{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0001","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[1,1],[-1,2]],\"b\":[4,2],\"c\":[3,-1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[1, 1], [-1, 2]], [4, 2], [3, -1], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[1, 1], [-1, 2]], [4, 2], [3, -1], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146001,"parameters":{"A":[[1,1],[-1,2]],"b":[4,2],"c":[3,-1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[1,1],[1,1]],[[-1,1],[2,1]]],\"b\":[[4,1],[2,1]],\"c\":[[3,1],[-1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0002","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[2,1],[-1,3]],\"b\":[6,3],\"c\":[4,-2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[2, 1], [-1, 3]], [6, 3], [4, -2], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[2, 1], [-1, 3]], [6, 3], [4, -2], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146002,"parameters":{"A":[[2,1],[-1,3]],"b":[6,3],"c":[4,-2],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[2,1],[1,1]],[[-1,1],[3,1]]],\"b\":[[6,1],[3,1]],\"c\":[[4,1],[-2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0003","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[3,1],[-1,4]],\"b\":[8,4],\"c\":[5,-3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[3, 1], [-1, 4]], [8, 4], [5, -3], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[3, 1], [-1, 4]], [8, 4], [5, -3], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146003,"parameters":{"A":[[3,1],[-1,4]],"b":[8,4],"c":[5,-3],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[3,1],[1,1]],[[-1,1],[4,1]]],\"b\":[[8,1],[4,1]],\"c\":[[5,1],[-3,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0004","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[4,1],[-1,5]],\"b\":[10,5],\"c\":[6,-4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[4, 1], [-1, 5]], [10, 5], [6, -4], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[4, 1], [-1, 5]], [10, 5], [6, -4], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146004,"parameters":{"A":[[4,1],[-1,5]],"b":[10,5],"c":[6,-4],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[4,1],[1,1]],[[-1,1],[5,1]]],\"b\":[[10,1],[5,1]],\"c\":[[6,1],[-4,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0005","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[5,1],[-1,6]],\"b\":[12,6],\"c\":[7,-5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[5, 1], [-1, 6]], [12, 6], [7, -5], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[5, 1], [-1, 6]], [12, 6], [7, -5], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146005,"parameters":{"A":[[5,1],[-1,6]],"b":[12,6],"c":[7,-5],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[5,1],[1,1]],[[-1,1],[6,1]]],\"b\":[[12,1],[6,1]],\"c\":[[7,1],[-5,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0006","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[6,1],[-1,7]],\"b\":[14,7],\"c\":[8,-6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[6, 1], [-1, 7]], [14, 7], [8, -6], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[6, 1], [-1, 7]], [14, 7], [8, -6], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146006,"parameters":{"A":[[6,1],[-1,7]],"b":[14,7],"c":[8,-6],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[6,1],[1,1]],[[-1,1],[7,1]]],\"b\":[[14,1],[7,1]],\"c\":[[8,1],[-6,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0007","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[7,1],[-1,8]],\"b\":[16,8],\"c\":[9,-7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[7, 1], [-1, 8]], [16, 8], [9, -7], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[7, 1], [-1, 8]], [16, 8], [9, -7], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146007,"parameters":{"A":[[7,1],[-1,8]],"b":[16,8],"c":[9,-7],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[7,1],[1,1]],[[-1,1],[8,1]]],\"b\":[[16,1],[8,1]],\"c\":[[9,1],[-7,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0008","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[8,1],[-1,9]],\"b\":[18,9],\"c\":[10,-8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[8, 1], [-1, 9]], [18, 9], [10, -8], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[8, 1], [-1, 9]], [18, 9], [10, -8], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146008,"parameters":{"A":[[8,1],[-1,9]],"b":[18,9],"c":[10,-8],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[8,1],[1,1]],[[-1,1],[9,1]]],\"b\":[[18,1],[9,1]],\"c\":[[10,1],[-8,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0009","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[9,1],[-1,10]],\"b\":[20,10],\"c\":[11,-9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[9, 1], [-1, 10]], [20, 10], [11, -9], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[9, 1], [-1, 10]], [20, 10], [11, -9], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146009,"parameters":{"A":[[9,1],[-1,10]],"b":[20,10],"c":[11,-9],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[9,1],[1,1]],[[-1,1],[10,1]]],\"b\":[[20,1],[10,1]],\"c\":[[11,1],[-9,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0010","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[10,1],[-1,11]],\"b\":[22,11],\"c\":[12,-10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[10, 1], [-1, 11]], [22, 11], [12, -10], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[10, 1], [-1, 11]], [22, 11], [12, -10], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146010,"parameters":{"A":[[10,1],[-1,11]],"b":[22,11],"c":[12,-10],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[10,1],[1,1]],[[-1,1],[11,1]]],\"b\":[[22,1],[11,1]],\"c\":[[12,1],[-10,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0011","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[11,1],[-1,12]],\"b\":[24,12],\"c\":[13,-11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[11, 1], [-1, 12]], [24, 12], [13, -11], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[11, 1], [-1, 12]], [24, 12], [13, -11], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146011,"parameters":{"A":[[11,1],[-1,12]],"b":[24,12],"c":[13,-11],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[11,1],[1,1]],[[-1,1],[12,1]]],\"b\":[[24,1],[12,1]],\"c\":[[13,1],[-11,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0012","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[12,1],[-1,13]],\"b\":[26,13],\"c\":[14,-12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[12, 1], [-1, 13]], [26, 13], [14, -12], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[12, 1], [-1, 13]], [26, 13], [14, -12], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146012,"parameters":{"A":[[12,1],[-1,13]],"b":[26,13],"c":[14,-12],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[12,1],[1,1]],[[-1,1],[13,1]]],\"b\":[[26,1],[13,1]],\"c\":[[14,1],[-12,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0013","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[13,1],[-1,14]],\"b\":[28,14],\"c\":[15,-13]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[13, 1], [-1, 14]], [28, 14], [15, -13], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[13, 1], [-1, 14]], [28, 14], [15, -13], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146013,"parameters":{"A":[[13,1],[-1,14]],"b":[28,14],"c":[15,-13],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[13,1],[1,1]],[[-1,1],[14,1]]],\"b\":[[28,1],[14,1]],\"c\":[[15,1],[-13,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0014","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[14,1],[-1,15]],\"b\":[30,15],\"c\":[16,-14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[14, 1], [-1, 15]], [30, 15], [16, -14], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[14, 1], [-1, 15]], [30, 