{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0001","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[1,2,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 1, 是, 是], [1, 1/2, 2, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 1, 是, 是], [1, 1/2, 2, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014001,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[1,2,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[1,2,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0002","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[2,3,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 2, 是, 是], [1, 1/2, 3, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 2, 是, 是], [1, 1/2, 3, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014002,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[2,3,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[2,3,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0003","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[3,4,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 3, 是, 是], [1, 1/2, 4, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 3, 是, 是], [1, 1/2, 4, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014003,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[3,4,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[3,4,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0004","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[4,5,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 4, 是, 是], [1, 1/2, 5, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 4, 是, 是], [1, 1/2, 5, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014004,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[4,5,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[4,5,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0005","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[5,6,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 5, 是, 是], [1, 1/2, 6, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 5, 是, 是], [1, 1/2, 6, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014005,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[5,6,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[5,6,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0006","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[6,7,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 6, 是, 是], [1, 1/2, 7, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 6, 是, 是], [1, 1/2, 7, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014006,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[6,7,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[6,7,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0007","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[7,8,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 7, 是, 是], [1, 1/2, 8, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 7, 是, 是], [1, 1/2, 8, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014007,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[7,8,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[7,8,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0008","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[8,9,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 8, 是, 是], [1, 1/2, 9, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 8, 是, 是], [1, 1/2, 9, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014008,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[8,9,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[8,9,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0009","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[9,10,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 9, 是, 是], [1, 1/2, 10, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 9, 是, 是], [1, 1/2, 10, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014009,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[9,10,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[9,10,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0010","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[10,11,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 10, 是, 是], [1, 1/2, 11, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 10, 是, 是], [1, 1/2, 11, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014010,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[10,11,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[10,11,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0011","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[11,12,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 11, 是, 是], [1, 1/2, 12, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 11, 是, 是], [1, 1/2, 12, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014011,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[11,12,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[11,12,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0012","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[12,13,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 12, 是, 是], [1, 1/2, 13, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 12, 是, 是], [1, 1/2, 13, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014012,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[12,13,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[12,13,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0013","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[13,14,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 13, 是, 是], [1, 1/2, 14, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 13, 是, 是], [1, 1/2, 14, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014013,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[13,14,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[13,14,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0014","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[14,15,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 14, 是, 是], [1, 1/2, 15, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 14, 是, 是], [1, 1/2, 15, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014014,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[14,15,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[14,15,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0015","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[15,16,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 15, 是, 是], [1, 1/2, 16, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 15, 是, 是], [1, 1/2, 16, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014015,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[15,16,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[15,16,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0016","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[16,17,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 16, 是, 是], [1, 1/2, 17, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 16, 是, 是], [1, 1/2, 17, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014016,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[16,17,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[16,17,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0017","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[17,18,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 17, 是, 是], [1, 1/2, 18, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 17, 是, 是], [1, 1/2, 18, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014017,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[17,18,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[17,18,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0018","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[18,19,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 18, 是, 是], [1, 1/2, 19, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 18, 是, 是], [1, 1/2, 19, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014018,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[18,19,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[18,19,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0019","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[19,20,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 19, 是, 是], [1, 1/2, 20, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 19, 是, 是], [1, 1/2, 20, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014019,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[19,20,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[19,20,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0020","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[20,21,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 20, 是, 是], [1, 1/2, 21, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 20, 是, 是], [1, 1/2, 21, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014020,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[20,21,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[20,21,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0021","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[21,22,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 21, 是, 是], [1, 1/2, 22, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 21, 是, 是], [1, 1/2, 22, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014021,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[21,22,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[21,22,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0022","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[22,23,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 22, 是, 是], [1, 1/2, 23, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 22, 是, 是], [1, 1/2, 23, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014022,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[22,23,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[22,23,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0023","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[23,24,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 23, 是, 是], [1, 1/2, 24, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 23, 是, 是], [1, 1/2, 24, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014023,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[23,24,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[23,24,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0024","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[24,25,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 24, 是, 是], [1, 1/2, 25, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 24, 是, 是], [1, 1/2, 25, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014024,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[24,25,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[24,25,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0025","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-qualification；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[25,26,null]}。