh":"現代橋梁核對=([-11, -1, -2, 1, 0, -1], -1, [-2, -1, 0], [[-2, -4], [-1, -8], [0, -10]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237052,"parameters":{"coefficients":[-11,-1,-2,1,0,-1],"y":-1,"xs":[-1,0,-2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[-11,-1,-2,1,0,-1],\"xs\":[-2,-1,0],\"y\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0053","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[-10,0,-1,1,1,-1],\"y\":0,\"xs\":[-1,0,-1]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([-10, 0, -1, 1, 1, -1], 0, [-1, 0], [[-1, -9], [0, -10]])","explanation_zh":"現代橋梁核對=([-10, 0, -1, 1, 1, -1], 0, [-1, 0], [[-1, -9], [0, -10]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237053,"parameters":{"coefficients":[-10,0,-1,1,1,-1],"y":0,"xs":[-1,0,-1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[-10,0,-1,1,1,-1],\"xs\":[-1,0],\"y\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0054","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[-9,1,0,1,-1,-1],\"y\":1,\"xs\":[-1,0,0]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([-9, 1, 0, 1, -1, -1], 1, [-1, 0], [[-1, -9], [0, -10]])","explanation_zh":"現代橋梁核對=([-9, 1, 0, 1, -1, -1], 1, [-1, 0], [[-1, -9], [0, -10]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237054,"parameters":{"coefficients":[-9,1,0,1,-1,-1],"y":1,"xs":[-1,0,0],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[-9,1,0,1,-1,-1],\"xs\":[-1,0],\"y\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0055","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[-8,2,1,1,0,-1],\"y\":2,\"xs\":[-1,0,1]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([-8, 2, 1, 1, 0, -1], 2, [-1, 0, 1], [[-1, -11], [0, -10], [1, -7]])","explanation_zh":"現代橋梁核對=([-8, 2, 1, 1, 0, -1], 2, [-1, 0, 1], [[-1, -11], [0, -10], [1, -7]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237055,"parameters":{"coefficients":[-8,2,1,1,0,-1],"y":2,"xs":[-1,0,1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[-8,2,1,1,0,-1],\"xs\":[-1,0,1],\"y\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0056","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[-7,-2,2,1,1,-1],\"y\":-2,\"xs\":[-1,0,2]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([-7, -2, 2, 1, 1, -1], -2, [-1, 0, 2], [[-1, -10], [0, -15], [2, -19]])","explanation_zh":"現代橋梁核對=([-7, -2, 2, 1, 1, -1], -2, [-1, 0, 2], [[-1, -10], [0, -15], [2, -19]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237056,"parameters":{"coefficients":[-7,-2,2,1,1,-1],"y":-2,"xs":[-1,0,2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[-7,-2,2,1,1,-1],\"xs\":[-1,0,2],\"y\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0057","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[-6,-1,3,1,-1,-1],\"y\":-1,\"xs\":[-1,0,3]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([-6, -1, 3, 1, -1, -1], -1, [-1, 0, 3], [[-1, -9], [0, -10], [3, -1]])","explanation_zh":"現代橋梁核對=([-6, -1, 3, 1, -1, -1], -1, [-1, 0, 3], [[-1, -9], [0, -10], [3, -1]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237057,"parameters":{"coefficients":[-6,-1,3,1,-1,-1],"y":-1,"xs":[-1,0,3],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[-6,-1,3,1,-1,-1],\"xs\":[-1,0,3],\"y\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0058","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[-5,0,-3,1,0,-1],\"y\":0,\"xs\":[-1,0,-3]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([-5, 0, -3, 1, 0, -1], 0, [-3, -1, 0], [[-3, 4], [-1, -4], [0, -5]])","explanation_zh":"現代橋梁核對=([-5, 0, -3, 1, 0, -1], 0, [-3, -1, 0], [[-3, 4], [-1, -4], [0, -5]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237058,"parameters":{"coefficients":[-5,0,-3,1,0,-1],"y":0,"xs":[-1,0,-3],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[-5,0,-3,1,0,-1],\"xs\":[-3,-1,0],\"y\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0059","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[-4,1,-2,1,1,-1],\"y\":1,\"xs\":[-1,0,-2]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([-4, 