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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0003","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-reflexivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[3,3],[4,4],[5,5],[0,1],[0,2]]}。請依 [n,missing_diagonal,reflexive] 欄序回答。","answer":{"kind":"expression","value":"(6, [2], 否)","explanation_zh":"結構深度核對=(6, [2], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-reflexivity-audit","seed":202610267003,"parameters":{"n":6,"pairs":[[0,0],[1,1],[3,3],[4,4],[5,5],[0,1],[0,2]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-reflexivity-audit","semantic_template":"qf-mod26-equiv-reflexivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[1,1],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0004","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-reflexivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[4,4],[5,5],[0,3]]}。請依 [n,missing_diagonal,reflexive] 欄序回答。","answer":{"kind":"expression","value":"(6, [3], 否)","explanation_zh":"結構深度核對=(6, [3], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-reflexivity-audit","seed":202610267004,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[4,4],[5,5],[0,3]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-reflexivity-audit","semantic_template":"qf-mod26-equiv-reflexivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,3],[1,1],[2,2],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0012","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-reflexivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[0,3],[0,4]]}。請依 [n,missing_diagonal,reflexive] 欄序回答。","answer":{"kind":"expression","value":"(6, [5], 否)","explanation_zh":"結構深度核對=(6, [5], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-reflexivity-audit","seed":202610267012,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[0,3],[0,4]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-reflexivity-audit","semantic_template":"qf-mod26-equiv-reflexivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,3],[0,4],[1,1],[2,2],[3,3],[4,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0021","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-reflexivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[3,3],[4,4],[5,5],[0,1],[0,3],[0,5]]}。請依 [n,missing_diagonal,reflexive] 欄序回答。","answer":{"kind":"expression","value":"(6, [2], 否)","explanation_zh":"結構深度核對=(6, [2], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-reflexivity-audit","seed":202610267021,"parameters":{"n":6,"pairs":[[0,0],[1,1],[3,3],[4,4],[5,5],[0,1],[0,3],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-reflexivity-audit","semantic_template":"qf-mod26-equiv-reflexivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,3],[0,5],[1,1],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0022","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-reflexivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[4,4],[5,5],[0,2],[0,3],[0,5]]}。請依 [n,missing_diagonal,reflexive] 欄序回答。","answer":{"kind":"expression","value":"(6, [3], 否)","explanation_zh":"結構深度核對=(6, [3], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-reflexivity-audit","seed":202610267022,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[4,4],[5,5],[0,2],[0,3],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-reflexivity-audit","semantic_template":"qf-mod26-equiv-reflexivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,3],[0,5],[1,1],[2,2],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0023","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-reflexivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[5,5],[0,1],[0,2],[0,3],[0,5]]}。請依 [n,missing_diagonal,reflexive] 欄序回答。","answer":{"kind":"expression","value":"(6, [4], 否)","explanation_zh":"結構深度核對=(6, [4], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-reflexivity-audit","seed":202610267023,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[5,5],[0,1],[0,2],[0,3],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-reflexivity-audit","semantic_template":"qf-mod26-equiv-reflexivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,3],[0,5],[1,1],[2,2],[3,3],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0025","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-reflexivity-audit；資料={\"n\":6,\"pairs\":[[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4],[0,5]]}。請依 [n,missing_diagonal,reflexive] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], 否)","explanation_zh":"結構深度核對=(6, [0], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-reflexivity-audit","seed":202610267025,"parameters":{"n":6,"pairs":[[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-reflexivity-audit","semantic_template":"qf-mod26-equiv-reflexivity-audit/{\"n\":6,\"pairs\":[[0,1],[0,4],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0026","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[1,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [], 是)","explanation_zh":"結構深度核對=(6, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267026,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[1,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[1,0],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0027","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 2]], 否)","explanation_zh":"結構深度核對=(6, [[0, 2]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267027,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0028","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[2,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 1]], 否)","explanation_zh":"結構深度核對=(6, [[0, 1]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267028,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[2,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[1,1],[2,0],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0029","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[3,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [], 是)","explanation_zh":"結構深度核對=(6, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267029,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[3,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,3],[1,1],[2,2],[3,0],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0030","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 1], [0, 3]], 否)","explanation_zh":"結構深度核對=(6, [[0, 1], [0, 3]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267030,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,3],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0031","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[3,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 2]], 否)","explanation_zh":"結構深度核對=(6, [[0, 2]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267031,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[3,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,3],[1,1],[2,2],[3,0],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0032","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[1,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 2], [0, 3]], 否)","explanation_zh":"結構深度核對=(6, [[0, 2], [0, 3]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267032,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[1,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0033","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,4]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 4]], 否)","explanation_zh":"結構深度核對=(6, [[0, 