請依 [atom_rows,exceptional_mass,positive_mass_failures,almost_sure] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 25, 是, 是], [1, 1/2, 26, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 25, 是, 是], [1, 1/2, 26, 是, 是], [2, 0, null, 否, 是]], 0, [], 是)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-qualification","seed":202611014025,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[25,26,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-qualification","semantic_template":"qf-mod32-asconv-qualification/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[25,26,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0026","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[1,2,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 1, 是, 是], [1, 1/2, 2, 是, 是]], 2, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 1, 是, 是], [1, 1/2, 2, 是, 是]], 2, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014026,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[1,2,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[1,2,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0027","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[2,3,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 2, 是, 是], [1, 1/2, 3, 是, 是]], 3, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 2, 是, 是], [1, 1/2, 3, 是, 是]], 3, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014027,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[2,3,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[2,3,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0028","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[3,4,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 3, 是, 是], [1, 1/2, 4, 是, 是]], 4, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 3, 是, 是], [1, 1/2, 4, 是, 是]], 4, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014028,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[3,4,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[3,4,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0029","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[4,5,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 4, 是, 是], [1, 1/2, 5, 是, 是]], 5, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 4, 是, 是], [1, 1/2, 5, 是, 是]], 5, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014029,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[4,5,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[4,5,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0030","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[5,6,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 5, 是, 是], [1, 1/2, 6, 是, 是]], 6, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 5, 是, 是], [1, 1/2, 6, 是, 是]], 6, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014030,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[5,6,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[5,6,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0031","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[6,7,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 6, 是, 是], [1, 1/2, 7, 是, 是]], 7, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 6, 是, 是], [1, 1/2, 7, 是, 是]], 7, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014031,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[6,7,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[6,7,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0032","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[7,8,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 7, 是, 是], [1, 1/2, 8, 是, 是]], 8, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 7, 是, 是], [1, 1/2, 8, 是, 是]], 8, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014032,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[7,8,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[7,8,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0033","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[8,9,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 8, 是, 是], [1, 1/2, 9, 是, 是]], 9, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 8, 是, 是], [1, 1/2, 9, 是, 是]], 9, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014033,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[8,9,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[8,9,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0034","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[9,10,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 9, 是, 是], [1, 1/2, 10, 是, 是]], 10, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 9, 是, 是], [1, 1/2, 10, 是, 是]], 10, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014034,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[9,10,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[9,10,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0035","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[10,11,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 10, 是, 是], [1, 1/2, 11, 是, 是]], 11, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 10, 是, 是], [1, 1/2, 11, 是, 是]], 11, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014035,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[10,11,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[10,11,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0036","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[11,12,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 11, 是, 是], [1, 1/2, 12, 是, 是]], 12, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 11, 是, 是], [1, 1/2, 12, 是, 是]], 12, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014036,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[11,12,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[11,12,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0037","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[12,13,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 12, 是, 是], [1, 1/2, 13, 是, 是]], 13, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 12, 是, 是], [1, 1/2, 13, 是, 是]], 13, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014037,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[12,13,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[12,13,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0038","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[13,14,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 13, 是, 是], [1, 1/2, 14, 是, 是]], 14, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 13, 是, 是], [1, 1/2, 14, 是, 是]], 14, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014038,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[13,14,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[13,14,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0039","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[14,15,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 14, 是, 是], [1, 1/2, 15, 是, 是]], 15, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 14, 是, 是], [1, 1/2, 15, 是, 是]], 15, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014039,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[14,15,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[14,15,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0040","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[15,16,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 15, 是, 是], [1, 1/2, 16, 是, 是]], 16, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 15, 是, 是], [1, 1/2, 16, 是, 是]], 16, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014040,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[15,16,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[15,16,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0041","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[16,17,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 16, 是, 是], [1, 1/2, 17, 是, 是]], 17, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 16, 是, 是], [1, 1/2, 17, 是, 是]], 17, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014041,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[16,17,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[16,17,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0042","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[17,18,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 17, 是, 是], [1, 1/2, 18, 是, 是]], 18, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 17, 是, 是], [1, 1/2, 18, 是, 是]], 18, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014042,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[17,18,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[17,18,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0043","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[18,19,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 18, 是, 是], [1, 1/2, 19, 是, 是]], 19, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 18, 是, 是], [1, 1/2, 19, 是, 是]], 19, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014043,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[18,19,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[18,19,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0044","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[19,20,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 19, 是, 是], [1, 1/2, 20, 是, 是]], 20, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 19, 是, 是], [1, 1/2, 20, 是, 是]], 20, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014044,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[19,20,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[19,20,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0045","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[20,21,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 20, 是, 是], [1, 1/2, 21, 是, 是]], 21, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 20, 是, 是], [1, 1/2, 21, 是, 是]], 21, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014045,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[20,21,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[20,21,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0046","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[21,22,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 21, 是, 是], [1, 1/2, 22, 是, 是]], 22, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 21, 是, 是], [1, 1/2, 22, 是, 是]], 22, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014046,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[21,22,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[21,22,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0047","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[22,23,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 22, 是, 是], [1, 1/2, 23, 是, 是]], 23, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 22, 是, 是], [1, 1/2, 23, 是, 是]], 23, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014047,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[22,23,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[22,23,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0048","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[23,24,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 23, 是, 是], [1, 1/2, 24, 是, 是]], 24, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 23, 是, 是], [1, 1/2, 24, 是, 是]], 24, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014048,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[23,24,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[23,24,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0049","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[24,25,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 24, 是, 是], [1, 1/2, 25, 是, 是]], 25, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 24, 是, 是], [1, 1/2, 25, 是, 是]], 25, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014049,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[24,25,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[24,25,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0050","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-settling-index；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[25,26,null]}。