{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r05-cardinality-comparison-0001","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[0,1],\"target\":[100,101,102],\"mapping\":[100,101]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [100, 101, 102], [100, 101], 是, 是)","explanation_zh":"Wave4第四層核對=([0, 1], [100, 101, 102], [100, 101], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305001,"parameters":{"source":[0,1],"target":[100,101,102],"mapping":[100,101],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[100,101],\"source\":[0,1],\"target\":[100,101,102]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0002","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[10,11,12],\"target\":[110,111,112,113],\"mapping\":[110,111,112]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([10, 11, 12], [110, 111, 112, 113], [110, 111, 112], 是, 是)","explanation_zh":"Wave4第四層核對=([10, 11, 12], [110, 111, 112, 113], [110, 111, 112], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305002,"parameters":{"source":[10,11,12],"target":[110,111,112,113],"mapping":[110,111,112],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[110,111,112],\"source\":[10,11,12],\"target\":[110,111,112,113]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0003","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[20,21,22,23],\"target\":[120,121,122,123,124],\"mapping\":[120,121,122,123]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([20, 21, 22, 23], [120, 121, 122, 123, 124], [120, 121, 122, 123], 是, 是)","explanation_zh":"Wave4第四層核對=([20, 21, 22, 23], [120, 121, 122, 123, 124], [120, 121, 122, 123], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305003,"parameters":{"source":[20,21,22,23],"target":[120,121,122,123,124],"mapping":[120,121,122,123],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[120,121,122,123],\"source\":[20,21,22,23],\"target\":[120,121,122,123,124]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0004","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[30,31,32,33,34],\"target\":[130,131],\"mapping\":[130,131,130,131,130]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([30, 31, 32, 33, 34], [130, 131], [130, 131, 130, 131, 130], 否, no_comparison_certificate)","explanation_zh":"Wave4第四層核對=([30, 31, 32, 33, 34], [130, 131], [130, 131, 130, 131, 130], 否, no_comparison_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305004,"parameters":{"source":[30,31,32,33,34],"target":[130,131],"mapping":[130,131,130,131,130],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[130,131,130,131,130],\"source\":[30,31,32,33,34],\"target\":[130,131]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0005","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[40,41],\"target\":[140,141,142],\"mapping\":[140,141]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([40, 41], [140, 141, 142], [140, 141], 是, 是)","explanation_zh":"Wave4第四層核對=([40, 41], [140, 141, 142], [140, 141], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305005,"parameters":{"source":[40,41],"target":[140,141,142],"mapping":[140,141],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[140,141],\"source\":[40,41],\"target\":[140,141,142]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0006","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[50,51,52],\"target\":[150,151,152,153],\"mapping\":[150,151,152]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([50, 51, 52], [150, 151, 152, 153], [150, 151, 152], 是, 是)","explanation_zh":"Wave4第四層核對=([50, 51, 52], [150, 151, 152, 153], [150, 151, 152], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305006,"parameters":{"source":[50,51,52],"target":[150,151,152,153],"mapping":[150,151,152],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[150,151,152],\"source\":[50,51,52],\"target\":[150,151,152,153]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0007","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[60,61,62,63],\"target\":[160,161,162,163,164],\"mapping\":[160,161,162,163]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([60, 61, 62, 63], [160, 161, 162, 163, 164], [160, 161, 162, 163], 是, 是)","explanation_zh":"Wave4第四層核對=([60, 61, 62, 63], [160, 161, 162, 163, 164], [160, 161, 162, 163], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305007,"parameters":{"source":[60,61,62,63],"target":[160,161,162,163,164],"mapping":[160,161,162,163],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[160,161,162,163],\"source\":[60,61,62,63],\"target\":[160,161,162,163,164]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0008","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[70,71,72,73,74],\"target\":[170,171],\"mapping\":[170,171,170,171,170]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([70, 71, 72, 73, 74], [170, 171], [170, 171, 170, 171, 170], 否, no_comparison_certificate)","explanation_zh":"Wave4第四層核對=([70, 71, 72, 73, 74], [170, 171], [170, 171, 170, 171, 170], 否, no_comparison_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305008,"parameters":{"source":[70,71,72,73,74],"target":[170,171],"mapping":[170,171,170,171,170],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[170,171,170,171,170],\"source\":[70,71,72,73,74],\"target\":[170,171]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0009","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[80,81],\"target\":[180,181,182],\"mapping\":[180,181]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([80, 81], [180, 181, 182], [180, 181], 是, 是)","explanation_zh":"Wave4第四層核對=([80, 81], [180, 181, 182], [180, 181], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305009,"parameters":{"source":[80,81],"target":[180,181,182],"mapping":[180,181],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[180,181],\"source\":[80,81],\"target\":[180,181,182]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0010","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[90,91,92],\"target\":[190,191,192,193],\"mapping\":[190,191,192]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([90, 91, 92], [190, 191, 192, 193], [190, 191, 192], 是, 是)","explanation_zh":"Wave4第四層核對=([90, 91, 92], [190, 191, 192, 193], [190, 191, 192], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305010,"parameters":{"source":[90,91,92],"target":[190,191,192,193],"mapping":[190,191,192],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[190,191,192],\"source\":[90,91,92],\"target\":[190,191,192,193]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0011","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[100,101,102,103],\"target\":[200,201,202,203,204],\"mapping\":[200,201,202,203]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([100, 101, 102, 103], [200, 201, 202, 203, 204], [200, 201, 202, 203], 是, 是)","explanation_zh":"Wave4第四層核對=([100, 101, 102, 103], [200, 201, 202, 203, 204], [200, 201, 202, 203], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305011,"parameters":{"source":[100,101,102,103],"target":[200,201,202,203,204],"mapping":[200,201,202,203],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[200,201,202,203],\"source\":[100,101,102,103],\"target\":[200,201,202,203,204]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0012","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[110,111,112,113,114],\"target\":[210,211],\"mapping\":[210,211,210,211,210]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([110, 111, 112, 113, 114], [210, 211], [210, 211, 210, 211, 210], 否, no_comparison_certificate)","explanation_zh":"Wave4第四層核對=([110, 111, 112, 113, 114], [210, 211], [210, 211, 210, 211, 210], 否, no_comparison_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305012,"parameters":{"source":[110,111,112,113,114],"target":[210,211],"mapping":[210,211,210,211,210],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[210,211,210,211,210],\"source\":[110,111,112,113,114],\"target\":[210,211]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0013","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[120,121],\"target\":[220,221,222],\"mapping\":[220,221]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([120, 