15], [16, -14], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146014,"parameters":{"A":[[14,1],[-1,15]],"b":[30,15],"c":[16,-14],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[14,1],[1,1]],[[-1,1],[15,1]]],\"b\":[[30,1],[15,1]],\"c\":[[16,1],[-14,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0015","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[15,1],[-1,16]],\"b\":[32,16],\"c\":[17,-15]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[15, 1], [-1, 16]], [32, 16], [17, -15], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[15, 1], [-1, 16]], [32, 16], [17, -15], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146015,"parameters":{"A":[[15,1],[-1,16]],"b":[32,16],"c":[17,-15],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[15,1],[1,1]],[[-1,1],[16,1]]],\"b\":[[32,1],[16,1]],\"c\":[[17,1],[-15,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0016","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[16,1],[-1,17]],\"b\":[34,17],\"c\":[18,-16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[16, 1], [-1, 17]], [34, 17], [18, -16], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[16, 1], [-1, 17]], [34, 17], [18, -16], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146016,"parameters":{"A":[[16,1],[-1,17]],"b":[34,17],"c":[18,-16],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[16,1],[1,1]],[[-1,1],[17,1]]],\"b\":[[34,1],[17,1]],\"c\":[[18,1],[-16,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0017","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[17,1],[-1,18]],\"b\":[36,18],\"c\":[19,-17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[17, 1], [-1, 18]], [36, 18], [19, -17], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[17, 1], [-1, 18]], [36, 18], [19, -17], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146017,"parameters":{"A":[[17,1],[-1,18]],"b":[36,18],"c":[19,-17],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[17,1],[1,1]],[[-1,1],[18,1]]],\"b\":[[36,1],[18,1]],\"c\":[[19,1],[-17,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0018","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[18,1],[-1,19]],\"b\":[38,19],\"c\":[20,-18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[18, 1], [-1, 19]], [38, 19], [20, -18], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[18, 1], [-1, 19]], [38, 19], [20, -18], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146018,"parameters":{"A":[[18,1],[-1,19]],"b":[38,19],"c":[20,-18],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[18,1],[1,1]],[[-1,1],[19,1]]],\"b\":[[38,1],[19,1]],\"c\":[[20,1],[-18,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0019","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[19,1],[-1,20]],\"b\":[40,20],\"c\":[21,-19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[19, 1], [-1, 20]], [40, 20], [21, -19], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[19, 1], [-1, 20]], [40, 20], [21, -19], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146019,"parameters":{"A":[[19,1],[-1,20]],"b":[40,20],"c":[21,-19],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[19,1],[1,1]],[[-1,1],[20,1]]],\"b\":[[40,1],[20,1]],\"c\":[[21,1],[-19,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0020","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[20,1],[-1,21]],\"b\":[42,21],\"c\":[22,-20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[20, 1], [-1, 21]], [42, 21], [22, -20], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[20, 1], [-1, 21]], [42, 21], [22, -20], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146020,"parameters":{"A":[[20,1],[-1,21]],"b":[42,21],"c":[22,-20],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[20,1],[1,1]],[[-1,1],[21,1]]],\"b\":[[42,1],[21,1]],\"c\":[[22,1],[-20,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0021","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[21,1],[-1,22]],\"b\":[44,22],\"c\":[23,-21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[21, 1], [-1, 22]], [44, 22], [23, -21], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[21, 1], [-1, 22]], [44, 22], [23, -21], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146021,"parameters":{"A":[[21,1],[-1,22]],"b":[44,22],"c":[23,-21],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[21,1],[1,1]],[[-1,1],[22,1]]],\"b\":[[44,1],[22,1]],\"c\":[[23,1],[-21,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0022","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[22,1],[-1,23]],\"b\":[46,23],\"c\":[24,-22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[22, 1], [-1, 23]], [46, 23], [24, -22], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[22, 1], [-1, 23]], [46, 23], [24, -22], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146022,"parameters":{"A":[[22,1],[-1,23]],"b":[46,23],"c":[24,-22],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[22,1],[1,1]],[[-1,1],[23,1]]],\"b\":[[46,1],[23,1]],\"c\":[[24,1],[-22,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0023","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[23,1],[-1,24]],\"b\":[48,24],\"c\":[25,-23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[23, 1], [-1, 24]], [48, 24], [25, -23], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[23, 1], [-1, 24]], [48, 24], [25, -23], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146023,"parameters":{"A":[[23,1],[-1,24]],"b":[48,24],"c":[25,-23],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[23,1],[1,1]],[[-1,1],[24,1]]],\"b\":[[48,1],[24,1]],\"c\":[[25,1],[-23,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0024","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[24,1],[-1,25]],\"b\":[50,25],\"c\":[26,-24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[24, 1], [-1, 25]], [50, 25], [26, -24], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[24, 1], [-1, 25]], [50, 25], [26, -24], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146024,"parameters":{"A":[[24,1],[-1,25]],"b":[50,25],"c":[26,-24],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[24,1],[1,1]],[[-1,1],[25,1]]],\"b\":[[50,1],[25,1]],\"c\":[[26,1],[-24,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0025","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={\"A\":[[25,1],[-1,26]],\"b\":[52,26],\"c\":[27,-25]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [[25, 1], [-1, 26]], [52, 26], [27, -25], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)","explanation_zh":"Wave6第八層核對=(2, 2, [[25, 1], [-1, 26]], [52, 26], [27, -25], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-dimension-sign-qualification","seed":202611146025,"parameters":{"A":[[25,1],[-1,26]],"b":[52,26],"c":[27,-25],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-dimension-sign-qualification","semantic_template":"qf-mod45-lp-standard-dimension-sign-qualification/{\"A\":[[[25,1],[1,1]],[[-1,1],[26,1]]],\"b\":[[52,1],[26,1]],\"c\":[[27,1],[-25,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0026","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[1,1],[1,1]],\"b\":[4,4],\"c\":[2,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [2, 2], [4, 4], [2, 2], 是, 是, 是, 是, 是, 3, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [2, 2], [4, 4], [2, 2], 是, 是, 是, 是, 是, 3, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146026,"parameters":{"A":[[1,1],[1,1]],"b":[4,4],"c":[2,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[1,1],[1,1]],[[1,1],[1,1]]],\"b\":[[4,1],[4,1]],\"c\":[[2,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0027","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[2,1],[1,2]],\"b\":[5,5],\"c\":[3,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [3, 3], [5, 5], [2, 2], 是, 是, 是, 是, 是, 4, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [3, 3], [5, 5], [2, 2], 是, 是, 是, 是, 是, 4, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146027,"parameters":{"A":[[2,1],[1,2]],"b":[5,5],"c":[3,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[2,1],[1,1]],[[1,1],[2,1]]],\"b\":[[5,1],[5,1]],\"c\":[[3,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0028","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[3,1],[1,3]],\"b\":[6,6],\"c\":[4,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [4, 4], [6, 6], [2, 2], 是, 是, 是, 是, 是, 5, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [4, 4], [6, 6], [2, 2], 是, 是, 是, 是, 是, 5, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146028,"parameters":{"A":[[3,1],[1,3]],"b":[6,6],"c":[4,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[3,1],[1,1]],[[1,1],[3,1]]],\"b\":[[6,1],[6,1]],\"c\":[[4,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0029","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[4,1],[1,4]],\"b\":[7,7],\"c\":[5,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [5, 5], [7, 7], [2, 2], 是, 是, 是, 是, 是, 6, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [5, 5], [7, 7], [2, 2], 是, 是, 是, 是, 是, 6, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146029,"parameters":{"A":[[4,1],[1,4]],"b":[7,7],"c":[5,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[4,1],[1,1]],[[1,1],[4,1]]],\"b\":[[7,1],[7,1]],\"c\":[[5,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0030","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[5,1],[1,5]],\"b\":[8,8],\"c\":[6,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [6, 6], [8, 8], [2, 2], 是, 是, 是, 是, 是, 7, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [6, 6], [8, 8], [2, 2], 是, 是, 是, 是, 是, 7, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146030,"parameters":{"A":[[5,1],[1,5]],"b":[8,8],"c":[6,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[5,1],[1,1]],[[1,1],[5,1]]],\"b\":[[8,1],[8,1]],\"c\":[[6,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0031","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[6,1],[1,6]],\"b\":[9,9],\"c\":[7,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [7, 7], [9, 9], [2, 2], 是, 是, 是, 是, 是, 8, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [7, 7], [9, 9], [2, 2], 是, 是, 是, 是, 是, 8, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146031,"parameters":{"A":[[6,1],[1,6]],"b":[9,9],"c":[7,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[6,1],[1,1]],[[1,1],[6,1]]],\"b\":[[9,1],[9,1]],\"c\":[[7,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0032","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[7,1],[1,7]],\"b\":[10,10],\"c\":[8,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [8, 8], [10, 10], [2, 2], 是, 是, 是, 是, 是, 9, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [8, 8], [10, 10], [2, 2], 是, 是, 是, 是, 是, 9, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146032,"parameters":{"A":[[7,1],[1,7]],"b":[10,10],"c":[8,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[7,1],[1,1]],[[1,1],[7,1]]],\"b\":[[10,1],[10,1]],\"c\":[[8,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0033","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[8,1],[1,8]],\"b\":[11,11],\"c\":[9,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [9, 9], [11, 11], [2, 2], 是, 是, 是, 是, 是, 10, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [9, 9], [11, 11], [2, 2], 是, 是, 是, 是, 是, 10, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146033,"parameters":{"A":[[8,1],[1,8]],"b":[11,11],"c":[9,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[8,1],[1,1]],[[1,1],[8,1]]],\"b\":[[11,1],[11,1]],\"c\":[[9,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0034","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[9,1],[1,9]],\"b\":[12,12],\"c\":[10,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [10, 10], [12, 12], [2, 2], 是, 是, 是, 是, 是, 11, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [10, 10], [12, 12], [2, 2], 是, 是, 是, 是, 是, 11, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146034,"parameters":{"A":[[9,1],[1,9]],"b":[12,12],"c":[10,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[9,1],[1,1]],[[1,1],[9,1]]],\"b\":[[12,1],[12,1]],\"c\":[[10,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0035","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[10,1],[1,10]],\"b\":[13,13],\"c\":[11,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [11, 11], [13, 13], [2, 2], 是, 是, 是, 是, 是, 12, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [11, 11], [13, 13], [2, 2], 是, 是, 是, 是, 是, 12, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146035,"parameters":{"A":[[10,1],[1,10]],"b":[13,13],"c":[11,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[10,1],[1,1]],[[1,1],[10,1]]],\"b\":[[13,1],[13,1]],\"c\":[[11,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0036","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[11,1],[1,11]],\"b\":[14,14],\"c\":[12,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [12, 12], [14, 14], [2, 2], 是, 是, 是, 是, 是, 13, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [12, 12], [14, 14], [2, 2], 是, 是, 是, 是, 是, 13, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146036,"parameters":{"A":[[11,1],[1,11]],"b":[14,14],"c":[12,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[11,1],[1,1]],[[1,1],[11,1]]],\"b\":[[14,1],[14,1]],\"c\":[[12,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0037","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[12,1],[1,12]],\"b\":[15,15],\"c\":[13,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [13, 13], [15, 15], [2, 2], 是, 是, 是, 是, 是, 14, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [13, 13], [15, 15], [2, 2], 是, 是, 是, 是, 是, 14, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146037,"parameters":{"A":[[12,1],[1,12]],"b":[15,15],"c":[13,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[12,1],[1,1]],[[1,1],[12,1]]],\"b\":[[15,1],[15,1]],\"c\":[[13,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0038","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[13,1],[1,13]],\"b\":[16,16],\"c\":[14,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [14, 14], [16, 16], [2, 2], 是, 是, 是, 是, 是, 15, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [14, 14], [16, 16], [2, 2], 是, 是, 是, 是, 是, 15, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146038,"parameters":{"A":[[13,1],[1,13]],"b":[16,16],"c":[14,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[13,1],[1,1]],[[1,1],[13,1]]],\"b\":[[16,1],[16,1]],\"c\":[[14,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0039","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[14,1],[1,14]],\"b\":[17,17],\"c\":[15,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [15, 15], [17, 17], [2, 2], 是, 是, 是, 是, 是, 16, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [15, 15], [17, 17], [2, 2], 是, 是, 是, 是, 是, 16, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146039,"parameters":{"A":[[14,1],[1,14]],"b":[17,17],"c":[15,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[14,1],[1,1]],[[1,1],[14,1]]],\"b\":[[17,1],[17,1]],\"c\":[[15,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0040","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[15,1],[1,15]],\"b\":[18,18],\"c\":[16,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [16, 16], [18, 18], [2, 2], 是, 是, 是, 是, 是, 17, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [16, 16], [18, 18], [2, 2], 是, 是, 是, 是, 是, 17, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146040,"parameters":{"A":[[15,1],[1,15]],"b":[18,18],"c":[16,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[15,1],[1,1]],[[1,1],[15,1]]],\"b\":[[18,1],[18,1]],\"c\":[[16,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0041","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[16,1],[1,16]],\"b\":[19,19],\"c\":[17,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [17, 17], [19, 19], [2, 2], 是, 是, 是, 是, 是, 18, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [17, 17], [19, 19], [2, 2], 是, 是, 是, 是, 是, 18, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146041,"parameters":{"A":[[16,1],[1,16]],"b":[19,19],"c":[17,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[16,1],[1,1]],[[1,1],[16,1]]],\"b\":[[19,1],[19,1]],\"c\":[[17,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0042","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[17,1],[1,17]],\"b\":[20,20],\"c\":[18,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [18, 18], [20, 20], [2, 2], 是, 是, 是, 是, 是, 19, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [18, 18], [20, 20], [2, 2], 是, 是, 是, 是, 是, 19, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146042,"parameters":{"A":[[17,1],[1,17]],"b":[20,20],"c":[18,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[17,1],[1,1]],[[1,1],[17,1]]],\"b\":[[20,1],[20,1]],\"c\":[[18,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0043","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[18,1],[1,18]],\"b\":[21,21],\"c\":[19,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [19, 19], [21, 21], [2, 2], 是, 是, 是, 是, 是, 20, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [19, 19], [21, 21], [2, 2], 是, 是, 是, 是, 是, 20, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146043,"parameters":{"A":[[18,1],[1,18]],"b":[21,21],"c":[19,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[18,1],[1,1]],[[1,1],[18,1]]],\"b\":[[21,1],[21,1]],\"c\":[[19,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0044","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[19,1],[1,19]],\"b\":[22,22],\"c\":[20,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [20, 20], [22, 22], [2, 2], 是, 是, 是, 是, 是, 21, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [20, 20], [22, 22], [2, 2], 是, 是, 是, 是, 是, 21, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146044,"parameters":{"A":[[19,1],[1,19]],"b":[22,22],"c":[20,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[19,1],[1,1]],[[1,1],[19,1]]],\"b\":[[22,1],[22,1]],\"c\":[[20,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0045","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[20,1],[1,20]],\"b\":[23,23],\"c\":[21,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [21, 21], [23, 23], [2, 2], 是, 是, 是, 是, 是, 22, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [21, 21], [23, 23], [2, 2], 是, 是, 是, 是, 是, 22, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146045,"parameters":{"A":[[20,1],[1,20]],"b":[23,23],"c":[21,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[20,1],[1,1]],[[1,1],[20,1]]],\"b\":[[23,1],[23,1]],\"c\":[[21,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0046","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[21,1],[1,21]],\"b\":[24,24],\"c\":[22,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [22, 22], [24, 24], [2, 2], 是, 是, 是, 是, 是, 23, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [22, 22], [24, 24], [2, 2], 是, 是, 是, 是, 是, 23, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146046,"parameters":{"A":[[21,1],[1,21]],"b":[24,24],"c":[22,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[21,1],[1,1]],[[1,1],[21,1]]],\"b\":[[24,1],[24,1]],\"c\":[[22,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0047","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[22,1],[1,22]],\"b\":[25,25],\"c\":[23,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [23, 23], [25, 25], [2, 2], 是, 是, 是, 是, 是, 24, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [23, 23], [25, 25], [2, 2], 是, 是, 是, 是, 是, 24, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146047,"parameters":{"A":[[22,1],[1,22]],"b":[25,25],"c":[23,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[22,1],[1,1]],[[1,1],[22,1]]],\"b\":[[25,1],[25,1]],\"c\":[[23,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0048","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[23,1],[1,23]],\"b\":[26,26],\"c\":[24,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [24, 24], [26, 26], [2, 2], 是, 是, 是, 是, 是, 25, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [24, 24], [26, 26], [2, 2], 是, 是, 是, 是, 是, 25, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146048,"parameters":{"A":[[23,1],[1,23]],"b":[26,26],"c":[24,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[23,1],[1,1]],[[1,1],[23,1]]],\"b\":[[26,1],[26,1]],\"c\":[[24,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0049","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[24,1],[1,24]],\"b\":[27,27],\"c\":[25,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [25, 25], [27, 27], [2, 2], 是, 是, 是, 是, 是, 26, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [25, 25], [27, 27], [2, 2], 是, 是, 是, 是, 是, 26, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146049,"parameters":{"A":[[24,1],[1,24]],"b":[27,27],"c":[25,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[24,1],[1,1]],[[1,1],[24,1]]],\"b\":[[27,1],[27,1]],\"c\":[[25,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0050","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={\"A\":[[25,1],[1,25]],\"b\":[28,28],\"c\":[26,1],\"x\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [26, 26], [28, 28], [2, 2], 是, 是, 是, 是, 是, 27, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)","explanation_zh":"Wave6第八層核對=([1, 1], [26, 26], [28, 28], [2, 2], 是, 是, 是, 是, 是, 27, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-slack-conversion","seed":202611146050,"parameters":{"A":[[25,1],[1,25]],"b":[28,28],"c":[26,1],"x":[1,1],"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-slack-conversion","semantic_template":"qf-mod45-lp-standard-slack-conversion/{\"A\":[[[25,1],[1,1]],[[1,1],[25,1]]],\"b\":[[28,1],[28,1]],\"c\":[[26,1],[1,1]],\"x\":[[1,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0051","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[1,-2,3],\"objective_coefficient\":4,\"value\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, -2, 3], 4, 1, 1, 0, 1, [1, -2, 3], [1, -2, 3], 是, 4, 4, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([1, -2, 3], 4, 1, 1, 0, 1, [1, -2, 3], [1, -2, 3], 是, 4, 4, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146051,"parameters":{"column":[1,-2,3],"objective_coefficient":4,"value":1,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[1,1],[-2,1],[3,1]],\"objective_coefficient\":[4,1],\"value\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0052","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[2,-3,4],\"objective_coefficient\":5,\"value\":-2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, -3, 4], 5, -2, 0, 2, -2, [-4, 6, -8], [-4, 6, -8], 是, -10, -10, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([2, -3, 4], 5, -2, 0, 2, -2, [-4, 6, -8], [-4, 6, -8], 是, -10, -10, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146052,"parameters":{"column":[2,-3,4],"objective_coefficient":5,"value":-2,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[2,1],[-3,1],[4,1]],\"objective_coefficient\":[5,1],\"value\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0053","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[3,-4,5],\"objective_coefficient\":6,\"value\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3, -4, 5], 6, 3, 3, 0, 3, [9, -12, 15], [9, -12, 15], 是, 18, 18, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([3, -4, 5], 6, 3, 3, 0, 3, [9, -12, 15], [9, -12, 15], 是, 18, 18, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146053,"parameters":{"column":[3,-4,5],"objective_coefficient":6,"value":3,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[3,1],[-4,1],[5,1]],\"objective_coefficient\":[6,1],\"value\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0054","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[4,-5,6],\"objective_coefficient\":7,\"value\":-4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([4, -5, 6], 7, -4, 0, 4, -4, [-16, 20, -24], [-16, 20, -24], 是, -28, -28, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([4, -5, 6], 7, -4, 0, 4, -4, [-16, 