1, -2, 1, 1, -1], 1, [-2, -1, 0], [[-2, -7], [-1, -8], [0, -7]])","explanation_zh":"現代橋梁核對=([-4, 1, -2, 1, 1, -1], 1, [-2, -1, 0], [[-2, -7], [-1, -8], [0, -7]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237059,"parameters":{"coefficients":[-4,1,-2,1,1,-1],"y":1,"xs":[-1,0,-2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[-4,1,-2,1,1,-1],\"xs\":[-2,-1,0],\"y\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0060","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[-3,2,-1,1,-1,-1],\"y\":2,\"xs\":[-1,0,-1]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([-3, 2, -1, 1, -1, -1], 2, [-1, 0], [[-1, -8], [0, -9]])","explanation_zh":"現代橋梁核對=([-3, 2, -1, 1, -1, -1], 2, [-1, 0], [[-1, -8], [0, -9]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237060,"parameters":{"coefficients":[-3,2,-1,1,-1,-1],"y":2,"xs":[-1,0,-1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[-3,2,-1,1,-1,-1],\"xs\":[-1,0],\"y\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0061","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[-2,-2,0,1,0,-1],\"y\":-2,\"xs\":[-1,0,0]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([-2, -2, 0, 1, 0, -1], -2, [-1, 0], [[-1, -3], [0, -6]])","explanation_zh":"現代橋梁核對=([-2, -2, 0, 1, 0, -1], -2, [-1, 0], [[-1, -3], [0, -6]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237061,"parameters":{"coefficients":[-2,-2,0,1,0,-1],"y":-2,"xs":[-1,0,0],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[-2,-2,0,1,0,-1],\"xs\":[-1,0],\"y\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0062","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[-1,-1,1,1,1,-1],\"y\":-1,\"xs\":[-1,0,1]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([-1, -1, 1, 1, 1, -1], -1, [-1, 0, 1], [[-1, 0], [0, -3], [1, -4]])","explanation_zh":"現代橋梁核對=([-1, -1, 1, 1, 1, -1], -1, [-1, 0, 1], [[-1, 0], [0, -3], [1, -4]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237062,"parameters":{"coefficients":[-1,-1,1,1,1,-1],"y":-1,"xs":[-1,0,1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[-1,-1,1,1,1,-1],\"xs\":[-1,0,1],\"y\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0063","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[0,0,2,1,-1,-1],\"y\":0,\"xs\":[-1,0,2]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 2, 1, -1, -1], 0, [-1, 0, 2], [[-1, 1], [0, 0], [2, 4]])","explanation_zh":"現代橋梁核對=([0, 0, 2, 1, -1, -1], 0, [-1, 0, 2], [[-1, 1], [0, 0], [2, 4]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237063,"parameters":{"coefficients":[0,0,2,1,-1,-1],"y":0,"xs":[-1,0,2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[0,0,2,1,-1,-1],\"xs\":[-1,0,2],\"y\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0064","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[1,1,3,1,0,-1],\"y\":1,\"xs\":[-1,0,3]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 3, 1, 0, -1], 1, [-1, 0, 3], [[-1, 3], [0, 3], [3, 15]])","explanation_zh":"現代橋梁核對=([1, 1, 3, 1, 0, -1], 1, [-1, 0, 3], [[-1, 3], [0, 3], [3, 15]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237064,"parameters":{"coefficients":[1,1,3,1,0,-1],"y":1,"xs":[-1,0,3],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[1,1,3,1,0,-1],\"xs\":[-1,0,3],\"y\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0065","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[2,2,-3,1,1,-1],\"y\":2,\"xs\":[-1,0,-3]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([2, 2, -3, 1, 1, -1], 2, [-3, -1, 0], [[-3, -11], [-1, -11], [0, -8]])","explanation_zh":"現代橋梁核對=([2, 2, -3, 1, 1, -1], 2, [-3, -1, 0], [[-3, -11], [-1, -11], [0, -8]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237065,"parameters":{"coefficients":[2,2,-3,1,1,-1],"y":2,"xs":[-1,0,-3],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[2,2,-3,1,1,-1],\"xs\":[-3,-1,0],\"y\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0066","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[3,-2,-2,1,-1,-1],\"y\":-2,\"xs\":[-1,0,-2]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([3, -2, -2, 