121], [220, 221, 222], [220, 221], 是, 是)","explanation_zh":"Wave4第四層核對=([120, 121], [220, 221, 222], [220, 221], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305013,"parameters":{"source":[120,121],"target":[220,221,222],"mapping":[220,221],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[220,221],\"source\":[120,121],\"target\":[220,221,222]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0014","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[130,131,132],\"target\":[230,231,232,233],\"mapping\":[230,231,232]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([130, 131, 132], [230, 231, 232, 233], [230, 231, 232], 是, 是)","explanation_zh":"Wave4第四層核對=([130, 131, 132], [230, 231, 232, 233], [230, 231, 232], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305014,"parameters":{"source":[130,131,132],"target":[230,231,232,233],"mapping":[230,231,232],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[230,231,232],\"source\":[130,131,132],\"target\":[230,231,232,233]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0015","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[140,141,142,143],\"target\":[240,241,242,243,244],\"mapping\":[240,241,242,243]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([140, 141, 142, 143], [240, 241, 242, 243, 244], [240, 241, 242, 243], 是, 是)","explanation_zh":"Wave4第四層核對=([140, 141, 142, 143], [240, 241, 242, 243, 244], [240, 241, 242, 243], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305015,"parameters":{"source":[140,141,142,143],"target":[240,241,242,243,244],"mapping":[240,241,242,243],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[240,241,242,243],\"source\":[140,141,142,143],\"target\":[240,241,242,243,244]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0016","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[150,151,152,153,154],\"target\":[250,251],\"mapping\":[250,251,250,251,250]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([150, 151, 152, 153, 154], [250, 251], [250, 251, 250, 251, 250], 否, no_comparison_certificate)","explanation_zh":"Wave4第四層核對=([150, 151, 152, 153, 154], [250, 251], [250, 251, 250, 251, 250], 否, no_comparison_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305016,"parameters":{"source":[150,151,152,153,154],"target":[250,251],"mapping":[250,251,250,251,250],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[250,251,250,251,250],\"source\":[150,151,152,153,154],\"target\":[250,251]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0017","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[160,161],\"target\":[260,261,262],\"mapping\":[260,261]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([160, 161], [260, 261, 262], [260, 261], 是, 是)","explanation_zh":"Wave4第四層核對=([160, 161], [260, 261, 262], [260, 261], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305017,"parameters":{"source":[160,161],"target":[260,261,262],"mapping":[260,261],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[260,261],\"source\":[160,161],\"target\":[260,261,262]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0018","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[170,171,172],\"target\":[270,271,272,273],\"mapping\":[270,271,272]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([170, 171, 172], [270, 271, 272, 273], [270, 271, 272], 是, 是)","explanation_zh":"Wave4第四層核對=([170, 171, 172], [270, 271, 272, 273], [270, 271, 272], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305018,"parameters":{"source":[170,171,172],"target":[270,271,272,273],"mapping":[270,271,272],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[270,271,272],\"source\":[170,171,172],\"target\":[270,271,272,273]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0019","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[180,181,182,183],\"target\":[280,281,282,283,284],\"mapping\":[280,281,282,283]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([180, 181, 182, 183], [280, 281, 282, 283, 284], [280, 281, 282, 283], 是, 是)","explanation_zh":"Wave4第四層核對=([180, 181, 182, 183], [280, 281, 282, 283, 284], [280, 281, 282, 283], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305019,"parameters":{"source":[180,181,182,183],"target":[280,281,282,283,284],"mapping":[280,281,282,283],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[280,281,282,283],\"source\":[180,181,182,183],\"target\":[280,281,282,283,284]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0020","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[190,191,192,193,194],\"target\":[290,291],\"mapping\":[290,291,290,291,290]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([190, 191, 192, 193, 194], [290, 291], [290, 291, 290, 291, 290], 否, no_comparison_certificate)","explanation_zh":"Wave4第四層核對=([190, 191, 192, 193, 194], [290, 291], [290, 291, 290, 291, 290], 否, no_comparison_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305020,"parameters":{"source":[190,191,192,193,194],"target":[290,291],"mapping":[290,291,290,291,290],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[290,291,290,291,290],\"source\":[190,191,192,193,194],\"target\":[290,291]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0021","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[200,201],\"target\":[300,301,302],\"mapping\":[300,301]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([200, 201], [300, 301, 302], [300, 301], 是, 是)","explanation_zh":"Wave4第四層核對=([200, 201], [300, 301, 302], [300, 301], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305021,"parameters":{"source":[200,201],"target":[300,301,302],"mapping":[300,301],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[300,301],\"source\":[200,201],\"target\":[300,301,302]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0022","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[210,211,212],\"target\":[310,311,312,313],\"mapping\":[310,311,312]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([210, 211, 212], [310, 311, 312, 313], [310, 311, 312], 是, 是)","explanation_zh":"Wave4第四層核對=([210, 211, 212], [310, 311, 312, 313], [310, 311, 312], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305022,"parameters":{"source":[210,211,212],"target":[310,311,312,313],"mapping":[310,311,312],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[310,311,312],\"source\":[210,211,212],\"target\":[310,311,312,313]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0023","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[220,221,222,223],\"target\":[320,321,322,323,324],\"mapping\":[320,321,322,323]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([220, 221, 222, 223], [320, 321, 322, 323, 324], [320, 321, 322, 323], 是, 是)","explanation_zh":"Wave4第四層核對=([220, 221, 222, 223], [320, 321, 322, 323, 324], [320, 321, 322, 323], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305023,"parameters":{"source":[220,221,222,223],"target":[320,321,322,323,324],"mapping":[320,321,322,323],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[320,321,322,323],\"source\":[220,221,222,223],\"target\":[320,321,322,323,324]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0024","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[230,231,232,233,234],\"target\":[330,331],\"mapping\":[330,331,330,331,330]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([230, 231, 232, 233, 234], [330, 331], [330, 331, 330, 331, 330], 否, no_comparison_certificate)","explanation_zh":"Wave4第四層核對=([230, 231, 232, 233, 234], [330, 331], [330, 331, 330, 331, 330], 否, no_comparison_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305024,"parameters":{"source":[230,231,232,233,234],"target":[330,331],"mapping":[330,331,330,331,330],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[330,331,330,331,330],\"source\":[230,231,232,233,234],\"target\":[330,331]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0025","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-injection；資料={\"source\":[240,241],\"target\":[340,341,342],\"mapping\":[340,341]}。