20, -24], [-16, 20, -24], 是, -28, -28, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146054,"parameters":{"column":[4,-5,6],"objective_coefficient":7,"value":-4,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[4,1],[-5,1],[6,1]],\"objective_coefficient\":[7,1],\"value\":[-4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0055","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[5,-6,7],\"objective_coefficient\":8,\"value\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([5, -6, 7], 8, 5, 5, 0, 5, [25, -30, 35], [25, -30, 35], 是, 40, 40, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([5, -6, 7], 8, 5, 5, 0, 5, [25, -30, 35], [25, -30, 35], 是, 40, 40, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146055,"parameters":{"column":[5,-6,7],"objective_coefficient":8,"value":5,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[5,1],[-6,1],[7,1]],\"objective_coefficient\":[8,1],\"value\":[5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0056","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[6,-7,8],\"objective_coefficient\":9,\"value\":-6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([6, -7, 8], 9, -6, 0, 6, -6, [-36, 42, -48], [-36, 42, -48], 是, -54, -54, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([6, -7, 8], 9, -6, 0, 6, -6, [-36, 42, -48], [-36, 42, -48], 是, -54, -54, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146056,"parameters":{"column":[6,-7,8],"objective_coefficient":9,"value":-6,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[6,1],[-7,1],[8,1]],\"objective_coefficient\":[9,1],\"value\":[-6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0057","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[7,-8,9],\"objective_coefficient\":10,\"value\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([7, -8, 9], 10, 7, 7, 0, 7, [49, -56, 63], [49, -56, 63], 是, 70, 70, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([7, -8, 9], 10, 7, 7, 0, 7, [49, -56, 63], [49, -56, 63], 是, 70, 70, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146057,"parameters":{"column":[7,-8,9],"objective_coefficient":10,"value":7,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[7,1],[-8,1],[9,1]],\"objective_coefficient\":[10,1],\"value\":[7,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0058","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[8,-9,10],\"objective_coefficient\":11,\"value\":-8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([8, -9, 10], 11, -8, 0, 8, -8, [-64, 72, -80], [-64, 72, -80], 是, -88, -88, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([8, -9, 10], 11, -8, 0, 8, -8, [-64, 72, -80], [-64, 72, -80], 是, -88, -88, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146058,"parameters":{"column":[8,-9,10],"objective_coefficient":11,"value":-8,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[8,1],[-9,1],[10,1]],\"objective_coefficient\":[11,1],\"value\":[-8,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0059","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[9,-10,11],\"objective_coefficient\":12,\"value\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([9, -10, 11], 12, 9, 9, 0, 9, [81, -90, 99], [81, -90, 99], 是, 108, 108, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([9, -10, 11], 12, 9, 9, 0, 9, [81, -90, 99], [81, -90, 99], 是, 108, 108, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146059,"parameters":{"column":[9,-10,11],"objective_coefficient":12,"value":9,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[9,1],[-10,1],[11,1]],\"objective_coefficient\":[12,1],\"value\":[9,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0060","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[10,-11,12],\"objective_coefficient\":13,\"value\":-10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([10, -11, 12], 13, -10, 0, 10, -10, [-100, 110, -120], [-100, 110, -120], 是, -130, -130, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([10, -11, 12], 13, -10, 0, 10, -10, [-100, 110, -120], [-100, 110, -120], 是, -130, -130, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146060,"parameters":{"column":[10,-11,12],"objective_coefficient":13,"value":-10,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[10,1],[-11,1],[12,1]],\"objective_coefficient\":[13,1],\"value\":[-10,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0061","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[11,-12,13],\"objective_coefficient\":14,\"value\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([11, -12, 13], 14, 11, 11, 0, 11, [121, -132, 143], [121, -132, 143], 是, 154, 154, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([11, -12, 13], 14, 11, 11, 0, 11, [121, -132, 143], [121, -132, 143], 是, 154, 154, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146061,"parameters":{"column":[11,-12,13],"objective_coefficient":14,"value":11,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[11,1],[-12,1],[13,1]],\"objective_coefficient\":[14,1],\"value\":[11,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0062","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[12,-13,14],\"objective_coefficient\":15,\"value\":-12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([12, -13, 14], 15, -12, 0, 12, -12, [-144, 156, -168], [-144, 156, -168], 是, -180, -180, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([12, -13, 14], 15, -12, 0, 12, -12, [-144, 156, -168], [-144, 156, -168], 是, -180, -180, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146062,"parameters":{"column":[12,-13,14],"objective_coefficient":15,"value":-12,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[12,1],[-13,1],[14,1]],\"objective_coefficient\":[15,1],\"value\":[-12,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0063","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[13,-14,15],\"objective_coefficient\":16,\"value\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([13, -14, 15], 16, 13, 13, 0, 13, [169, -182, 195], [169, -182, 195], 是, 208, 208, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([13, -14, 15], 16, 13, 13, 0, 13, [169, -182, 195], [169, -182, 195], 是, 208, 208, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146063,"parameters":{"column":[13,-14,15],"objective_coefficient":16,"value":13,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[13,1],[-14,1],[15,1]],\"objective_coefficient\":[16,1],\"value\":[13,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0064","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[14,-15,16],\"objective_coefficient\":17,\"value\":-14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([14, -15, 16], 17, -14, 0, 14, -14, [-196, 210, -224], [-196, 210, -224], 是, -238, -238, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([14, -15, 16], 17, -14, 0, 14, -14, [-196, 210, -224], [-196, 210, -224], 是, -238, -238, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146064,"parameters":{"column":[14,-15,16],"objective_coefficient":17,"value":-14,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[14,1],[-15,1],[16,1]],\"objective_coefficient\":[17,1],\"value\":[-14,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0065","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[15,-16,17],\"objective_coefficient\":18,\"value\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([15, -16, 17], 18, 15, 15, 0, 15, [225, -240, 255], [225, -240, 255], 是, 270, 270, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([15, -16, 17], 18, 15, 15, 0, 15, [225, -240, 255], [225, -240, 255], 是, 270, 270, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146065,"parameters":{"column":[15,-16,17],"objective_coefficient":18,"value":15,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[15,1],[-16,1],[17,1]],\"objective_coefficient\":[18,1],\"value\":[15,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0066","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[16,-17,18],\"objective_coefficient\":19,\"value\":-16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([16, -17, 