{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0001","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[1,-2,40]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([1, -2, 40], [[1, 0], [-2, 1], [40, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([1, -2, 40], [[1, 0], [-2, 1], [40, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311001,"parameters":{"elements":[1,-2,40],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-2,1,40]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0002","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[2,-3,42]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([2, -3, 42], [[2, 0], [-3, 1], [42, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([2, -3, 42], [[2, 0], [-3, 1], [42, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311002,"parameters":{"elements":[2,-3,42],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-3,2,42]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0003","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[3,-4,44]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([3, -4, 44], [[3, 0], [-4, 1], [44, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([3, -4, 44], [[3, 0], [-4, 1], [44, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311003,"parameters":{"elements":[3,-4,44],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-4,3,44]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0004","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[4,-5,46]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([4, -5, 46], [[4, 0], [-5, 1], [46, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([4, -5, 46], [[4, 0], [-5, 1], [46, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311004,"parameters":{"elements":[4,-5,46],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-5,4,46]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0005","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[5,-6,48]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([5, -6, 48], [[5, 0], [-6, 1], [48, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([5, -6, 48], [[5, 0], [-6, 1], [48, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311005,"parameters":{"elements":[5,-6,48],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-6,5,48]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0006","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[6,-7,50]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([6, -7, 50], [[6, 0], [-7, 1], [50, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([6, -7, 50], [[6, 0], [-7, 1], [50, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311006,"parameters":{"elements":[6,-7,50],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-7,6,50]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0007","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[7,-8,52]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([7, -8, 52], [[7, 0], [-8, 1], [52, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([7, -8, 52], [[7, 0], [-8, 1], [52, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311007,"parameters":{"elements":[7,-8,52],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-8,7,52]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0008","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[8,-9,54]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([8, -9, 54], [[8, 0], [-9, 1], [54, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([8, -9, 54], [[8, 0], [-9, 1], [54, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311008,"parameters":{"elements":[8,-9,54],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-9,8,54]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0009","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[9,-10,56]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([9, -10, 56], [[9, 0], [-10, 1], [56, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([9, -10, 56], [[9, 0], [-10, 1], [56, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311009,"parameters":{"elements":[9,-10,56],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-10,9,56]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0010","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[10,-11,58]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([10, -11, 58], [[10, 0], [-11, 1], [58, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([10, -11, 58], [[10, 0], [-11, 1], [58, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311010,"parameters":{"elements":[10,-11,58],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-11,10,58]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0011","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[11,-12,60]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([11, -12, 60], [[11, 0], [-12, 1], [60, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([11, -12, 60], [[11, 0], [-12, 1], [60, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311011,"parameters":{"elements":[11,-12,60],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-12,11,60]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0012","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[12,-13,62]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([12, -13, 62], [[12, 0], [-13, 1], [62, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([12, -13, 62], [[12, 0], [-13, 1], [62, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311012,"parameters":{"elements":[12,-13,62],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-13,12,62]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0013","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[13,-14,64]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([13, -14, 64], [[13, 0], [-14, 1], [64, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([13, -14, 64], [[13, 0], [-14, 1], [64, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311013,"parameters":{"elements":[13,-14,64],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-14,13,64]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0014","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[14,-15,66]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([14, -15, 66], [[14, 0], [-15, 1], [66, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([14, -15, 66], [[14, 0], [-15, 1], [66, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311014,"parameters":{"elements":[14,-15,66],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-15,14,66]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0015","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[15,-16,68]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([15, -16, 