4]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267033,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,4]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,4],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0034","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4],[4,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 1]], 否)","explanation_zh":"結構深度核對=(6, [[0, 1]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267034,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4],[4,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,4],[1,1],[2,2],[3,3],[4,0],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0035","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,4],[2,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 4]], 否)","explanation_zh":"結構深度核對=(6, [[0, 4]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267035,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,4],[2,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,4],[1,1],[2,0],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0036","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,4],[4,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 1], [0, 2]], 否)","explanation_zh":"結構深度核對=(6, [[0, 1], [0, 2]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267036,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,4],[4,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,4],[1,1],[2,2],[3,3],[4,0],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0037","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[0,4],[4,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 3]], 否)","explanation_zh":"結構深度核對=(6, [[0, 3]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267037,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[0,4],[4,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,3],[0,4],[1,1],[2,2],[3,3],[4,0],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0038","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[0,4],[1,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 3], [0, 4]], 否)","explanation_zh":"結構深度核對=(6, [[0, 3], [0, 4]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267038,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[0,4],[1,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,3],[0,4],[1,0],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0039","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[0,4],[4,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 2], [0, 3]], 否)","explanation_zh":"結構深度核對=(6, [[0, 2], [0, 3]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267039,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[0,4],[4,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,3],[0,4],[1,1],[2,2],[3,3],[4,0],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0040","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[0,4],[2,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 1], [0, 3], [0, 4]], 否)","explanation_zh":"結構深度核對=(6, [[0, 1], [0, 3], [0, 4]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267040,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[0,4],[2,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[2,0],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0041","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,5],[5,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [], 是)","explanation_zh":"結構深度核對=(6, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267041,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,5],[5,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,5],[1,1],[2,2],[3,3],[4,4],[5,0],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0042","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,5]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 1], [0, 5]], 否)","explanation_zh":"結構深度核對=(6, [[0, 1], [0, 5]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267042,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0043","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,5],[5,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 2]], 否)","explanation_zh":"結構深度核對=(6, [[0, 2]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267043,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,5],[5,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,5],[1,1],[2,2],[3,3],[4,4],[5,0],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0044","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,5],[1,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 2], [0, 5]], 否)","explanation_zh":"結構深度核對=(6, [[0, 2], [0, 5]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267044,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,5],[1,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,5],[1,0],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0045","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[0,5]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 3], [0, 5]], 否)","explanation_zh":"結構深度核對=(6, [[0, 3], [0, 5]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267045,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,3],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0046","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[0,5],[3,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 1], [0, 5]], 否)","explanation_zh":"結構深度核對=(6, [[0, 1], [0, 5]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267046,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[0,5],[3,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,3],[0,5],[1,1],[2,2],[3,0],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0047","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[0,5],[2,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 3], [0, 5]], 否)","explanation_zh":"結構深度核對=(6, [[0, 3], [0, 5]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267047,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[0,5],[2,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,3],[0,5],[1,1],[2,0],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0048","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[0,5],[3,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 1], [0, 2], [0, 5]], 否)","explanation_zh":"結構深度核對=(6, [[0, 1], [0, 2], [0, 5]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267048,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[0,5],[3,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,3],[0,5],[1,1],[2,2],[3,0],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0049","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,4],[0,5],[5,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 4]], 否)","explanation_zh":"結構深度核對=(6, [[0, 4]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267049,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,4],[0,5],[5,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,4],[0,5],[1,1],[2,2],[3,3],[4,4],[5,0],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0050","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-symmetry-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4],[0,5],[1,0]]}。