1, -1, -1], -2, [-2, -1, 0], [[-2, 7], [-1, 4], [0, 3]])","explanation_zh":"現代橋梁核對=([3, -2, -2, 1, -1, -1], -2, [-2, -1, 0], [[-2, 7], [-1, 4], [0, 3]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237066,"parameters":{"coefficients":[3,-2,-2,1,-1,-1],"y":-2,"xs":[-1,0,-2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[3,-2,-2,1,-1,-1],\"xs\":[-2,-1,0],\"y\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0067","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[4,-1,-1,1,0,-1],\"y\":-1,\"xs\":[-1,0,-1]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([4, -1, -1, 1, 0, -1], -1, [-1, 0], [[-1, 6], [0, 4]])","explanation_zh":"現代橋梁核對=([4, -1, -1, 1, 0, -1], -1, [-1, 0], [[-1, 6], [0, 4]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237067,"parameters":{"coefficients":[4,-1,-1,1,0,-1],"y":-1,"xs":[-1,0,-1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[4,-1,-1,1,0,-1],\"xs\":[-1,0],\"y\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0068","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[5,0,0,1,1,-1],\"y\":0,\"xs\":[-1,0,0]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([5, 0, 0, 1, 1, -1], 0, [-1, 0], [[-1, 6], [0, 5]])","explanation_zh":"現代橋梁核對=([5, 0, 0, 1, 1, -1], 0, [-1, 0], [[-1, 6], [0, 5]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237068,"parameters":{"coefficients":[5,0,0,1,1,-1],"y":0,"xs":[-1,0,0],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[5,0,0,1,1,-1],\"xs\":[-1,0],\"y\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0069","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[6,1,1,1,-1,-1],\"y\":1,\"xs\":[-1,0,1]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([6, 1, 1, 1, -1, -1], 1, [-1, 0, 1], [[-1, 7], [0, 6], [1, 7]])","explanation_zh":"現代橋梁核對=([6, 1, 1, 1, -1, -1], 1, [-1, 0, 1], [[-1, 7], [0, 6], [1, 7]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237069,"parameters":{"coefficients":[6,1,1,1,-1,-1],"y":1,"xs":[-1,0,1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[6,1,1,1,-1,-1],\"xs\":[-1,0,1],\"y\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0070","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[7,2,2,1,0,-1],\"y\":2,\"xs\":[-1,0,2]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([7, 2, 2, 1, 0, -1], 2, [-1, 0, 2], [[-1, 6], [0, 7], [2, 15]])","explanation_zh":"現代橋梁核對=([7, 2, 2, 1, 0, -1], 2, [-1, 0, 2], [[-1, 6], [0, 7], [2, 15]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237070,"parameters":{"coefficients":[7,2,2,1,0,-1],"y":2,"xs":[-1,0,2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[7,2,2,1,0,-1],\"xs\":[-1,0,2],\"y\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0071","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[8,-2,3,1,1,-1],\"y\":-2,\"xs\":[-1,0,3]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([8, -2, 3, 1, 1, -1], -2, [-1, 0, 3], [[-1, 3], [0, -2], [3, -5]])","explanation_zh":"現代橋梁核對=([8, -2, 3, 1, 1, -1], -2, [-1, 0, 3], [[-1, 3], [0, -2], [3, -5]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237071,"parameters":{"coefficients":[8,-2,3,1,1,-1],"y":-2,"xs":[-1,0,3],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[8,-2,3,1,1,-1],\"xs\":[-1,0,3],\"y\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0072","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[9,-1,-3,1,-1,-1],\"y\":-1,\"xs\":[-1,0,-3]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([9, -1, -3, 1, -1, -1], -1, [-3, -1, 0], [[-3, 20], [-1, 12], [0, 11]])","explanation_zh":"現代橋梁核對=([9, -1, -3, 1, -1, -1], -1, [-3, -1, 0], [[-3, 20], [-1, 12], [0, 11]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237072,"parameters":{"coefficients":[9,-1,-3,1,-1,-1],"y":-1,"xs":[-1,0,-3],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[9,-1,-3,1,-1,-1],\"xs\":[-3,-1,0],\"y\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0073","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[10,0,-2,1,0,-1],\"y\":0,\"xs\":[-1,0,-2]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([10, 