68], [[15, 0], [-16, 1], [68, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([15, -16, 68], [[15, 0], [-16, 1], [68, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311015,"parameters":{"elements":[15,-16,68],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-16,15,68]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0016","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[16,-17,70]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([16, -17, 70], [[16, 0], [-17, 1], [70, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([16, -17, 70], [[16, 0], [-17, 1], [70, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311016,"parameters":{"elements":[16,-17,70],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-17,16,70]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0017","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[17,-18,72]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([17, -18, 72], [[17, 0], [-18, 1], [72, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([17, -18, 72], [[17, 0], [-18, 1], [72, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311017,"parameters":{"elements":[17,-18,72],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-18,17,72]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0018","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[18,-19,74]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([18, -19, 74], [[18, 0], [-19, 1], [74, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([18, -19, 74], [[18, 0], [-19, 1], [74, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311018,"parameters":{"elements":[18,-19,74],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-19,18,74]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0019","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[19,-20,76]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([19, -20, 76], [[19, 0], [-20, 1], [76, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([19, -20, 76], [[19, 0], [-20, 1], [76, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311019,"parameters":{"elements":[19,-20,76],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-20,19,76]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0020","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[20,-21,78]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([20, -21, 78], [[20, 0], [-21, 1], [78, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([20, -21, 78], [[20, 0], [-21, 1], [78, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311020,"parameters":{"elements":[20,-21,78],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-21,20,78]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0021","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[21,-22,80]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([21, -22, 80], [[21, 0], [-22, 1], [80, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([21, -22, 80], [[21, 0], [-22, 1], [80, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311021,"parameters":{"elements":[21,-22,80],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-22,21,80]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0022","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[22,-23,82]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([22, -23, 82], [[22, 0], [-23, 1], [82, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([22, -23, 82], [[22, 0], [-23, 1], [82, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311022,"parameters":{"elements":[22,-23,82],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-23,22,82]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0023","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[23,-24,84]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([23, -24, 84], [[23, 0], [-24, 1], [84, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([23, -24, 84], [[23, 0], [-24, 1], [84, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311023,"parameters":{"elements":[23,-24,84],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-24,23,84]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0024","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[24,-25,86]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([24, -25, 86], [[24, 0], [-25, 1], [86, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([24, -25, 86], [[24, 0], [-25, 1], [86, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311024,"parameters":{"elements":[24,-25,86],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-25,24,86]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0025","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-finite-certificate；資料={\"elements\":[25,-26,88]}。請依 [elements,injection_pairs,injective,certificate] 欄序回答。","answer":{"kind":"expression","value":"([25, -26, 88], [[25, 0], [-26, 1], [88, 2]], 是, finite_implies_at_most_countable)","explanation_zh":"Wave4收束核對=([25, -26, 88], [[25, 0], [-26, 1], [88, 2]], 是, finite_implies_at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-finite-certificate","seed":202610311025,"parameters":{"elements":[25,-26,88],"domain":"Explicit_at_most_countable_certificate","operation":"countable-finite-certificate","semantic_template":"qf-mod31-countable-finite-certificate/{\"elements\":[-26,25,88]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0026","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":1,\"intercept\":-12,\"left\":-1,\"right\":2}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, -12, -1, 2, -13, -10, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(1, -12, -1, 2, -13, -10, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311026,"parameters":{"slope":1,"intercept":-12,"left":-1,"right":2,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":-12,\"left\":-1,\"right\":2,\"slope\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0027","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":2,\"intercept\":-11,\"left\":-2,\"right\":3}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, -11, -2, 3, -15, -5, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(2, -11, -2, 3, -15, -5, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311027,"parameters":{"slope":2,"intercept":-11,"left":-2,"right":3,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":-11,\"left\":-2,\"right\":3,\"slope\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0028","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":3,\"intercept\":-10,\"left\":-3,\"right\":4}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, -10, -3, 4, -19, 2, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(3, -10, -3, 4, -19, 2, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311028,"parameters":{"slope":3,"intercept":-10,"left":-3,"right":4,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":-10,\"left\":-3,\"right\":4,\"slope\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0029","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":4,\"intercept\":-9,\"left\":-4,\"right\":5}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, -9, -4, 5, -25, 11, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(4, -9, -4, 5, -25, 11, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311029,"parameters":{"slope":4,"intercept":-9,"left":-4,"right":5,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":-9,\"left\":-4,\"right\":5,\"slope\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0030","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":5,\"intercept\":-8,\"left\":-5,\"right\":6}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, -8, -5, 6, -33, 22, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(5, -8, -5, 6, -33, 22, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311030,"parameters":{"slope":5,"intercept":-8,"left":-5,"right":6,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":-8,\"left\":-5,\"right\":6,\"slope\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0031","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":1,\"intercept\":-7,\"left\":-6,\"right\":7}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, -7, -6, 7, -13, 0, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(1, -7, -6, 7, -13, 0, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311031,"parameters":{"slope":1,"intercept":-7,"left":-6,"right":7,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":-7,\"left\":-6,\"right\":7,\"slope\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0032","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":2,\"intercept\":-6,\"left\":-7,\"right\":8}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, -6, -7, 8, -20, 10, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(2, -6, -7, 8, -20, 10, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311032,"parameters":{"slope":2,"intercept":-6,"left":-7,"right":8,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":-6,\"left\":-7,\"right\":8,\"slope\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0033","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":3,\"intercept\":-5,\"left\":-8,\"right\":9}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, -5, -8, 9, -29, 22, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(3, -5, -8, 9, -29, 22, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311033,"parameters":{"slope":3,"intercept":-5,"left":-8,"right":9,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":-5,\"left\":-8,\"right\":9,\"slope\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0034","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":4,\"intercept\":-4,\"left\":-9,\"right\":10}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, -4, -9, 10, -40, 36, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(4, -4, -9, 10, -40, 36, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311034,"parameters":{"slope":4,"intercept":-4,"left":-9,"right":10,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":-4,\"left\":-9,\"right\":10,\"slope\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0035","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":5,\"intercept\":-3,\"left\":-10,\"right\":11}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, -3, -10, 11, -53, 52, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(5, -3, -10, 11, -53, 52, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311035,"parameters":{"slope":5,"intercept":-3,"left":-10,"right":11,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":-3,\"left\":-10,\"right\":11,\"slope\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0036","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":1,\"intercept\":-2,\"left\":-11,\"right\":12}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, -2, -11, 12, -13, 10, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(1, -2, -11, 12, -13, 10, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311036,"parameters":{"slope":1,"intercept":-2,"left":-11,"right":12,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":-2,\"left\":-11,\"right\":12,\"slope\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0037","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":2,\"intercept\":-1,\"left\":-12,\"right\":13}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, -1, -12, 13, -25, 25, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(2, -1, -12, 13, -25, 25, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311037,"parameters":{"slope":2,"intercept":-1,"left":-12,"right":13,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":-1,\"left\":-12,\"right\":13,\"slope\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0038","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":3,\"intercept\":0,\"left\":-13,\"right\":14}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 0, -13, 14, -39, 42, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(3, 0, -13, 14, -39, 42, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311038,"parameters":{"slope":3,"intercept":0,"left":-13,"right":14,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":0,\"left\":-13,\"right\":14,\"slope\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0039","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":4,\"intercept\":1,\"left\":-14,\"right\":15}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, 1, -14, 15, -55, 61, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(4, 1, -14, 15, -55, 61, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311039,"parameters":{"slope":4,"intercept":1,"left":-14,"right":15,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":1,\"left\":-14,\"right\":15,\"slope\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0040","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":5,\"intercept\":2,\"left\":-15,\"right\":16}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, -15, 16, -73, 82, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(5, 2, -15, 16, -73, 82, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311040,"parameters":{"slope":5,"intercept":2,"left":-15,"right":16,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":2,\"left\":-15,\"right\":16,\"slope\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0041","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":1,\"intercept\":3,\"left\":-16,\"right\":17}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, -16, 