請依 [n,missing_reverses,symmetric] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 4], [0, 5]], 否)","explanation_zh":"結構深度核對=(6, [[0, 4], [0, 5]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-symmetry-audit","seed":202610267050,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4],[0,5],[1,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-symmetry-audit","semantic_template":"qf-mod26-equiv-symmetry-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,4],[0,5],[1,0],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0051","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[1,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [], 是)","explanation_zh":"結構深度核對=(6, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267051,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[1,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[1,0],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0052","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [], 是)","explanation_zh":"結構深度核對=(6, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267052,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0053","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[1,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[1, 0, 2]], 否)","explanation_zh":"結構深度核對=(6, [[1, 0, 2]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267053,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[1,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0054","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [], 是)","explanation_zh":"結構深度核對=(6, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267054,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,3],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0055","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[1,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[1, 0, 3]], 否)","explanation_zh":"結構深度核對=(6, [[1, 0, 3]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267055,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[1,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,3],[1,0],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0056","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[3,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[3, 0, 2]], 否)","explanation_zh":"結構深度核對=(6, [[3, 0, 2]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267056,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[3,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,3],[1,1],[2,2],[3,0],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0057","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[1,0],[3,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[1, 0, 2], [1, 0, 3], [3, 0, 1], [3, 0, 2]], 否)","explanation_zh":"結構深度核對=(6, [[1, 0, 2], [1, 0, 3], [3, 0, 1], [3, 0, 2]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267057,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[1,0],[3,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,2],[3,0],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0058","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,4]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [], 是)","explanation_zh":"結構深度核對=(6, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267058,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,4]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,4],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0059","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4],[1,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[1, 0, 4]], 否)","explanation_zh":"結構深度核對=(6, [[1, 0, 4]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267059,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4],[1,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,4],[1,0],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0060","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,4],[4,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[4, 0, 2]], 否)","explanation_zh":"結構深度核對=(6, [[4, 0, 2]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267060,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,4],[4,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,4],[1,1],[2,2],[3,3],[4,0],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0061","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,4],[1,0],[4,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[1, 0, 2], [1, 0, 4], [4, 0, 1], [4, 0, 2]], 否)","explanation_zh":"結構深度核對=(6, [[1, 0, 2], [1, 0, 4], [4, 0, 1], [4, 0, 2]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267061,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,4],[1,0],[4,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,4],[1,0],[1,1],[2,2],[3,3],[4,0],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0062","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[0,4],[4,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[4, 0, 3]], 否)","explanation_zh":"結構深度核對=(6, [[4, 0, 3]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267062,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[0,4],[4,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,3],[0,4],[1,1],[2,2],[3,3],[4,0],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0063","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[0,4],[1,0],[4,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[1, 0, 3], [1, 0, 4], [4, 0, 1], [4, 0, 3]], 否)","explanation_zh":"結構深度核對=(6, [[1, 0, 3], [1, 0, 4], [4, 0, 1], [4, 0, 3]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267063,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[0,4],[1,0],[4,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,3],[0,4],[1,0],[1,1],[2,2],[3,3],[4,0],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0064","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[0,4],[3,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[3, 0, 2], [3, 0, 4]], 否)","explanation_zh":"結構深度核對=(6, [[3, 0, 2], [3, 0, 4]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267064,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[0,4],[3,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,3],[0,4],[1,1],[2,2],[3,0],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0065","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[0,4],[1,0],[3,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[1, 0, 2], [1, 0, 3], [1, 0, 4], [3, 0, 1], [3, 0, 2], [3, 0, 4]], 否)","explanation_zh":"結構深度核對=(6, [[1, 0, 2], [1, 0, 3], [1, 0, 4], [3, 0, 1], [3, 0, 2], [3, 0, 4]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267065,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[0,4],[1,0],[3,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[2,2],[3,0],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0066","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,5]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [], 是)","explanation_zh":"結構深度核對=(6, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267066,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0067","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,5],[1,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[1, 0, 5]], 否)","explanation_zh":"結構深度核對=(6, [[1, 0, 5]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267067,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,5],[1,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,5],[1,0],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0068","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,5],[5,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[5, 0, 2]], 否)","explanation_zh":"結構深度核對=(6, [[5, 0, 2]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267068,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,5],[5,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,5],[1,1],[2,2],[3,3],[4,4],[5,0],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0069","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,5],[1,0],[5,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[1, 