請依 [source,target,mapping,injective,comparison] 欄序回答。","answer":{"kind":"expression","value":"([240, 241], [340, 341, 342], [340, 341], 是, 是)","explanation_zh":"Wave4第四層核對=([240, 241], [340, 341, 342], [340, 341], 是, 是)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-injection","seed":202610305025,"parameters":{"source":[240,241],"target":[340,341,342],"mapping":[340,341],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-injection","semantic_template":"qf-mod30-cardinality-injection/{\"mapping\":[340,341],\"source\":[240,241],\"target\":[340,341,342]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0026","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[0,1],\"target\":[100,101,102],\"mapping\":[100,101]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [100, 101, 102], [100, 101], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([0, 1], [100, 101, 102], [100, 101], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305026,"parameters":{"source":[0,1],"target":[100,101,102],"mapping":[100,101],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[100,101],\"source\":[0,1],\"target\":[100,101,102]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0027","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[10,11,12],\"target\":[110,111,112,113],\"mapping\":[110,111,112]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([10, 11, 12], [110, 111, 112, 113], [110, 111, 112], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([10, 11, 12], [110, 111, 112, 113], [110, 111, 112], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305027,"parameters":{"source":[10,11,12],"target":[110,111,112,113],"mapping":[110,111,112],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[110,111,112],\"source\":[10,11,12],\"target\":[110,111,112,113]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0028","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[20,21,22,23],\"target\":[120,121,122,123,124],\"mapping\":[120,121,122,123]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([20, 21, 22, 23], [120, 121, 122, 123, 124], [120, 121, 122, 123], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([20, 21, 22, 23], [120, 121, 122, 123, 124], [120, 121, 122, 123], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305028,"parameters":{"source":[20,21,22,23],"target":[120,121,122,123,124],"mapping":[120,121,122,123],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[120,121,122,123],\"source\":[20,21,22,23],\"target\":[120,121,122,123,124]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0029","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[30,31,32,33,34],\"target\":[130,131],\"mapping\":[130,131,130,131,130]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([30, 31, 32, 33, 34], [130, 131], [130, 131, 130, 131, 130], 是, 是, finite_only)","explanation_zh":"Wave4第四層核對=([30, 31, 32, 33, 34], [130, 131], [130, 131, 130, 131, 130], 是, 是, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305029,"parameters":{"source":[30,31,32,33,34],"target":[130,131],"mapping":[130,131,130,131,130],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[130,131,130,131,130],\"source\":[30,31,32,33,34],\"target\":[130,131]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0030","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[40,41],\"target\":[140,141,142],\"mapping\":[140,141]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([40, 41], [140, 141, 142], [140, 141], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([40, 41], [140, 141, 142], [140, 141], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305030,"parameters":{"source":[40,41],"target":[140,141,142],"mapping":[140,141],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[140,141],\"source\":[40,41],\"target\":[140,141,142]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0031","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[50,51,52],\"target\":[150,151,152,153],\"mapping\":[150,151,152]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([50, 51, 52], [150, 151, 152, 153], [150, 151, 152], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([50, 51, 52], [150, 151, 152, 153], [150, 151, 152], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305031,"parameters":{"source":[50,51,52],"target":[150,151,152,153],"mapping":[150,151,152],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[150,151,152],\"source\":[50,51,52],\"target\":[150,151,152,153]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0032","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[60,61,62,63],\"target\":[160,161,162,163,164],\"mapping\":[160,161,162,163]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([60, 61, 62, 63], [160, 161, 162, 163, 164], [160, 161, 162, 163], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([60, 61, 62, 63], [160, 161, 162, 163, 164], [160, 161, 162, 163], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305032,"parameters":{"source":[60,61,62,63],"target":[160,161,162,163,164],"mapping":[160,161,162,163],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[160,161,162,163],\"source\":[60,61,62,63],\"target\":[160,161,162,163,164]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0033","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[70,71,72,73,74],\"target\":[170,171],\"mapping\":[170,171,170,171,170]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([70, 71, 72, 73, 74], [170, 171], [170, 171, 170, 171, 170], 是, 是, finite_only)","explanation_zh":"Wave4第四層核對=([70, 71, 72, 73, 74], [170, 171], [170, 171, 170, 171, 170], 是, 是, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305033,"parameters":{"source":[70,71,72,73,74],"target":[170,171],"mapping":[170,171,170,171,170],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[170,171,170,171,170],\"source\":[70,71,72,73,74],\"target\":[170,171]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0034","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[80,81],\"target\":[180,181,182],\"mapping\":[180,181]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([80, 81], [180, 181, 182], [180, 181], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([80, 81], [180, 181, 182], [180, 181], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305034,"parameters":{"source":[80,81],"target":[180,181,182],"mapping":[180,181],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[180,181],\"source\":[80,81],\"target\":[180,181,182]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0035","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[90,91,92],\"target\":[190,191,192,193],\"mapping\":[190,191,192]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([90, 91, 92], [190, 191, 192, 193], [190, 191, 192], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([90, 91, 92], [190, 191, 192, 193], [190, 191, 192], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305035,"parameters":{"source":[90,91,92],"target":[190,191,192,193],"mapping":[190,191,192],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[190,191,192],\"source\":[90,91,92],\"target\":[190,191,192,193]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0036","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[100,101,102,103],\"target\":[200,201,202,203,204],\"mapping\":[200,201,202,203]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([100, 101, 102, 103], [200, 201, 202, 203, 204], [200, 201, 202, 203], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([100, 101, 102, 103], [200, 201, 202, 203, 204], [200, 201, 202, 203], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305036,"parameters":{"source":[100,101,102,103],"target":[200,201,202,203,204],"mapping":[200,201,202,203],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[200,201,202,203],\"source\":[100,101,102,103],\"target\":[200,201,202,203,204]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0037","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[110,111,112,113,114],\"target\":[210,211],\"mapping\":[210,211,210,211,210]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([110, 111, 112, 113, 114], [210, 211], [210, 211, 210, 211, 210], 是, 是, finite_only)","explanation_zh":"Wave4第四層核對=([110, 111, 112, 113, 114], [210, 211], [210, 211, 210, 211, 210], 是, 是, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305037,"parameters":{"source":[110,111,112,113,114],"target":[210,211],"mapping":[210,211,210,211,210],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[210,211,210,211,210],\"source\":[110,111,112,113,114],\"target\":[210,211]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0038","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[120,121],\"target\":[220,221,222],\"mapping\":[220,221]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([120, 121], [220, 221, 222], [220, 221], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([120, 121], [220, 221, 222], [220, 221], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305038,"parameters":{"source":[120,121],"target":[220,221,222],"mapping":[220,221],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[220,221],\"source\":[120,121],\"target\":[220,221,222]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0039","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[130,131,132],\"target\":[230,231,232,233],\"mapping\":[230,231,232]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([130, 131, 132], [230, 231, 232, 233], [230, 231, 232], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([130, 131, 132], [230, 231, 232, 233], [230, 231, 232], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305039,"parameters":{"source":[130,131,132],"target":[230,231,232,233],"mapping":[230,231,232],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[230,231,232],\"source\":[130,131,132],\"target\":[230,231,232,233]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0040","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[140,141,142,143],\"target\":[240,241,242,243,244],\"mapping\":[240,241,242,243]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([140, 141, 142, 143], [240, 241, 242, 243, 244], [240, 241, 242, 243], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([140, 141, 142, 143], [240, 241, 242, 243, 244], [240, 241, 242, 243], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305040,"parameters":{"source":[140,141,142,143],"target":[240,241,242,243,244],"mapping":[240,241,242,243],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[240,241,242,243],\"source\":[140,141,142,143],\"target\":[240,241,242,243,244]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0041","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[150,151,152,153,154],\"target\":[250,251],\"mapping\":[250,251,250,251,250]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([150, 151, 152, 153, 154], [250, 251], [250, 251, 250, 251, 250], 是, 是, finite_only)","explanation_zh":"Wave4第四層核對=([150, 151, 152, 153, 154], [250, 251], [250, 251, 250, 251, 250], 是, 是, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305041,"parameters":{"source":[150,151,152,153,154],"target":[250,251],"mapping":[250,251,250,251,250],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[250,251,250,251,250],\"source\":[150,151,152,153,154],\"target\":[250,251]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0042","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[160,161],\"target\":[260,261,262],\"mapping\":[260,261]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([160, 161], [260, 261, 262], [260, 261], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([160, 161], [260, 261, 262], [260, 261], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305042,"parameters":{"source":[160,161],"target":[260,261,262],"mapping":[260,261],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[260,261],\"source\":[160,161],\"target\":[260,261,262]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0043","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[170,171,172],\"target\":[270,271,272,273],\"mapping\":[270,271,272]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([170, 171, 172], [270, 271, 272, 273], [270, 271, 272], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([170, 171, 172], [270, 271, 272, 273], [270, 271, 272], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305043,"parameters":{"source":[170,171,172],"target":[270,271,272,273],"mapping":[270,271,272],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[270,271,272],\"source\":[170,171,172],\"target\":[270,271,272,273]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0044","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[180,181,182,183],\"target\":[280,281,282,283,284],\"mapping\":[280,281,282,283]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([180, 181, 182, 183], [280, 281, 282, 283, 284], [280, 281, 282, 283], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([180, 181, 182, 183], [280, 281, 282, 283, 284], [280, 281, 282, 283], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305044,"parameters":{"source":[180,181,182,183],"target":[280,281,282,283,284],"mapping":[280,281,282,283],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[280,281,282,283],\"source\":[180,181,182,183],\"target\":[280,281,282,283,284]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0045","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[190,191,192,193,194],\"target\":[290,291],\"mapping\":[290,291,290,291,290]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([190, 191, 192, 193, 194], [290, 291], [290, 291, 290, 291, 290], 是, 是, finite_only)","explanation_zh":"Wave4第四層核對=([190, 191, 192, 193, 194], [290, 291], [290, 291, 290, 291, 290], 是, 是, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305045,"parameters":{"source":[190,191,192,193,194],"target":[290,291],"mapping":[290,291,290,291,290],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[290,291,290,291,290],\"source\":[190,191,192,193,194],\"target\":[290,291]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0046","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[200,201],\"target\":[300,301,302],\"mapping\":[300,301]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([200, 201], [300, 301, 302], [300, 301], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([200, 201], [300, 301, 302], [300, 301], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305046,"parameters":{"source":[200,201],"target":[300,301,302],"mapping":[300,301],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[300,301],\"source\":[200,201],\"target\":[300,301,302]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0047","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[210,211,212],\"target\":[310,311,312,313],\"mapping\":[310,311,312]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([210, 211, 212], [310, 311, 312, 313], [310, 311, 312], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([210, 211, 212], [310, 311, 312, 313], [310, 311, 312], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305047,"parameters":{"source":[210,211,212],"target":[310,311,312,313],"mapping":[310,311,312],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[310,311,312],\"source\":[210,211,212],\"target\":[310,311,312,313]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0048","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[220,221,222,223],\"target\":[320,321,322,323,324],\"mapping\":[320,321,322,323]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([220, 221, 222, 223], [320, 