17, -13, 20, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(1, 3, -16, 17, -13, 20, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311041,"parameters":{"slope":1,"intercept":3,"left":-16,"right":17,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":3,\"left\":-16,\"right\":17,\"slope\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0042","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":2,\"intercept\":4,\"left\":-17,\"right\":18}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, 4, -17, 18, -30, 40, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(2, 4, -17, 18, -30, 40, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311042,"parameters":{"slope":2,"intercept":4,"left":-17,"right":18,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":4,\"left\":-17,\"right\":18,\"slope\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0043","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":3,\"intercept\":5,\"left\":-18,\"right\":19}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 5, -18, 19, -49, 62, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(3, 5, -18, 19, -49, 62, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311043,"parameters":{"slope":3,"intercept":5,"left":-18,"right":19,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":5,\"left\":-18,\"right\":19,\"slope\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0044","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":4,\"intercept\":6,\"left\":-19,\"right\":20}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, 6, -19, 20, -70, 86, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(4, 6, -19, 20, -70, 86, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311044,"parameters":{"slope":4,"intercept":6,"left":-19,"right":20,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":6,\"left\":-19,\"right\":20,\"slope\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0045","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":5,\"intercept\":7,\"left\":-20,\"right\":21}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 7, -20, 21, -93, 112, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(5, 7, -20, 21, -93, 112, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311045,"parameters":{"slope":5,"intercept":7,"left":-20,"right":21,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":7,\"left\":-20,\"right\":21,\"slope\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0046","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":1,\"intercept\":8,\"left\":-21,\"right\":22}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 8, -21, 22, -13, 30, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(1, 8, -21, 22, -13, 30, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311046,"parameters":{"slope":1,"intercept":8,"left":-21,"right":22,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":8,\"left\":-21,\"right\":22,\"slope\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0047","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":2,\"intercept\":9,\"left\":-22,\"right\":23}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, 9, -22, 23, -35, 55, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(2, 9, -22, 23, -35, 55, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311047,"parameters":{"slope":2,"intercept":9,"left":-22,"right":23,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":9,\"left\":-22,\"right\":23,\"slope\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0048","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":3,\"intercept\":10,\"left\":-23,\"right\":24}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 10, -23, 24, -59, 82, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(3, 10, -23, 24, -59, 82, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311048,"parameters":{"slope":3,"intercept":10,"left":-23,"right":24,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":10,\"left\":-23,\"right\":24,\"slope\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0049","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":4,\"intercept\":11,\"left\":-24,\"right\":25}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, 11, -24, 25, -85, 111, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(4, 11, -24, 25, -85, 111, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311049,"parameters":{"slope":4,"intercept":11,"left":-24,"right":25,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":11,\"left\":-24,\"right\":25,\"slope\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0050","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-affine-injection；資料={\"slope\":5,\"intercept\":12,\"left\":-25,\"right\":26}。請依 [slope,intercept,left,right,image_left,image_right,injective_check,universal_certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 12, -25, 26, -113, 142, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)","explanation_zh":"Wave4收束核對=(5, 12, -25, 26, -113, 142, 是, universal_nonzero_slope_injection_Z_to_Z_then_encode_N)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-affine-injection","seed":202610311050,"parameters":{"slope":5,"intercept":12,"left":-25,"right":26,"domain":"Explicit_at_most_countable_certificate","operation":"countable-affine-injection","semantic_template":"qf-mod31-countable-affine-injection/{\"intercept\":12,\"left\":-25,\"right\":26,\"slope\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0051","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[0,50,-1],\"index\":0}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [[0, 0], [1, 50], [2, -1]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(0, 0, [[0, 0], [1, 50], [2, -1]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311051,"parameters":{"elements":[0,50,-1],"index":0,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-1,0,50],\"index\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0052","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[1,51,-2],\"index\":1}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 51, [[0, 1], [1, 51], [2, -2]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(1, 51, [[0, 1], [1, 51], [2, -2]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311052,"parameters":{"elements":[1,51,-2],"index":1,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-2,1,51],\"index\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0053","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[2,52,-3],\"index\":2}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, -3, [[0, 2], [1, 52], [2, -3]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(2, -3, [[0, 2], [1, 