0, -2, 1, 0, -1], 0, [-2, -1, 0], [[-2, 14], [-1, 11], [0, 10]])","explanation_zh":"現代橋梁核對=([10, 0, -2, 1, 0, -1], 0, [-2, -1, 0], [[-2, 14], [-1, 11], [0, 10]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237073,"parameters":{"coefficients":[10,0,-2,1,0,-1],"y":0,"xs":[-1,0,-2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[10,0,-2,1,0,-1],\"xs\":[-2,-1,0],\"y\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0074","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[11,1,-1,1,1,-1],\"y\":1,\"xs\":[-1,0,-1]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([11, 1, -1, 1, 1, -1], 1, [-1, 0], [[-1, 8], [0, 9]])","explanation_zh":"現代橋梁核對=([11, 1, -1, 1, 1, -1], 1, [-1, 0], [[-1, 8], [0, 9]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237074,"parameters":{"coefficients":[11,1,-1,1,1,-1],"y":1,"xs":[-1,0,-1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[11,1,-1,1,1,-1],\"xs\":[-1,0],\"y\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0075","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-x-slice-table；資料={\"coefficients\":[12,2,0,1,-1,-1],\"y\":2,\"xs\":[-1,0,0]}。請依 [coefficients,fixed_y,xs,table] 欄序回答。","answer":{"kind":"expression","value":"([12, 2, 0, 1, -1, -1], 2, [-1, 0], [[-1, 9], [0, 8]])","explanation_zh":"現代橋梁核對=([12, 2, 0, 1, -1, -1], 2, [-1, 0], [[-1, 9], [0, 8]])；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-x-slice-table","seed":202610237075,"parameters":{"coefficients":[12,2,0,1,-1,-1],"y":2,"xs":[-1,0,0],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-x-slice-table","semantic_template":"qf-mod23-multivar-x-slice-table/{\"coefficients\":[12,2,0,1,-1,-1],\"xs\":[-1,0],\"y\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0076","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[-12,-2,-3,1,-1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[-12,-13,-15]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([-12, -2, -3, 1, -1, -1], [[0, 0, -12, -12, 是], [1, 0, -13, -13, 是], [0, 1, -15, -16, 否]], 否)","explanation_zh":"現代橋梁核對=([-12, -2, -3, 1, -1, -1], [[0, 0, -12, -12, 是], [1, 0, -13, -13, 是], [0, 1, -15, -16, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237076,"parameters":{"coefficients":[-12,-2,-3,1,-1,-1],"points":[[0,0],[1,0],[0,1]],"values":[-12,-13,-15],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[-12,-2,-3,1,-1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[-12,-13,-15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0077","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[-11,-1,-2,1,0,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[-11,-11,-14]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([-11, -1, -2, 1, 0, -1], [[0, 0, -11, -11, 是], [1, 0, -11, -11, 是], [0, 1, -14, -14, 是]], 是)","explanation_zh":"現代橋梁核對=([-11, -1, -2, 1, 0, -1], [[0, 0, -11, -11, 是], [1, 0, -11, -11, 是], [0, 1, -14, -14, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237077,"parameters":{"coefficients":[-11,-1,-2,1,0,-1],"points":[[0,0],[1,0],[0,1]],"values":[-11,-11,-14],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[-11,-1,-2,1,0,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[-11,-11,-14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0078","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[-10,0,-1,1,1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[-10,-9,-12]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([-10, 0, -1, 1, 1, -1], [[0, 0, -10, -10, 是], [1, 0, -9, -9, 是], [0, 1, -12, -12, 是]], 是)","explanation_zh":"現代橋梁核對=([-10, 0, -1, 1, 1, -1], [[0, 0, -10, -10, 是], [1, 0, -9, -9, 是], [0, 1, -12, -12, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237078,"parameters":{"coefficients":[-10,0,-1,1,1,-1],"points":[[0,0],[1,0],[0,1]],"values":[-10,-9,-12],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[-10,0,-1,1,1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[-10,-9,-12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0079","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[-9,1,0,1,-1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[-9,-7,-10]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([-9, 