321, 322, 323, 324], [320, 321, 322, 323], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([220, 221, 222, 223], [320, 321, 322, 323, 324], [320, 321, 322, 323], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305048,"parameters":{"source":[220,221,222,223],"target":[320,321,322,323,324],"mapping":[320,321,322,323],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[320,321,322,323],\"source\":[220,221,222,223],\"target\":[320,321,322,323,324]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0049","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[230,231,232,233,234],\"target\":[330,331],\"mapping\":[330,331,330,331,330]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([230, 231, 232, 233, 234], [330, 331], [330, 331, 330, 331, 330], 是, 是, finite_only)","explanation_zh":"Wave4第四層核對=([230, 231, 232, 233, 234], [330, 331], [330, 331, 330, 331, 330], 是, 是, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305049,"parameters":{"source":[230,231,232,233,234],"target":[330,331],"mapping":[330,331,330,331,330],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[330,331,330,331,330],\"source\":[230,231,232,233,234],\"target\":[330,331]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0050","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-surjection-finite；資料={\"source\":[240,241],\"target\":[340,341,342],\"mapping\":[340,341]}。請依 [source,target,mapping,surjective,comparison,boundary] 欄序回答。","answer":{"kind":"expression","value":"([240, 241], [340, 341, 342], [340, 341], 否, no_comparison_certificate, finite_only)","explanation_zh":"Wave4第四層核對=([240, 241], [340, 341, 342], [340, 341], 否, no_comparison_certificate, finite_only)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-surjection-finite","seed":202610305050,"parameters":{"source":[240,241],"target":[340,341,342],"mapping":[340,341],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-surjection-finite","semantic_template":"qf-mod30-cardinality-surjection-finite/{\"mapping\":[340,341],\"source\":[240,241],\"target\":[340,341,342]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0051","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[0,1],\"target\":[100,101,102],\"mapping\":[100,101]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [100, 101, 102], [100, 101], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([0, 1], [100, 101, 102], [100, 101], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305051,"parameters":{"source":[0,1],"target":[100,101,102],"mapping":[100,101],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[100,101],\"source\":[0,1],\"target\":[100,101,102]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0052","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[10,11,12],\"target\":[110,111,112,113],\"mapping\":[110,111,112]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([10, 11, 12], [110, 111, 112, 113], [110, 111, 112], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([10, 11, 12], [110, 111, 112, 113], [110, 111, 112], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305052,"parameters":{"source":[10,11,12],"target":[110,111,112,113],"mapping":[110,111,112],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[110,111,112],\"source\":[10,11,12],\"target\":[110,111,112,113]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0053","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[20,21,22,23],\"target\":[120,121,122,123,124],\"mapping\":[120,121,122,123]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([20, 21, 22, 23], [120, 121, 122, 123, 124], [120, 121, 122, 123], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([20, 21, 22, 23], [120, 121, 122, 123, 124], [120, 121, 122, 123], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305053,"parameters":{"source":[20,21,22,23],"target":[120,121,122,123,124],"mapping":[120,121,122,123],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[120,121,122,123],\"source\":[20,21,22,23],\"target\":[120,121,122,123,124]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0054","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[30,31,32,33,34],\"target\":[130,131],\"mapping\":[130,131,130,131,130]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([30, 31, 32, 33, 34], [130, 131], [130, 131, 130, 131, 130], 否, 是, 否, 否)","explanation_zh":"Wave4第四層核對=([30, 31, 32, 33, 34], [130, 131], [130, 131, 130, 131, 130], 否, 是, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305054,"parameters":{"source":[30,31,32,33,34],"target":[130,131],"mapping":[130,131,130,131,130],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[130,131,130,131,130],\"source\":[30,31,32,33,34],\"target\":[130,131]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0055","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[40,41],\"target\":[140,141,142],\"mapping\":[140,141]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([40, 41], [140, 141, 142], [140, 141], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([40, 41], [140, 141, 142], [140, 141], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305055,"parameters":{"source":[40,41],"target":[140,141,142],"mapping":[140,141],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[140,141],\"source\":[40,41],\"target\":[140,141,142]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0056","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[50,51,52],\"target\":[150,151,152,153],\"mapping\":[150,151,152]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([50, 51, 52], [150, 151, 152, 153], [150, 151, 152], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([50, 51, 52], [150, 151, 152, 153], [150, 151, 152], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305056,"parameters":{"source":[50,51,52],"target":[150,151,152,153],"mapping":[150,151,152],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[150,151,152],\"source\":[50,51,52],\"target\":[150,151,152,153]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0057","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[60,61,62,63],\"target\":[160,161,162,163,164],\"mapping\":[160,161,162,163]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([60, 61, 62, 63], [160, 161, 162, 163, 164], [160, 161, 162, 163], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([60, 61, 62, 63], [160, 161, 162, 163, 164], [160, 161, 162, 163], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305057,"parameters":{"source":[60,61,62,63],"target":[160,161,162,163,164],"mapping":[160,161,162,163],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[160,161,162,163],\"source\":[60,61,62,63],\"target\":[160,161,162,163,164]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0058","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[70,71,72,73,74],\"target\":[170,171],\"mapping\":[170,171,170,171,170]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([70, 71, 72, 73, 74], [170, 171], [170, 171, 170, 171, 170], 否, 是, 否, 否)","explanation_zh":"Wave4第四層核對=([70, 71, 72, 73, 74], [170, 171], [170, 171, 170, 171, 170], 否, 是, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305058,"parameters":{"source":[70,71,72,73,74],"target":[170,171],"mapping":[170,171,170,171,170],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[170,171,170,171,170],\"source\":[70,71,72,73,74],\"target\":[170,171]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0059","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[80,81],\"target\":[180,181,182],\"mapping\":[180,181]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([80, 81], [180, 181, 182], [180, 181], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([80, 81], [180, 181, 182], [180, 181], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305059,"parameters":{"source":[80,81],"target":[180,181,182],"mapping":[180,181],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[180,181],\"source\":[80,81],\"target\":[180,181,182]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0060","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[90,91,92],\"target\":[190,191,192,193],\"mapping\":[190,191,192]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([90, 