0, 2], [1, 0, 5], [5, 0, 1], [5, 0, 2]], 否)","explanation_zh":"結構深度核對=(6, [[1, 0, 2], [1, 0, 5], [5, 0, 1], [5, 0, 2]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267069,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,5],[1,0],[5,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,5],[1,0],[1,1],[2,2],[3,3],[4,4],[5,0],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0070","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[0,5],[5,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[5, 0, 3]], 否)","explanation_zh":"結構深度核對=(6, [[5, 0, 3]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267070,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[0,5],[5,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,3],[0,5],[1,1],[2,2],[3,3],[4,4],[5,0],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0071","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[0,5],[1,0],[5,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[1, 0, 3], [1, 0, 5], [5, 0, 1], [5, 0, 3]], 否)","explanation_zh":"結構深度核對=(6, [[1, 0, 3], [1, 0, 5], [5, 0, 1], [5, 0, 3]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267071,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[0,5],[1,0],[5,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,3],[0,5],[1,0],[1,1],[2,2],[3,3],[4,4],[5,0],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0072","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[0,5],[3,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[3, 0, 2], [3, 0, 5]], 否)","explanation_zh":"結構深度核對=(6, [[3, 0, 2], [3, 0, 5]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267072,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[0,5],[3,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,3],[0,5],[1,1],[2,2],[3,0],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0073","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[0,5],[1,0],[3,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[1, 0, 2], [1, 0, 3], [1, 0, 5], [3, 0, 1], [3, 0, 2], [3, 0, 5]], 否)","explanation_zh":"結構深度核對=(6, [[1, 0, 2], [1, 0, 3], [1, 0, 5], [3, 0, 1], [3, 0, 2], [3, 0, 5]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267073,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[0,5],[1,0],[3,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,3],[0,5],[1,0],[1,1],[2,2],[3,0],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0074","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,4],[0,5],[5,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[5, 0, 4]], 否)","explanation_zh":"結構深度核對=(6, [[5, 0, 4]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267074,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,4],[0,5],[5,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,4],[0,5],[1,1],[2,2],[3,3],[4,4],[5,0],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0075","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-transitivity-audit；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4],[0,5],[1,0],[5,0]]}。請依 [n,missing_transitive_pairs,transitive] 欄序回答。","answer":{"kind":"expression","value":"(6, [[1, 0, 4], [1, 0, 5], [5, 0, 1], [5, 0, 4]], 否)","explanation_zh":"結構深度核對=(6, [[1, 0, 4], [1, 0, 5], [5, 0, 1], [5, 0, 4]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-transitivity-audit","seed":202610267075,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4],[0,5],[1,0],[5,0]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-transitivity-audit","semantic_template":"qf-mod26-equiv-transitivity-audit/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,4],[0,5],[1,0],[1,1],[2,2],[3,3],[4,4],[5,0],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0076","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [], [], 是, [[0], [1], [2], [3], [4], [5]])","explanation_zh":"結構深度核對=(6, [], [], [], 是, [[0], [1], [2], [3], [4], [5]])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267076,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0077","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3],[2,4],[2,5],[3,0],[3,1],[3,2],[3,3],[3,4],[3,5],[4,0],[4,1],[4,2],[4,3],[4,4],[4,5],[5,0],[5,1],[5,2],[5,3],[5,4],[5,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [], [], 是, [[0, 1, 2, 3, 4, 5]])","explanation_zh":"結構深度核對=(6, [], [], [], 是, [[0, 1, 2, 3, 4, 5]])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267077,"parameters":{"n":6,"pairs":[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3],[2,4],[2,5],[3,0],[3,1],[3,2],[3,3],[3,4],[3,5],[4,0],[4,1],[4,2],[4,3],[4,4],[4,5],[5,0],[5,1],[5,2],[5,3],[5,4],[5,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3],[2,4],[2,5],[3,0],[3,1],[3,2],[3,3],[3,4],[3,5],[4,0],[4,1],[4,2],[4,3],[4,4],[4,5],[5,0],[5,1],[5,2],[5,3],[5,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0078","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[0,1],[1,0],[1,1],[2,2],[2,3],[3,2],[3,3],[4,4],[4,5],[5,4],[5,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [], [], 是, [[0, 1], [2, 3], [4, 5]])","explanation_zh":"結構深度核對=(6, [], [], [], 是, [[0, 1], [2, 3], [4, 5]])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267078,"parameters":{"n":6,"pairs":[[0,0],[0,1],[1,0],[1,1],[2,2],[2,3],[3,2],[3,3],[4,4],[4,5],[5,4],[5,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[1,0],[1,1],[2,2],[2,3],[3,2],[3,3],[4,4],[4,5],[5,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0079","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,3],[3,4],[3,5],[4,3],[4,4],[4,5],[5,3],[5,4],[5,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [], [], 是, [[0, 1, 2], [3, 4, 5]])","explanation_zh":"結構深度核對=(6, [], [], [], 是, [[0, 1, 2], [3, 4, 5]])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267079,"parameters":{"n":6,"pairs":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,3],[3,4],[3,5],[4,3],[4,4],[4,5],[5,3],[5,4],[5,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,3],[3,4],[3,5],[4,3],[4,4],[4,5],[5,3],[5,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0080","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[0,2],[1,1],[1,3],[2,0],[2,2],[3,1],[3,3],[4,4],[4,5],[5,4],[5,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [], [], 是, [[0, 2], [1, 3], [4, 5]])","explanation_zh":"結構深度核對=(6, [], [], [], 是, [[0, 2], [1, 3], [4, 5]])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267080,"parameters":{"n":6,"pairs":[[0,0],[0,2],[1,1],[1,3],[2,0],[2,2],[3,1],[3,3],[4,4],[4,5],[5,4],[5,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,2],[1,1],[1,3],[2,0],[2,2],[3,1],[3,3],[4,4],[4,5],[5,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0081","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 2], [0, 3]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 2], [0, 3]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267081,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,3],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0082","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 1], [0, 2], [0, 3]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 1], [0, 2], [0, 3]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267082,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,3],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0083","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,4]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 4]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 