18], 19, -16, 0, 16, -16, [-256, 272, -288], [-256, 272, -288], 是, -304, -304, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([16, -17, 18], 19, -16, 0, 16, -16, [-256, 272, -288], [-256, 272, -288], 是, -304, -304, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146066,"parameters":{"column":[16,-17,18],"objective_coefficient":19,"value":-16,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[16,1],[-17,1],[18,1]],\"objective_coefficient\":[19,1],\"value\":[-16,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0067","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[17,-18,19],\"objective_coefficient\":20,\"value\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([17, -18, 19], 20, 17, 17, 0, 17, [289, -306, 323], [289, -306, 323], 是, 340, 340, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([17, -18, 19], 20, 17, 17, 0, 17, [289, -306, 323], [289, -306, 323], 是, 340, 340, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146067,"parameters":{"column":[17,-18,19],"objective_coefficient":20,"value":17,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[17,1],[-18,1],[19,1]],\"objective_coefficient\":[20,1],\"value\":[17,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0068","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[18,-19,20],\"objective_coefficient\":21,\"value\":-18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([18, -19, 20], 21, -18, 0, 18, -18, [-324, 342, -360], [-324, 342, -360], 是, -378, -378, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([18, -19, 20], 21, -18, 0, 18, -18, [-324, 342, -360], [-324, 342, -360], 是, -378, -378, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146068,"parameters":{"column":[18,-19,20],"objective_coefficient":21,"value":-18,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[18,1],[-19,1],[20,1]],\"objective_coefficient\":[21,1],\"value\":[-18,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0069","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[19,-20,21],\"objective_coefficient\":22,\"value\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([19, -20, 21], 22, 19, 19, 0, 19, [361, -380, 399], [361, -380, 399], 是, 418, 418, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([19, -20, 21], 22, 19, 19, 0, 19, [361, -380, 399], [361, -380, 399], 是, 418, 418, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146069,"parameters":{"column":[19,-20,21],"objective_coefficient":22,"value":19,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[19,1],[-20,1],[21,1]],\"objective_coefficient\":[22,1],\"value\":[19,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0070","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[20,-21,22],\"objective_coefficient\":23,\"value\":-20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([20, -21, 22], 23, -20, 0, 20, -20, [-400, 420, -440], [-400, 420, -440], 是, -460, -460, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([20, -21, 22], 23, -20, 0, 20, -20, [-400, 420, -440], [-400, 420, -440], 是, -460, -460, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146070,"parameters":{"column":[20,-21,22],"objective_coefficient":23,"value":-20,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[20,1],[-21,1],[22,1]],\"objective_coefficient\":[23,1],\"value\":[-20,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0071","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[21,-22,23],\"objective_coefficient\":24,\"value\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([21, -22, 23], 24, 21, 21, 0, 21, [441, -462, 483], [441, -462, 483], 是, 504, 504, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([21, -22, 23], 24, 21, 21, 0, 21, [441, -462, 483], [441, -462, 483], 是, 504, 504, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146071,"parameters":{"column":[21,-22,23],"objective_coefficient":24,"value":21,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[21,1],[-22,1],[23,1]],\"objective_coefficient\":[24,1],\"value\":[21,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0072","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[22,-23,24],\"objective_coefficient\":25,\"value\":-22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([22, -23, 24], 25, -22, 0, 22, -22, [-484, 506, -528], [-484, 506, -528], 是, -550, -550, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([22, -23, 24], 25, -22, 0, 22, -22, [-484, 506, -528], [-484, 506, -528], 是, -550, -550, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146072,"parameters":{"column":[22,-23,24],"objective_coefficient":25,"value":-22,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[22,1],[-23,1],[24,1]],\"objective_coefficient\":[25,1],\"value\":[-22,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0073","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[23,-24,25],\"objective_coefficient\":26,\"value\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([23, -24, 25], 26, 23, 23, 0, 23, [529, -552, 575], [529, -552, 575], 是, 598, 598, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([23, -24, 25], 26, 23, 23, 0, 23, [529, -552, 575], [529, -552, 575], 是, 598, 598, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146073,"parameters":{"column":[23,-24,25],"objective_coefficient":26,"value":23,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[23,1],[-24,1],[25,1]],\"objective_coefficient\":[26,1],\"value\":[23,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0074","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[24,-25,26],\"objective_coefficient\":27,\"value\":-24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([24, -25, 26], 27, -24, 0, 24, -24, [-576, 600, -624], [-576, 600, -624], 是, -648, -648, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([24, -25, 26], 27, -24, 0, 24, -24, [-576, 600, -624], [-576, 600, -624], 是, -648, -648, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146074,"parameters":{"column":[24,-25,26],"objective_coefficient":27,"value":-24,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[24,1],[-25,1],[26,1]],\"objective_coefficient\":[27,1],\"value\":[-24,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0075","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={\"column\":[25,-26,27],\"objective_coefficient\":28,\"value\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([25, -26, 27], 28, 25, 25, 0, 25, [625, -650, 675], [625, -650, 675], 是, 700, 700, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)","explanation_zh":"Wave6第八層核對=([25, -26, 27], 28, 25, 25, 0, 25, [625, -650, 675], [625, -650, 675], 是, 700, 700, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-unrestricted-split","seed":202611146075,"parameters":{"column":[25,-26,27],"objective_coefficient":28,"value":25,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-unrestricted-split","semantic_template":"qf-mod45-lp-standard-unrestricted-split/{\"column\":[[25,1],[-26,1],[27,1]],\"objective_coefficient\":[28,1],\"value\":[25,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0076","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"greater_equal\",\"coefficients\":[1,-2,1],\"rhs\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(greater_equal, [1, -2, 1], 3, [-1, 2, -1], -3, multiply_constraint_by_minus_one_to_obtain_less_equal)","explanation_zh":"Wave6第八層核對=(greater_equal, [1, -2, 1], 3, [-1, 2, -1], -3, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146076,"parameters":{"mode":"greater_equal","coefficients":[1,-2,1],"rhs":3,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[1,1],[-2,1],[1,1]],\"mode\":\"greater_equal\",\"rhs\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0077","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"equality\",\"coefficients\":[2,-3,1],\"rhs\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(equality, [2, -3, 