91, 92], [190, 191, 192, 193], [190, 191, 192], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([90, 91, 92], [190, 191, 192, 193], [190, 191, 192], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305060,"parameters":{"source":[90,91,92],"target":[190,191,192,193],"mapping":[190,191,192],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[190,191,192],\"source\":[90,91,92],\"target\":[190,191,192,193]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0061","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[100,101,102,103],\"target\":[200,201,202,203,204],\"mapping\":[200,201,202,203]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([100, 101, 102, 103], [200, 201, 202, 203, 204], [200, 201, 202, 203], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([100, 101, 102, 103], [200, 201, 202, 203, 204], [200, 201, 202, 203], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305061,"parameters":{"source":[100,101,102,103],"target":[200,201,202,203,204],"mapping":[200,201,202,203],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[200,201,202,203],\"source\":[100,101,102,103],\"target\":[200,201,202,203,204]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0062","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[110,111,112,113,114],\"target\":[210,211],\"mapping\":[210,211,210,211,210]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([110, 111, 112, 113, 114], [210, 211], [210, 211, 210, 211, 210], 否, 是, 否, 否)","explanation_zh":"Wave4第四層核對=([110, 111, 112, 113, 114], [210, 211], [210, 211, 210, 211, 210], 否, 是, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305062,"parameters":{"source":[110,111,112,113,114],"target":[210,211],"mapping":[210,211,210,211,210],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[210,211,210,211,210],\"source\":[110,111,112,113,114],\"target\":[210,211]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0063","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[120,121],\"target\":[220,221,222],\"mapping\":[220,221]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([120, 121], [220, 221, 222], [220, 221], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([120, 121], [220, 221, 222], [220, 221], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305063,"parameters":{"source":[120,121],"target":[220,221,222],"mapping":[220,221],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[220,221],\"source\":[120,121],\"target\":[220,221,222]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0064","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[130,131,132],\"target\":[230,231,232,233],\"mapping\":[230,231,232]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([130, 131, 132], [230, 231, 232, 233], [230, 231, 232], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([130, 131, 132], [230, 231, 232, 233], [230, 231, 232], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305064,"parameters":{"source":[130,131,132],"target":[230,231,232,233],"mapping":[230,231,232],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[230,231,232],\"source\":[130,131,132],\"target\":[230,231,232,233]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0065","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[140,141,142,143],\"target\":[240,241,242,243,244],\"mapping\":[240,241,242,243]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([140, 141, 142, 143], [240, 241, 242, 243, 244], [240, 241, 242, 243], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([140, 141, 142, 143], [240, 241, 242, 243, 244], [240, 241, 242, 243], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305065,"parameters":{"source":[140,141,142,143],"target":[240,241,242,243,244],"mapping":[240,241,242,243],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[240,241,242,243],\"source\":[140,141,142,143],\"target\":[240,241,242,243,244]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0066","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[150,151,152,153,154],\"target\":[250,251],\"mapping\":[250,251,250,251,250]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([150, 151, 152, 153, 154], [250, 251], [250, 251, 250, 251, 250], 否, 是, 否, 否)","explanation_zh":"Wave4第四層核對=([150, 151, 152, 153, 154], [250, 251], [250, 251, 250, 251, 250], 否, 是, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305066,"parameters":{"source":[150,151,152,153,154],"target":[250,251],"mapping":[250,251,250,251,250],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[250,251,250,251,250],\"source\":[150,151,152,153,154],\"target\":[250,251]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0067","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[160,161],\"target\":[260,261,262],\"mapping\":[260,261]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([160, 161], [260, 261, 262], [260, 261], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([160, 161], [260, 261, 262], [260, 261], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305067,"parameters":{"source":[160,161],"target":[260,261,262],"mapping":[260,261],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[260,261],\"source\":[160,161],\"target\":[260,261,262]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0068","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[170,171,172],\"target\":[270,271,272,273],\"mapping\":[270,271,272]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([170, 171, 172], [270, 271, 272, 273], [270, 271, 272], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([170, 171, 172], [270, 271, 272, 273], [270, 271, 272], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305068,"parameters":{"source":[170,171,172],"target":[270,271,272,273],"mapping":[270,271,272],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[270,271,272],\"source\":[170,171,172],\"target\":[270,271,272,273]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0069","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[180,181,182,183],\"target\":[280,281,282,283,284],\"mapping\":[280,281,282,283]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([180, 181, 182, 183], [280, 281, 282, 283, 284], [280, 281, 282, 283], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([180, 181, 182, 183], [280, 281, 282, 283, 284], [280, 281, 282, 283], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305069,"parameters":{"source":[180,181,182,183],"target":[280,281,282,283,284],"mapping":[280,281,282,283],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[280,281,282,283],\"source\":[180,181,182,183],\"target\":[280,281,282,283,284]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0070","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[190,191,192,193,194],\"target\":[290,291],\"mapping\":[290,291,290,291,290]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([190, 191, 192, 193, 194], [290, 291], [290, 291, 290, 291, 290], 否, 是, 否, 否)","explanation_zh":"Wave4第四層核對=([190, 191, 192, 193, 194], [290, 291], [290, 291, 290, 291, 290], 否, 是, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305070,"parameters":{"source":[190,191,192,193,194],"target":[290,291],"mapping":[290,291,290,291,290],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[290,291,290,291,290],\"source\":[190,191,192,193,194],\"target\":[290,291]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0071","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[200,201],\"target\":[300,301,302],\"mapping\":[300,301]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([200, 201], [300, 301, 302], [300, 301], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([200, 201], [300, 301, 302], [300, 301], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305071,"parameters":{"source":[200,201],"target":[300,301,302],"mapping":[300,301],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[300,301],\"source\":[200,201],\"target\":[300,301,302]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0072","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[210,211,212],\"target\":[310,311,312,313],\"mapping\":[310,311,312]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([210, 211, 212], [310, 311, 312, 313], [310, 311, 312], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([210, 211, 212], [310, 311, 312, 313], [310, 311, 312], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305072,"parameters":{"source":[210,211,212],"target":[310,311,312,313],"mapping":[310,311,312],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[310,311,312],\"source\":[210,211,212],\"target\":[310,311,312,313]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0073","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[220,221,222,223],\"target\":[320,321,322,323,324],\"mapping\":[320,321,322,323]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([220, 221, 222, 223], [320, 321, 322, 323, 324], [320, 321, 322, 323], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([220, 221, 222, 223], [320, 321, 322, 323, 324], [320, 321, 322, 323], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305073,"parameters":{"source":[220,221,222,223],"target":[320,321,322,323,324],"mapping":[320,321,322,323],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[320,321,322,323],\"source\":[220,221,222,223],\"target\":[320,321,322,323,324]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0074","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[230,231,232,233,234],\"target\":[330,331],\"mapping\":[330,331,330,331,330]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([230, 231, 232, 233, 234], [330, 331], [330, 331, 330, 331, 330], 否, 是, 否, 否)","explanation_zh":"Wave4第四層核對=([230, 231, 232, 233, 234], [330, 331], [330, 331, 330, 331, 330], 否, 是, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305074,"parameters":{"source":[230,231,232,233,234],"target":[330,331],"mapping":[330,331,330,331,330],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[330,331,330,331,330],\"source\":[230,231,232,233,234],\"target\":[330,331]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0075","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-bijection；資料={\"source\":[240,241],\"target\":[340,341,342],\"mapping\":[340,341]}。請依 [source,target,mapping,injective,surjective,bijective,equal_cardinality] 欄序回答。","answer":{"kind":"expression","value":"([240, 241], [340, 341, 342], [340, 341], 是, 否, 否, 否)","explanation_zh":"Wave4第四層核對=([240, 241], [340, 341, 342], [340, 341], 是, 否, 否, 否)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-bijection","seed":202610305075,"parameters":{"source":[240,241],"target":[340,341,342],"mapping":[340,341],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-bijection","semantic_template":"qf-mod30-cardinality-bijection/{\"mapping\":[340,341],\"source\":[240,241],\"target\":[340,341,342]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0076","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[0,1],\"target\":[100,101,102]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(2, 3, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305076,"parameters":{"source":[0,1],"target":[100,101,102],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[0,1],\"target\":[100,101,102]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0077","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[10,11,12],\"target\":[110,111,112,113]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(3, 4, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(3, 4, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305077,"parameters":{"source":[10,11,12],"target":[110,111,112,113],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[10,11,12],\"target\":[110,111,112,113]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0078","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[20,21,22,23],\"target\":[120,121,122,123,124]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(4, 5, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(4, 5, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305078,"parameters":{"source":[20,21,22,23],"target":[120,121,122,123,124],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[20,21,22,23],\"target\":[120,121,122,123,124]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0079","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[30,31,32,33,34],\"target\":[130,131]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, 是, no_injection_finite_pigeonhole)","explanation_zh":"Wave4第四層核對=(5, 2, 是, no_injection_finite_pigeonhole)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305079,"parameters":{"source":[30,31,32,33,34],"target":[130,131],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[30,31,32,33,34],\"target\":[130,131]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0080","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[40,41],\"target\":[140,141,142]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(2, 3, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305080,"parameters":{"source":[40,41],"target":[140,141,142],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[40,41],\"target\":[140,141,142]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0081","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[50,51,52],\"target\":[150,151,152,153]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(3, 4, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(3, 4, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305081,"parameters":{"source":[50,51,52],"target":[150,151,152,153],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[50,51,52],\"target\":[150,151,152,153]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0082","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[60,61,62,63],\"target\":[160,161,162,163,164]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(4, 5, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(4, 5, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305082,"parameters":{"source":[60,61,62,63],"target":[160,161,162,163,164],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[60,61,62,63],\"target\":[160,161,162,163,164]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0083","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[70,71,72,73,74],\"target\":[170,171]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, 是, no_injection_finite_pigeonhole)","explanation_zh":"Wave4第四層核對=(5, 2, 是, no_injection_finite_pigeonhole)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305083,"parameters":{"source":[70,71,72,73,74],"target":[170,171],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[70,71,72,73,74],\"target\":[170,171]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0084","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[80,81],\"target\":[180,181,182]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(2, 3, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305084,"parameters":{"source":[80,81],"target":[180,181,182],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[80,81],\"target\":[180,181,182]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0085","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[90,91,92],\"target\":[190,191,192,193]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(3, 4, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(3, 4, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305085,"parameters":{"source":[90,91,92],"target":[190,191,192,193],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[90,91,92],\"target\":[190,191,192,193]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0086","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[100,101,102,103],\"target\":[200,201,202,203,204]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(4, 5, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(4, 5, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305086,"parameters":{"source":[100,101,102,103],"target":[200,201,202,203,204],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[100,101,102,103],\"target\":[200,201,202,203,204]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0087","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[110,111,112,113,114],\"target\":[210,211]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, 是, no_injection_finite_pigeonhole)","explanation_zh":"Wave4第四層核對=(5, 2, 是, no_injection_finite_pigeonhole)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305087,"parameters":{"source":[110,111,112,113,114],"target":[210,211],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[110,111,112,113,114],\"target\":[210,211]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0088","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[120,121],\"target\":[220,221,222]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(2, 3, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305088,"parameters":{"source":[120,121],"target":[220,221,222],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[120,121],\"target\":[220,221,222]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0089","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[130,131,132],\"target\":[230,231,232,233]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(3, 4, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(3, 4, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305089,"parameters":{"source":[130,131,132],"target":[230,231,232,233],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[130,131,132],\"target\":[230,231,232,233]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0090","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[140,141,142,143],\"target\":[240,241,242,243,244]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(4, 5, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(4, 5, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305090,"parameters":{"source":[140,141,142,143],"target":[240,241,242,243,244],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[140,141,142,143],\"target\":[240,241,242,243,244]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0091","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[150,151,152,153,154],\"target\":[250,251]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, 是, no_injection_finite_pigeonhole)","explanation_zh":"Wave4第四層核對=(5, 2, 是, no_injection_finite_pigeonhole)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305091,"parameters":{"source":[150,151,152,153,154],"target":[250,251],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[150,151,152,153,154],\"target\":[250,251]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0092","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[160,161],\"target\":[260,261,262]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(2, 3, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305092,"parameters":{"source":[160,161],"target":[260,261,262],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[160,161],\"target\":[260,261,262]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0093","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[170,171,172],\"target\":[270,271,272,273]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(3, 4, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(3, 4, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305093,"parameters":{"source":[170,171,172],"target":[270,271,272,273],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[170,171,172],\"target\":[270,271,272,273]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0094","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[180,181,182,183],\"target\":[280,281,282,283,284]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(4, 5, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(4, 5, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305094,"parameters":{"source":[180,181,182,183],"target":[280,281,282,283,284],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[180,181,182,183],\"target\":[280,281,282,283,284]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0095","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[190,191,192,193,194],\"target\":[290,291]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, 是, no_injection_finite_pigeonhole)","explanation_zh":"Wave4第四層核對=(5, 2, 是, no_injection_finite_pigeonhole)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305095,"parameters":{"source":[190,191,192,193,194],"target":[290,291],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[190,191,192,193,194],\"target\":[290,291]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0096","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[200,201],\"target\":[300,301,302]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(2, 3, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305096,"parameters":{"source":[200,201],"target":[300,301,302],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[200,201],\"target\":[300,301,302]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0097","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[210,211,212],\"target\":[310,311,312,313]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(3, 4, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(3, 4, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305097,"parameters":{"source":[210,211,212],"target":[310,311,312,313],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[210,211,212],\"target\":[310,311,312,313]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0098","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[220,221,222,223],\"target\":[320,321,322,323,324]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(4, 5, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(4, 5, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305098,"parameters":{"source":[220,221,222,223],"target":[320,321,322,323,324],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[220,221,222,223],\"target\":[320,321,322,323,324]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0099","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[230,231,232,233,234],\"target\":[330,331]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, 是, no_injection_finite_pigeonhole)","explanation_zh":"Wave4第四層核對=(5, 2, 是, no_injection_finite_pigeonhole)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305099,"parameters":{"source":[230,231,232,233,234],"target":[330,331],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[230,231,232,233,234],\"target\":[330,331]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或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-20261030-r05-cardinality-comparison-0100","batch_id":"batch-20261014-advance-20261030-r05-cardinality-comparison-foundations","language":"zh-Hant","source_mko_ids":["mko-cardinality-comparison"],"title_zh":"集合基數比較","stem_zh":"mapping綁精確有限source與target。操作=cardinality-pigeonhole；資料={\"source\":[240,241],\"target\":[340,341,342]}。請依 [source_size,target_size,larger,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, 否, no_impossibility_certificate)","explanation_zh":"Wave4第四層核對=(2, 3, 否, no_impossibility_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；injective surjective bijective責任分開；surjection逆向比較限有限集合且不外推無限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合基數比較"]},"variant":{"family_id":"qf-mod30-cardinality-pigeonhole","seed":202610305100,"parameters":{"source":[240,241],"target":[340,341,342],"domain":"Exact_finite_cardinality_mapping","operation":"cardinality-pigeonhole","semantic_template":"qf-mod30-cardinality-pigeonhole/{\"source\":[240,241],\"target\":[340,341,342]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}