52], [2, -3]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311053,"parameters":{"elements":[2,52,-3],"index":2,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-3,2,52],\"index\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0054","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[3,53,-4],\"index\":0}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(0, 3, [[0, 3], [1, 53], [2, -4]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(0, 3, [[0, 3], [1, 53], [2, -4]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311054,"parameters":{"elements":[3,53,-4],"index":0,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-4,3,53],\"index\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0055","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[4,54,-5],\"index\":1}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 54, [[0, 4], [1, 54], [2, -5]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(1, 54, [[0, 4], [1, 54], [2, -5]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311055,"parameters":{"elements":[4,54,-5],"index":1,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-5,4,54],\"index\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0056","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[5,55,-6],\"index\":2}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, -6, [[0, 5], [1, 55], [2, -6]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(2, -6, [[0, 5], [1, 55], [2, -6]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311056,"parameters":{"elements":[5,55,-6],"index":2,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-6,5,55],\"index\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0057","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[6,56,-7],\"index\":0}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(0, 6, [[0, 6], [1, 56], [2, -7]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(0, 6, [[0, 6], [1, 56], [2, -7]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311057,"parameters":{"elements":[6,56,-7],"index":0,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-7,6,56],\"index\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0058","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[7,57,-8],\"index\":1}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 57, [[0, 7], [1, 57], [2, -8]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(1, 57, [[0, 7], [1, 57], [2, -8]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311058,"parameters":{"elements":[7,57,-8],"index":1,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-8,7,57],\"index\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0059","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[8,58,-9],\"index\":2}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, -9, [[0, 8], [1, 58], [2, -9]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(2, -9, [[0, 8], [1, 58], [2, -9]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311059,"parameters":{"elements":[8,58,-9],"index":2,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-9,8,58],\"index\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0060","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[9,59,-10],\"index\":0}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(0, 9, [[0, 9], [1, 59], [2, -10]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(0, 9, [[0, 9], [1, 59], [2, -10]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311060,"parameters":{"elements":[9,59,-10],"index":0,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-10,9,59],\"index\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0061","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[10,60,-11],\"index\":1}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 60, [[0, 10], [1, 60], [2, -11]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(1, 60, [[0, 10], [1, 60], [2, -11]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311061,"parameters":{"elements":[10,60,-11],"index":1,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-11,10,60],\"index\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0062","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[11,61,-12],\"index\":2}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, -12, [[0, 11], [1, 61], [2, -12]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(2, -12, [[0, 11], [1, 61], [2, -12]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311062,"parameters":{"elements":[11,61,-12],"index":2,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-12,11,61],\"index\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0063","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[12,62,-13],\"index\":0}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(0, 12, [[0, 12], [1, 62], [2, -13]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(0, 12, [[0, 12], [1, 62], [2, -13]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311063,"parameters":{"elements":[12,62,-13],"index":0,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-13,12,62],\"index\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0064","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[13,63,-14],\"index\":1}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 63, [[0, 13], [1, 63], [2, -14]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(1, 63, [[0, 13], [1, 63], [2, -14]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311064,"parameters":{"elements":[13,63,-14],"index":1,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-14,13,63],\"index\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0065","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[14,64,-15],\"index\":2}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, -15, [[0, 14], [1, 64], [2, -15]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(2, -15, [[0, 14], [1, 64], [2, -15]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311065,"parameters":{"elements":[14,64,-15],"index":2,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-15,14,64],\"index\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0066","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[15,65,-16],\"index\":0}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(0, 15, [[0, 15], [1, 65], [2, -16]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(0, 15, [[0, 15], [1, 65], [2, -16]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311066,"parameters":{"elements":[15,65,-16],"index":0,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-16,15,65],\"index\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0067","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[16,66,-17],\"index\":1}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 