1, 0, 1, -1, -1], [[0, 0, -9, -9, 是], [1, 0, -7, -7, 是], [0, 1, -10, -10, 是]], 是)","explanation_zh":"現代橋梁核對=([-9, 1, 0, 1, -1, -1], [[0, 0, -9, -9, 是], [1, 0, -7, -7, 是], [0, 1, -10, -10, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237079,"parameters":{"coefficients":[-9,1,0,1,-1,-1],"points":[[0,0],[1,0],[0,1]],"values":[-9,-7,-10],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[-9,1,0,1,-1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[-9,-7,-10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0080","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[-8,2,1,1,0,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[-8,-5,-7]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([-8, 2, 1, 1, 0, -1], [[0, 0, -8, -8, 是], [1, 0, -5, -5, 是], [0, 1, -7, -8, 否]], 否)","explanation_zh":"現代橋梁核對=([-8, 2, 1, 1, 0, -1], [[0, 0, -8, -8, 是], [1, 0, -5, -5, 是], [0, 1, -7, -8, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237080,"parameters":{"coefficients":[-8,2,1,1,0,-1],"points":[[0,0],[1,0],[0,1]],"values":[-8,-5,-7],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[-8,2,1,1,0,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[-8,-5,-7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0081","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[-7,-2,2,1,1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[-7,-8,-6]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([-7, -2, 2, 1, 1, -1], [[0, 0, -7, -7, 是], [1, 0, -8, -8, 是], [0, 1, -6, -6, 是]], 是)","explanation_zh":"現代橋梁核對=([-7, -2, 2, 1, 1, -1], [[0, 0, -7, -7, 是], [1, 0, -8, -8, 是], [0, 1, -6, -6, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237081,"parameters":{"coefficients":[-7,-2,2,1,1,-1],"points":[[0,0],[1,0],[0,1]],"values":[-7,-8,-6],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[-7,-2,2,1,1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[-7,-8,-6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0082","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[-6,-1,3,1,-1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[-6,-6,-4]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([-6, -1, 3, 1, -1, -1], [[0, 0, -6, -6, 是], [1, 0, -6, -6, 是], [0, 1, -4, -4, 是]], 是)","explanation_zh":"現代橋梁核對=([-6, -1, 3, 1, -1, -1], [[0, 0, -6, -6, 是], [1, 0, -6, -6, 是], [0, 1, -4, -4, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237082,"parameters":{"coefficients":[-6,-1,3,1,-1,-1],"points":[[0,0],[1,0],[0,1]],"values":[-6,-6,-4],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[-6,-1,3,1,-1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[-6,-6,-4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0083","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[-5,0,-3,1,0,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[-5,-4,-9]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([-5, 0, -3, 1, 0, -1], [[0, 0, -5, -5, 是], [1, 0, -4, -4, 是], [0, 1, -9, -9, 是]], 是)","explanation_zh":"現代橋梁核對=([-5, 0, -3, 1, 0, -1], [[0, 0, -5, -5, 是], [1, 0, -4, -4, 是], [0, 1, -9, -9, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237083,"parameters":{"coefficients":[-5,0,-3,1,0,-1],"points":[[0,0],[1,0],[0,1]],"values":[-5,-4,-9],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[-5,0,-3,1,0,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[-5,-4,-9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0084","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[-4,1,-2,1,1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[-4,-2,-6]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([-4, 1, -2, 1, 1, -1], [[0, 0, -4, -4, 是], [1, 0, -2, -2, 是], [0, 1, -6, -7, 否]], 否)","explanation_zh":"現代橋梁核對=([-4, 1, -2, 1, 1, -1], [[0, 0, -4, -4, 是], [1, 