1], 4, [[2, -3, 1], 4], [[-2, 3, -1], -4], replace_equality_by_two_opposite_less_equal_constraints)","explanation_zh":"Wave6第八層核對=(equality, [2, -3, 1], 4, [[2, -3, 1], 4], [[-2, 3, -1], -4], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146077,"parameters":{"mode":"equality","coefficients":[2,-3,1],"rhs":4,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[2,1],[-3,1],[1,1]],\"mode\":\"equality\",\"rhs\":[4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0078","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"minimize\",\"coefficients\":[3,-4,1],\"rhs\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(minimize, [3, -4, 1], [-3, 4, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)","explanation_zh":"Wave6第八層核對=(minimize, [3, -4, 1], [-3, 4, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146078,"parameters":{"mode":"minimize","coefficients":[3,-4,1],"rhs":0,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[3,1],[-4,1],[1,1]],\"mode\":\"minimize\",\"rhs\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0079","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"greater_equal\",\"coefficients\":[4,-5,1],\"rhs\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(greater_equal, [4, -5, 1], 6, [-4, 5, -1], -6, multiply_constraint_by_minus_one_to_obtain_less_equal)","explanation_zh":"Wave6第八層核對=(greater_equal, [4, -5, 1], 6, [-4, 5, -1], -6, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146079,"parameters":{"mode":"greater_equal","coefficients":[4,-5,1],"rhs":6,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[4,1],[-5,1],[1,1]],\"mode\":\"greater_equal\",\"rhs\":[6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0080","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"equality\",\"coefficients\":[5,-6,1],\"rhs\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(equality, [5, -6, 1], 7, [[5, -6, 1], 7], [[-5, 6, -1], -7], replace_equality_by_two_opposite_less_equal_constraints)","explanation_zh":"Wave6第八層核對=(equality, [5, -6, 1], 7, [[5, -6, 1], 7], [[-5, 6, -1], -7], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146080,"parameters":{"mode":"equality","coefficients":[5,-6,1],"rhs":7,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[5,1],[-6,1],[1,1]],\"mode\":\"equality\",\"rhs\":[7,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0081","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"minimize\",\"coefficients\":[6,-7,1],\"rhs\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(minimize, [6, -7, 1], [-6, 7, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)","explanation_zh":"Wave6第八層核對=(minimize, [6, -7, 1], [-6, 7, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146081,"parameters":{"mode":"minimize","coefficients":[6,-7,1],"rhs":0,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[6,1],[-7,1],[1,1]],\"mode\":\"minimize\",\"rhs\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0082","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"greater_equal\",\"coefficients\":[7,-8,1],\"rhs\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(greater_equal, [7, -8, 1], 9, [-7, 8, -1], -9, multiply_constraint_by_minus_one_to_obtain_less_equal)","explanation_zh":"Wave6第八層核對=(greater_equal, [7, -8, 1], 9, [-7, 8, -1], -9, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146082,"parameters":{"mode":"greater_equal","coefficients":[7,-8,1],"rhs":9,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[7,1],[-8,1],[1,1]],\"mode\":\"greater_equal\",\"rhs\":[9,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0083","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"equality\",\"coefficients\":[8,-9,1],\"rhs\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(equality, [8, -9, 1], 10, [[8, -9, 1], 10], [[-8, 9, -1], -10], replace_equality_by_two_opposite_less_equal_constraints)","explanation_zh":"Wave6第八層核對=(equality, [8, -9, 1], 10, [[8, -9, 1], 10], [[-8, 9, -1], -10], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146083,"parameters":{"mode":"equality","coefficients":[8,-9,1],"rhs":10,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[8,1],[-9,1],[1,1]],\"mode\":\"equality\",\"rhs\":[10,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0084","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"minimize\",\"coefficients\":[9,-10,1],\"rhs\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(minimize, [9, -10, 1], [-9, 10, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)","explanation_zh":"Wave6第八層核對=(minimize, [9, -10, 1], [-9, 10, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146084,"parameters":{"mode":"minimize","coefficients":[9,-10,1],"rhs":0,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[9,1],[-10,1],[1,1]],\"mode\":\"minimize\",\"rhs\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0085","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"greater_equal\",\"coefficients\":[10,-11,1],\"rhs\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(greater_equal, [10, -11, 1], 12, [-10, 11, -1], -12, multiply_constraint_by_minus_one_to_obtain_less_equal)","explanation_zh":"Wave6第八層核對=(greater_equal, [10, -11, 1], 12, [-10, 11, -1], -12, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146085,"parameters":{"mode":"greater_equal","coefficients":[10,-11,1],"rhs":12,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[10,1],[-11,1],[1,1]],\"mode\":\"greater_equal\",\"rhs\":[12,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0086","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"equality\",\"coefficients\":[11,-12,1],\"rhs\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(equality, [11, -12, 1], 13, [[11, -12, 1], 13], [[-11, 12, -1], -13], replace_equality_by_two_opposite_less_equal_constraints)","explanation_zh":"Wave6第八層核對=(equality, [11, -12, 1], 13, [[11, -12, 1], 13], [[-11, 12, -1], -13], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146086,"parameters":{"mode":"equality","coefficients":[11,-12,1],"rhs":13,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[11,1],[-12,1],[1,1]],\"mode\":\"equality\",\"rhs\":[13,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0087","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"minimize\",\"coefficients\":[12,-13,1],\"rhs\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(minimize, [12, -13, 1], [-12, 13, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)","explanation_zh":"Wave6第八層核對=(minimize, [12, -13, 1], [-12, 13, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146087,"parameters":{"mode":"minimize","coefficients":[12,-13,1],"rhs":0,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[12,1],[-13,1],[1,1]],\"mode\":\"minimize\",\"rhs\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0088","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"greater_equal\",\"coefficients\":[13,-14,1],\"rhs\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(greater_equal, [13, -14, 1], 15, [-13, 14, -1], -15, multiply_constraint_by_minus_one_to_obtain_less_equal)","explanation_zh":"Wave6第八層核對=(greater_equal, [13, -14, 1], 15, [-13, 14, -1], -15, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146088,"parameters":{"mode":"greater_equal","coefficients":[13,-14,1],"rhs":15,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[13,1],[-14,1],[1,1]],\"mode\":\"greater_equal\",\"rhs\":[15,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0089","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"equality\",\"coefficients\":[14,-15,1],\"rhs\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(equality, [14, -15, 1], 16, [[14, -15, 1], 16], [[-14, 15, -1], -16], replace_equality_by_two_opposite_less_equal_constraints)","explanation_zh":"Wave6第八層核對=(equality, [14, -15, 1], 16, [[14, -15, 1], 16], [[-14, 