66, [[0, 16], [1, 66], [2, -17]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(1, 66, [[0, 16], [1, 66], [2, -17]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311067,"parameters":{"elements":[16,66,-17],"index":1,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-17,16,66],\"index\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0068","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[17,67,-18],\"index\":2}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, -18, [[0, 17], [1, 67], [2, -18]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(2, -18, [[0, 17], [1, 67], [2, -18]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311068,"parameters":{"elements":[17,67,-18],"index":2,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-18,17,67],\"index\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0069","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[18,68,-19],\"index\":0}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(0, 18, [[0, 18], [1, 68], [2, -19]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(0, 18, [[0, 18], [1, 68], [2, -19]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311069,"parameters":{"elements":[18,68,-19],"index":0,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-19,18,68],\"index\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0070","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[19,69,-20],\"index\":1}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 69, [[0, 19], [1, 69], [2, -20]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(1, 69, [[0, 19], [1, 69], [2, -20]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311070,"parameters":{"elements":[19,69,-20],"index":1,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-20,19,69],\"index\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0071","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[20,70,-21],\"index\":2}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, -21, [[0, 20], [1, 70], [2, -21]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(2, -21, [[0, 20], [1, 70], [2, -21]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311071,"parameters":{"elements":[20,70,-21],"index":2,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-21,20,70],\"index\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0072","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[21,71,-22],\"index\":0}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(0, 21, [[0, 21], [1, 71], [2, -22]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(0, 21, [[0, 21], [1, 71], [2, -22]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311072,"parameters":{"elements":[21,71,-22],"index":0,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-22,21,71],\"index\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0073","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[22,72,-23],\"index\":1}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 72, [[0, 22], [1, 72], [2, -23]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(1, 72, [[0, 22], [1, 72], [2, -23]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311073,"parameters":{"elements":[22,72,-23],"index":1,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-23,22,72],\"index\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0074","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[23,73,-24],\"index\":2}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, -24, [[0, 23], [1, 73], [2, -24]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(2, -24, [[0, 23], [1, 73], [2, -24]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311074,"parameters":{"elements":[23,73,-24],"index":2,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-24,23,73],\"index\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0075","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-enumeration；資料={\"elements\":[24,74,-25],\"index\":0}。請依 [index,element,enumeration_pairs,certificate] 欄序回答。","answer":{"kind":"expression","value":"(0, 24, [[0, 24], [1, 74], [2, -25]], finite_enumeration_complete)","explanation_zh":"Wave4收束核對=(0, 24, [[0, 24], [1, 74], [2, -25]], finite_enumeration_complete)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-enumeration","seed":202610311075,"parameters":{"elements":[24,74,-25],"index":0,"domain":"Explicit_at_most_countable_certificate","operation":"countable-enumeration","semantic_template":"qf-mod31-countable-enumeration/{\"elements\":[-25,24,74],\"index\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0076","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"complete_finite_list\",\"certificate_parameter\":1}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(complete_finite_list, 1, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(complete_finite_list, 1, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311076,"parameters":{"evidence_mode":"complete_finite_list","certificate_parameter":1,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":1,\"evidence_mode\":\"complete_finite_list\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0077","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"universal_affine_injection\",\"certificate_parameter\":2}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(universal_affine_injection, 2, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(universal_affine_injection, 2, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311077,"parameters":{"evidence_mode":"universal_affine_injection","certificate_parameter":2,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":2,\"evidence_mode\":\"universal_affine_injection\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0078","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"failed_candidate_encoding\",\"certificate_parameter\":3}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(failed_candidate_encoding, 3, 否, no_classification_from_failed_witness)","explanation_zh":"Wave4收束核對=(failed_candidate_encoding, 3, 否, no_classification_from_failed_witness)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311078,"parameters":{"evidence_mode":"failed_candidate_encoding","certificate_parameter":3,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":3,\"evidence_mode\":\"failed_candidate_encoding\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0079","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"complete_finite_list\",\"certificate_parameter\":4}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(complete_finite_list, 4, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(complete_finite_list, 4, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311079,"parameters":{"evidence_mode":"complete_finite_list","certificate_parameter":4,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":4,\"evidence_mode\":\"complete_finite_list\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0080","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"universal_affine_injection\",\"certificate_parameter\":5}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(universal_affine_injection, 5, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(universal_affine_injection, 5, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311080,"parameters":{"evidence_mode":"universal_affine_injection","certificate_parameter":5,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":5,\"evidence_mode\":\"universal_affine_injection\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0081","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"failed_candidate_encoding\",\"certificate_parameter\":6}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(failed_candidate_encoding, 6, 否, no_classification_from_failed_witness)","explanation_zh":"Wave4收束核對=(failed_candidate_encoding, 6, 否, no_classification_from_failed_witness)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311081,"parameters":{"evidence_mode":"failed_candidate_encoding","certificate_parameter":6,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":6,\"evidence_mode\":\"failed_candidate_encoding\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0082","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"complete_finite_list\",\"certificate_parameter\":7}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(complete_finite_list, 7, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(complete_finite_list, 7, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311082,"parameters":{"evidence_mode":"complete_finite_list","certificate_parameter":7,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":7,\"evidence_mode\":\"complete_finite_list\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0083","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"universal_affine_injection\",\"certificate_parameter\":8}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(universal_affine_injection, 8, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(universal_affine_injection, 8, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311083,"parameters":{"evidence_mode":"universal_affine_injection","certificate_parameter":8,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":8,\"evidence_mode\":\"universal_affine_injection\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0084","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"failed_candidate_encoding\",\"certificate_parameter\":9}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(failed_candidate_encoding, 9, 否, no_classification_from_failed_witness)","explanation_zh":"Wave4收束核對=(failed_candidate_encoding, 9, 否, no_classification_from_failed_witness)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311084,"parameters":{"evidence_mode":"failed_candidate_encoding","certificate_parameter":9,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":9,\"evidence_mode\":\"failed_candidate_encoding\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0085","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"complete_finite_list\",\"certificate_parameter\":10}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(complete_finite_list, 10, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(complete_finite_list, 10, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311085,"parameters":{"evidence_mode":"complete_finite_list","certificate_parameter":10,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":10,\"evidence_mode\":\"complete_finite_list\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0086","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"universal_affine_injection\",\"certificate_parameter\":11}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(universal_affine_injection, 11, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(universal_affine_injection, 11, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311086,"parameters":{"evidence_mode":"universal_affine_injection","certificate_parameter":11,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":11,\"evidence_mode\":\"universal_affine_injection\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0087","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"failed_candidate_encoding\",\"certificate_parameter\":12}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(failed_candidate_encoding, 12, 否, no_classification_from_failed_witness)","explanation_zh":"Wave4收束核對=(failed_candidate_encoding, 12, 否, no_classification_from_failed_witness)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311087,"parameters":{"evidence_mode":"failed_candidate_encoding","certificate_parameter":12,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":12,\"evidence_mode\":\"failed_candidate_encoding\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0088","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"complete_finite_list\",\"certificate_parameter\":13}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(complete_finite_list, 13, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(complete_finite_list, 13, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311088,"parameters":{"evidence_mode":"complete_finite_list","certificate_parameter":13,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":13,\"evidence_mode\":\"complete_finite_list\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0089","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"universal_affine_injection\",\"certificate_parameter\":14}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(universal_affine_injection, 14, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(universal_affine_injection, 14, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311089,"parameters":{"evidence_mode":"universal_affine_injection","certificate_parameter":14,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":14,\"evidence_mode\":\"universal_affine_injection\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0090","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"failed_candidate_encoding\",\"certificate_parameter\":15}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(failed_candidate_encoding, 15, 否, no_classification_from_failed_witness)","explanation_zh":"Wave4收束核對=(failed_candidate_encoding, 15, 