0, -2, -2, 是], [0, 1, -6, -7, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237084,"parameters":{"coefficients":[-4,1,-2,1,1,-1],"points":[[0,0],[1,0],[0,1]],"values":[-4,-2,-6],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[-4,1,-2,1,1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[-4,-2,-6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0085","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[-3,2,-1,1,-1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[-3,0,-5]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([-3, 2, -1, 1, -1, -1], [[0, 0, -3, -3, 是], [1, 0, 0, 0, 是], [0, 1, -5, -5, 是]], 是)","explanation_zh":"現代橋梁核對=([-3, 2, -1, 1, -1, -1], [[0, 0, -3, -3, 是], [1, 0, 0, 0, 是], [0, 1, -5, -5, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237085,"parameters":{"coefficients":[-3,2,-1,1,-1,-1],"points":[[0,0],[1,0],[0,1]],"values":[-3,0,-5],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[-3,2,-1,1,-1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[-3,0,-5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0086","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[-2,-2,0,1,0,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[-2,-3,-3]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([-2, -2, 0, 1, 0, -1], [[0, 0, -2, -2, 是], [1, 0, -3, -3, 是], [0, 1, -3, -3, 是]], 是)","explanation_zh":"現代橋梁核對=([-2, -2, 0, 1, 0, -1], [[0, 0, -2, -2, 是], [1, 0, -3, -3, 是], [0, 1, -3, -3, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237086,"parameters":{"coefficients":[-2,-2,0,1,0,-1],"points":[[0,0],[1,0],[0,1]],"values":[-2,-3,-3],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[-2,-2,0,1,0,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[-2,-3,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0087","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[-1,-1,1,1,1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[-1,-1,-1]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([-1, -1, 1, 1, 1, -1], [[0, 0, -1, -1, 是], [1, 0, -1, -1, 是], [0, 1, -1, -1, 是]], 是)","explanation_zh":"現代橋梁核對=([-1, -1, 1, 1, 1, -1], [[0, 0, -1, -1, 是], [1, 0, -1, -1, 是], [0, 1, -1, -1, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237087,"parameters":{"coefficients":[-1,-1,1,1,1,-1],"points":[[0,0],[1,0],[0,1]],"values":[-1,-1,-1],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[-1,-1,1,1,1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[-1,-1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0088","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[0,0,2,1,-1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[0,1,2]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 2, 1, -1, -1], [[0, 0, 0, 0, 是], [1, 0, 1, 1, 是], [0, 1, 2, 1, 否]], 否)","explanation_zh":"現代橋梁核對=([0, 0, 2, 1, -1, -1], [[0, 0, 0, 0, 是], [1, 0, 1, 1, 是], [0, 1, 2, 1, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237088,"parameters":{"coefficients":[0,0,2,1,-1,-1],"points":[[0,0],[1,0],[0,1]],"values":[0,1,2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[0,0,2,1,-1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0089","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[1,1,3,1,0,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[1,3,3]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 3, 1, 0, -1], [[0, 0, 1, 1, 是], [1, 0, 3, 3, 是], [0, 1, 3, 3, 是]], 是)","explanation_zh":"現代橋梁核對=([1, 1, 3, 1, 0, -1], [[0, 0, 1, 1, 是], [1, 0, 3, 3, 是], [0, 1, 3, 3, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237089,"parameters":{"coefficients":[1,1,3,1,0,-1],"points":[[0,0],[1,0],[0,1]],"values":[1,3,3],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[1,1,3,1,0,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[1,3,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0090","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[2,2,-3,1,1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[2,5,-2]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([2, 