15, -1], -16], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146089,"parameters":{"mode":"equality","coefficients":[14,-15,1],"rhs":16,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[14,1],[-15,1],[1,1]],\"mode\":\"equality\",\"rhs\":[16,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0090","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"minimize\",\"coefficients\":[15,-16,1],\"rhs\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(minimize, [15, -16, 1], [-15, 16, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)","explanation_zh":"Wave6第八層核對=(minimize, [15, -16, 1], [-15, 16, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146090,"parameters":{"mode":"minimize","coefficients":[15,-16,1],"rhs":0,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[15,1],[-16,1],[1,1]],\"mode\":\"minimize\",\"rhs\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0091","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"greater_equal\",\"coefficients\":[16,-17,1],\"rhs\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(greater_equal, [16, -17, 1], 18, [-16, 17, -1], -18, multiply_constraint_by_minus_one_to_obtain_less_equal)","explanation_zh":"Wave6第八層核對=(greater_equal, [16, -17, 1], 18, [-16, 17, -1], -18, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146091,"parameters":{"mode":"greater_equal","coefficients":[16,-17,1],"rhs":18,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[16,1],[-17,1],[1,1]],\"mode\":\"greater_equal\",\"rhs\":[18,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0092","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"equality\",\"coefficients\":[17,-18,1],\"rhs\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(equality, [17, -18, 1], 19, [[17, -18, 1], 19], [[-17, 18, -1], -19], replace_equality_by_two_opposite_less_equal_constraints)","explanation_zh":"Wave6第八層核對=(equality, [17, -18, 1], 19, [[17, -18, 1], 19], [[-17, 18, -1], -19], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146092,"parameters":{"mode":"equality","coefficients":[17,-18,1],"rhs":19,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[17,1],[-18,1],[1,1]],\"mode\":\"equality\",\"rhs\":[19,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0093","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"minimize\",\"coefficients\":[18,-19,1],\"rhs\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(minimize, [18, -19, 1], [-18, 19, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)","explanation_zh":"Wave6第八層核對=(minimize, [18, -19, 1], [-18, 19, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146093,"parameters":{"mode":"minimize","coefficients":[18,-19,1],"rhs":0,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[18,1],[-19,1],[1,1]],\"mode\":\"minimize\",\"rhs\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0094","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"greater_equal\",\"coefficients\":[19,-20,1],\"rhs\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(greater_equal, [19, -20, 1], 21, [-19, 20, -1], -21, multiply_constraint_by_minus_one_to_obtain_less_equal)","explanation_zh":"Wave6第八層核對=(greater_equal, [19, -20, 1], 21, [-19, 20, -1], -21, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146094,"parameters":{"mode":"greater_equal","coefficients":[19,-20,1],"rhs":21,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[19,1],[-20,1],[1,1]],\"mode\":\"greater_equal\",\"rhs\":[21,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0095","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"equality\",\"coefficients\":[20,-21,1],\"rhs\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(equality, [20, -21, 1], 22, [[20, -21, 1], 22], [[-20, 21, -1], -22], replace_equality_by_two_opposite_less_equal_constraints)","explanation_zh":"Wave6第八層核對=(equality, [20, -21, 1], 22, [[20, -21, 1], 22], [[-20, 21, -1], -22], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146095,"parameters":{"mode":"equality","coefficients":[20,-21,1],"rhs":22,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[20,1],[-21,1],[1,1]],\"mode\":\"equality\",\"rhs\":[22,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0096","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"minimize\",\"coefficients\":[21,-22,1],\"rhs\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(minimize, [21, -22, 1], [-21, 22, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)","explanation_zh":"Wave6第八層核對=(minimize, [21, -22, 1], [-21, 22, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146096,"parameters":{"mode":"minimize","coefficients":[21,-22,1],"rhs":0,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[21,1],[-22,1],[1,1]],\"mode\":\"minimize\",\"rhs\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0097","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"greater_equal\",\"coefficients\":[22,-23,1],\"rhs\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(greater_equal, [22, -23, 1], 24, [-22, 23, -1], -24, multiply_constraint_by_minus_one_to_obtain_less_equal)","explanation_zh":"Wave6第八層核對=(greater_equal, [22, -23, 1], 24, [-22, 23, -1], -24, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146097,"parameters":{"mode":"greater_equal","coefficients":[22,-23,1],"rhs":24,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[22,1],[-23,1],[1,1]],\"mode\":\"greater_equal\",\"rhs\":[24,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0098","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"equality\",\"coefficients\":[23,-24,1],\"rhs\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(equality, [23, -24, 1], 25, [[23, -24, 1], 25], [[-23, 24, -1], -25], replace_equality_by_two_opposite_less_equal_constraints)","explanation_zh":"Wave6第八層核對=(equality, [23, -24, 1], 25, [[23, -24, 1], 25], [[-23, 24, -1], -25], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146098,"parameters":{"mode":"equality","coefficients":[23,-24,1],"rhs":25,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[23,1],[-24,1],[1,1]],\"mode\":\"equality\",\"rhs\":[25,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0099","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"minimize\",\"coefficients\":[24,-25,1],\"rhs\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(minimize, [24, -25, 1], [-24, 25, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)","explanation_zh":"Wave6第八層核對=(minimize, [24, -25, 1], [-24, 25, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146099,"parameters":{"mode":"minimize","coefficients":[24,-25,1],"rhs":0,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[24,1],[-25,1],[1,1]],\"mode\":\"minimize\",\"rhs\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261114-r06-linear-program-standard-form-0100","batch_id":"batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-program-standard-form"],"title_zh":"線性規劃標準形","stem_zh":"固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={\"mode\":\"greater_equal\",\"coefficients\":[25,-26,1],\"rhs\":27}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(greater_equal, [25, -26, 1], 27, [-25, 26, -1], -27, multiply_constraint_by_minus_one_to_obtain_less_equal)","explanation_zh":"Wave6第八層核對=(greater_equal, [25, -26, 1], 27, [-25, 26, -1], -27, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["線性規劃標準形"]},"variant":{"family_id":"qf-mod45-lp-standard-convention-boundary","seed":202611146100,"parameters":{"mode":"greater_equal","coefficients":[25,-26,1],"rhs":27,"domain":"Exact_max_le_nonnegative_LP_standard_form","operation":"lp-standard-convention-boundary","semantic_template":"qf-mod45-lp-standard-convention-boundary/{\"coefficients\":[[25,1],[-26,1],[1,1]],\"mode\":\"greater_equal\",\"rhs\":[27,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、非同態kernel、未驗normal的quotient、class-size公式、finite-quadrature Gaussian定理、bias-variance decomposition、LP最優性、minimum vertex cover、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}