否, no_classification_from_failed_witness)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311090,"parameters":{"evidence_mode":"failed_candidate_encoding","certificate_parameter":15,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":15,\"evidence_mode\":\"failed_candidate_encoding\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0091","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"complete_finite_list\",\"certificate_parameter\":16}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(complete_finite_list, 16, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(complete_finite_list, 16, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311091,"parameters":{"evidence_mode":"complete_finite_list","certificate_parameter":16,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":16,\"evidence_mode\":\"complete_finite_list\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0092","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"universal_affine_injection\",\"certificate_parameter\":17}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(universal_affine_injection, 17, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(universal_affine_injection, 17, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311092,"parameters":{"evidence_mode":"universal_affine_injection","certificate_parameter":17,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":17,\"evidence_mode\":\"universal_affine_injection\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0093","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"failed_candidate_encoding\",\"certificate_parameter\":18}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(failed_candidate_encoding, 18, 否, no_classification_from_failed_witness)","explanation_zh":"Wave4收束核對=(failed_candidate_encoding, 18, 否, no_classification_from_failed_witness)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311093,"parameters":{"evidence_mode":"failed_candidate_encoding","certificate_parameter":18,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":18,\"evidence_mode\":\"failed_candidate_encoding\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0094","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"complete_finite_list\",\"certificate_parameter\":19}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(complete_finite_list, 19, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(complete_finite_list, 19, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311094,"parameters":{"evidence_mode":"complete_finite_list","certificate_parameter":19,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":19,\"evidence_mode\":\"complete_finite_list\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0095","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"universal_affine_injection\",\"certificate_parameter\":20}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(universal_affine_injection, 20, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(universal_affine_injection, 20, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311095,"parameters":{"evidence_mode":"universal_affine_injection","certificate_parameter":20,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":20,\"evidence_mode\":\"universal_affine_injection\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0096","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"failed_candidate_encoding\",\"certificate_parameter\":21}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(failed_candidate_encoding, 21, 否, no_classification_from_failed_witness)","explanation_zh":"Wave4收束核對=(failed_candidate_encoding, 21, 否, no_classification_from_failed_witness)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311096,"parameters":{"evidence_mode":"failed_candidate_encoding","certificate_parameter":21,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":21,\"evidence_mode\":\"failed_candidate_encoding\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0097","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"complete_finite_list\",\"certificate_parameter\":22}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(complete_finite_list, 22, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(complete_finite_list, 22, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311097,"parameters":{"evidence_mode":"complete_finite_list","certificate_parameter":22,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":22,\"evidence_mode\":\"complete_finite_list\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0098","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"universal_affine_injection\",\"certificate_parameter\":23}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(universal_affine_injection, 23, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(universal_affine_injection, 23, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311098,"parameters":{"evidence_mode":"universal_affine_injection","certificate_parameter":23,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":23,\"evidence_mode\":\"universal_affine_injection\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0099","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"failed_candidate_encoding\",\"certificate_parameter\":24}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(failed_candidate_encoding, 24, 否, no_classification_from_failed_witness)","explanation_zh":"Wave4收束核對=(failed_candidate_encoding, 24, 否, no_classification_from_failed_witness)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311099,"parameters":{"evidence_mode":"failed_candidate_encoding","certificate_parameter":24,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":24,\"evidence_mode\":\"failed_candidate_encoding\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r01-at-most-countable-set-0100","batch_id":"batch-20261014-advance-20261031-r01-at-most-countable-set-foundations","language":"zh-Hant","source_mko_ids":["mko-at-most-countable-set"],"title_zh":"至多可數集","stem_zh":"有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"complete_finite_list\",\"certificate_parameter\":25}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。","answer":{"kind":"expression","value":"(complete_finite_list, 25, 是, at_most_countable)","explanation_zh":"Wave4收束核對=(complete_finite_list, 25, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多可數集"]},"variant":{"family_id":"qf-mod31-countable-classification","seed":202610311100,"parameters":{"evidence_mode":"complete_finite_list","certificate_parameter":25,"domain":"Explicit_at_most_countable_certificate","operation":"countable-classification","semantic_template":"qf-mod31-countable-classification/{\"certificate_parameter\":25,\"evidence_mode\":\"complete_finite_list\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}