2, -3, 1, 1, -1], [[0, 0, 2, 2, 是], [1, 0, 5, 5, 是], [0, 1, -2, -2, 是]], 是)","explanation_zh":"現代橋梁核對=([2, 2, -3, 1, 1, -1], [[0, 0, 2, 2, 是], [1, 0, 5, 5, 是], [0, 1, -2, -2, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237090,"parameters":{"coefficients":[2,2,-3,1,1,-1],"points":[[0,0],[1,0],[0,1]],"values":[2,5,-2],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[2,2,-3,1,1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[2,5,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0091","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[3,-2,-2,1,-1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[3,2,0]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([3, -2, -2, 1, -1, -1], [[0, 0, 3, 3, 是], [1, 0, 2, 2, 是], [0, 1, 0, 0, 是]], 是)","explanation_zh":"現代橋梁核對=([3, -2, -2, 1, -1, -1], [[0, 0, 3, 3, 是], [1, 0, 2, 2, 是], [0, 1, 0, 0, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237091,"parameters":{"coefficients":[3,-2,-2,1,-1,-1],"points":[[0,0],[1,0],[0,1]],"values":[3,2,0],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[3,-2,-2,1,-1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[3,2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0092","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[4,-1,-1,1,0,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[4,4,3]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([4, -1, -1, 1, 0, -1], [[0, 0, 4, 4, 是], [1, 0, 4, 4, 是], [0, 1, 3, 2, 否]], 否)","explanation_zh":"現代橋梁核對=([4, -1, -1, 1, 0, -1], [[0, 0, 4, 4, 是], [1, 0, 4, 4, 是], [0, 1, 3, 2, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237092,"parameters":{"coefficients":[4,-1,-1,1,0,-1],"points":[[0,0],[1,0],[0,1]],"values":[4,4,3],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[4,-1,-1,1,0,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[4,4,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0093","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[5,0,0,1,1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[5,6,4]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([5, 0, 0, 1, 1, -1], [[0, 0, 5, 5, 是], [1, 0, 6, 6, 是], [0, 1, 4, 4, 是]], 是)","explanation_zh":"現代橋梁核對=([5, 0, 0, 1, 1, -1], [[0, 0, 5, 5, 是], [1, 0, 6, 6, 是], [0, 1, 4, 4, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237093,"parameters":{"coefficients":[5,0,0,1,1,-1],"points":[[0,0],[1,0],[0,1]],"values":[5,6,4],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[5,0,0,1,1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[5,6,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0094","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[6,1,1,1,-1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[6,8,6]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([6, 1, 1, 1, -1, -1], [[0, 0, 6, 6, 是], [1, 0, 8, 8, 是], [0, 1, 6, 6, 是]], 是)","explanation_zh":"現代橋梁核對=([6, 1, 1, 1, -1, -1], [[0, 0, 6, 6, 是], [1, 0, 8, 8, 是], [0, 1, 6, 6, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237094,"parameters":{"coefficients":[6,1,1,1,-1,-1],"points":[[0,0],[1,0],[0,1]],"values":[6,8,6],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[6,1,1,1,-1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[6,8,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0095","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[7,2,2,1,0,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[7,10,8]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([7, 2, 2, 1, 0, -1], [[0, 0, 7, 7, 是], [1, 0, 10, 10, 是], [0, 1, 8, 8, 是]], 是)","explanation_zh":"現代橋梁核對=([7, 2, 2, 1, 0, -1], [[0, 0, 7, 7, 是], [1, 0, 10, 10, 是], [0, 1, 8, 8, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237095,"parameters":{"coefficients":[7,2,2,1,0,-1],"points":[[0,0],[1,0],[0,1]],"values":[7,10,8],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[7,2,2,1,0,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[7,10,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0096","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[8,-2,3,1,1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[8,7,11]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([8, -2, 