4]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267083,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,4]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,4],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0084","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 1], [0, 4]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 1], [0, 4]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267084,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,4],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0085","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,4]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 2], [0, 4]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 2], [0, 4]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267085,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,4]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,4],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0086","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,4]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 1], [0, 2], [0, 4]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 1], [0, 2], [0, 4]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267086,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,4]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,4],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0087","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[0,4]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 3], [0, 4]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 3], [0, 4]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267087,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[0,4]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,3],[0,4],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0088","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[0,4]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 1], [0, 3], [0, 4]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 1], [0, 3], [0, 4]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267088,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[0,4]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,3],[0,4],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0089","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[0,4]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 2], [0, 3], [0, 4]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 2], [0, 3], [0, 4]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267089,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[0,4]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,3],[0,4],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0090","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[0,4]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 1], [0, 2], [0, 3], [0, 4]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 1], [0, 2], [0, 3], [0, 4]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267090,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[0,4]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0091","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 5]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 5]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267091,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0092","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 1], [0, 5]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 1], [0, 5]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267092,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0093","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 2], [0, 5]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 2], [0, 5]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267093,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0094","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 1], [0, 2], [0, 5]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 1], [0, 2], [0, 5]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267094,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0095","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[0,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 3], [0, 5]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 3], [0, 5]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267095,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,3],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,3],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0096","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[0,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 1], [0, 3], [0, 5]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 1], [0, 3], [0, 5]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267096,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,3],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,3],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0097","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[0,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 2], [0, 3], [0, 5]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 2], [0, 3], [0, 5]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267097,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,2],[0,3],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,2],[0,3],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0098","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[0,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 1], [0, 2], [0, 3], [0, 5]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 1], [0, 2], [0, 3], [0, 5]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267098,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,2],[0,3],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,2],[0,3],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0099","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,4],[0,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 4], [0, 5]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 4], [0, 5]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267099,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,4],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,4],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r07-equivalence-relation-0100","batch_id":"batch-20261013-advance-20261026-r07-equivalence-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-equivalence-relation"],"title_zh":"等價關係","stem_zh":"固定完整有限載體與關係對集合。操作=equiv-qualification-classes；資料={\"n\":6,\"pairs\":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4],[0,5]]}。請依 [n,missing_reflexive,missing_symmetric,missing_transitive,equivalence,classes] 欄序回答。","answer":{"kind":"expression","value":"(6, [], [[0, 1], [0, 4], [0, 5]], [], 否, [])","explanation_zh":"結構深度核對=(6, [], [[0, 1], [0, 4], [0, 5]], [], 否, [])；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；反身對稱傳遞三責任分開；類別只在完整等價資格後輸出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["等價關係"]},"variant":{"family_id":"qf-mod26-equiv-qualification-classes","seed":202610267100,"parameters":{"n":6,"pairs":[[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[0,1],[0,4],[0,5]],"domain":"Complete_finite_equivalence_relation","operation":"equiv-qualification-classes","semantic_template":"qf-mod26-equiv-qualification-classes/{\"n\":6,\"pairs\":[[0,0],[0,1],[0,4],[0,5],[1,1],[2,2],[3,3],[4,4],[5,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}