3, 1, 1, -1], [[0, 0, 8, 8, 是], [1, 0, 7, 7, 是], [0, 1, 11, 10, 否]], 否)","explanation_zh":"現代橋梁核對=([8, -2, 3, 1, 1, -1], [[0, 0, 8, 8, 是], [1, 0, 7, 7, 是], [0, 1, 11, 10, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237096,"parameters":{"coefficients":[8,-2,3,1,1,-1],"points":[[0,0],[1,0],[0,1]],"values":[8,7,11],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[8,-2,3,1,1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[8,7,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0097","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[9,-1,-3,1,-1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[9,9,5]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([9, -1, -3, 1, -1, -1], [[0, 0, 9, 9, 是], [1, 0, 9, 9, 是], [0, 1, 5, 5, 是]], 是)","explanation_zh":"現代橋梁核對=([9, -1, -3, 1, -1, -1], [[0, 0, 9, 9, 是], [1, 0, 9, 9, 是], [0, 1, 5, 5, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237097,"parameters":{"coefficients":[9,-1,-3,1,-1,-1],"points":[[0,0],[1,0],[0,1]],"values":[9,9,5],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[9,-1,-3,1,-1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[9,9,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0098","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[10,0,-2,1,0,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[10,11,7]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([10, 0, -2, 1, 0, -1], [[0, 0, 10, 10, 是], [1, 0, 11, 11, 是], [0, 1, 7, 7, 是]], 是)","explanation_zh":"現代橋梁核對=([10, 0, -2, 1, 0, -1], [[0, 0, 10, 10, 是], [1, 0, 11, 11, 是], [0, 1, 7, 7, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237098,"parameters":{"coefficients":[10,0,-2,1,0,-1],"points":[[0,0],[1,0],[0,1]],"values":[10,11,7],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[10,0,-2,1,0,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[10,11,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0099","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[11,1,-1,1,1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[11,13,9]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([11, 1, -1, 1, 1, -1], [[0, 0, 11, 11, 是], [1, 0, 13, 13, 是], [0, 1, 9, 9, 是]], 是)","explanation_zh":"現代橋梁核對=([11, 1, -1, 1, 1, -1], [[0, 0, 11, 11, 是], [1, 0, 13, 13, 是], [0, 1, 9, 9, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237099,"parameters":{"coefficients":[11,1,-1,1,1,-1],"points":[[0,0],[1,0],[0,1]],"values":[11,13,9],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[11,1,-1,1,1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[11,13,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r07-multivariable-real-function-0100","batch_id":"batch-20261013-advance-20261023-r07-multivariable-real-function-foundations","language":"zh-Hant","source_mko_ids":["mko-multivariable-real-function"],"title_zh":"二變數實函數","stem_zh":"明示R2到R多項式與座標角色。操作=multivar-point-table-audit；資料={\"coefficients\":[12,2,0,1,-1,-1],\"points\":[[0,0],[1,0],[0,1]],\"values\":[12,15,12]}。請依 [coefficients,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"([12, 2, 0, 1, -1, -1], [[0, 0, 12, 12, 是], [1, 0, 15, 15, 是], [0, 1, 12, 11, 否]], 否)","explanation_zh":"現代橋梁核對=([12, 2, 0, 1, -1, -1], [[0, 0, 12, 12, 是], [1, 0, 15, 15, 是], [0, 1, 12, 11, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；未聲明全域連續或可微；不外推向量值函數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["二變數實函數"]},"variant":{"family_id":"qf-mod23-multivar-point-table-audit","seed":202610237100,"parameters":{"coefficients":[12,2,0,1,-1,-1],"points":[[0,0],[1,0],[0,1]],"values":[12,15,12],"domain":"Polynomial_R2_to_R_slice","operation":"multivar-point-table-audit","semantic_template":"qf-mod23-multivar-point-table-audit/{\"coefficients\":[12,2,0,1,-1,-1],\"points\":[[0,0],[0,1],[1,0]],\"values\":[12,15,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}