請依 [positive_mass_rows,maximum_settling_index,almost_sure,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2, 25, 是, 是], [1, 1/2, 26, 是, 是]], 26, 是, uniform_finite_atom_tail_after_maximum)","explanation_zh":"Wave5根節點核對=([[0, 1/2, 25, 是, 是], [1, 1/2, 26, 是, 是]], 26, 是, uniform_finite_atom_tail_after_maximum)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-settling-index","seed":202611014050,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[25,26,null],"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-settling-index","semantic_template":"qf-mod32-asconv-settling-index/{\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[25,26,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0051","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[1,2,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014051,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[1,2,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[1,2,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0052","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[2,3,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014052,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[2,3,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[2,3,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0053","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[3,4,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014053,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[3,4,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[3,4,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0054","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[4,5,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014054,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[4,5,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[4,5,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0055","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[5,6,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014055,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[5,6,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[5,6,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0056","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[6,7,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014056,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[6,7,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[6,7,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0057","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[7,8,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014057,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[7,8,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[7,8,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0058","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[8,9,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014058,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[8,9,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[8,9,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0059","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[9,10,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014059,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[9,10,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[9,10,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0060","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[10,11,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014060,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[10,11,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[10,11,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0061","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[11,12,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014061,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[11,12,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[11,12,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0062","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[12,13,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014062,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[12,13,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[12,13,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0063","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[13,14,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014063,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[13,14,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[13,14,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0064","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[14,15,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014064,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[14,15,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[14,15,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0065","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[15,16,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014065,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[15,16,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[15,16,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0066","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[16,17,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014066,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[16,17,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[16,17,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0067","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[17,18,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014067,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[17,18,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[17,18,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0068","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[18,19,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014068,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[18,19,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[18,19,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0069","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[19,20,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014069,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[19,20,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[19,20,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0070","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[20,21,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014070,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[20,21,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[20,21,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0071","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[21,22,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014071,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[21,22,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[21,22,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0072","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[22,23,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014072,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[22,23,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[22,23,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0073","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[23,24,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014073,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[23,24,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[23,24,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0074","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[24,25,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014074,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[24,25,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[24,25,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0075","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-zero-mass-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[25,26,null],\"atom\":2}。請依 [atom,mass,settling_index,ignored,almost_sure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)","explanation_zh":"Wave5根節點核對=(2, 0, null, 是, 是, zero_mass_failure_ignored_only_for_almost_sure_claim)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-zero-mass-boundary","seed":202611014075,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[25,26,null],"atom":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-zero-mass-boundary","semantic_template":"qf-mod32-asconv-zero-mass-boundary/{\"atom\":2,\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[25,26,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0076","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[1,2,null],\"prefix_length\":1}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 1/2, 1, 是, 是], [1, 1/2, 2, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(1, [[0, 1/2, 1, 是, 是], [1, 1/2, 2, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014076,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[1,2,null],"prefix_length":1,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":1,\"settling_indices\":[1,2,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0077","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[2,3,null],\"prefix_length\":2}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 1/2, 2, 是, 是], [1, 1/2, 3, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(2, [[0, 1/2, 2, 是, 是], [1, 1/2, 3, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014077,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[2,3,null],"prefix_length":2,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":2,\"settling_indices\":[2,3,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0078","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[3,4,null],\"prefix_length\":3}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, [[0, 1/2, 3, 是, 是], [1, 1/2, 4, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(3, [[0, 1/2, 3, 是, 是], [1, 1/2, 4, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014078,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[3,4,null],"prefix_length":3,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":3,\"settling_indices\":[3,4,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0079","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[4,5,null],\"prefix_length\":4}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [[0, 1/2, 4, 是, 是], [1, 1/2, 5, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(4, [[0, 1/2, 4, 是, 是], [1, 1/2, 5, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014079,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[4,5,null],"prefix_length":4,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":4,\"settling_indices\":[4,5,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0080","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[5,6,null],\"prefix_length\":5}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1/2, 5, 是, 是], [1, 1/2, 6, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(5, [[0, 1/2, 5, 是, 是], [1, 1/2, 6, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014080,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[5,6,null],"prefix_length":5,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":5,\"settling_indices\":[5,6,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0081","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[6,7,null],\"prefix_length\":6}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(6, [[0, 1/2, 6, 是, 是], [1, 1/2, 7, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(6, [[0, 1/2, 6, 是, 是], [1, 1/2, 7, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014081,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[6,7,null],"prefix_length":6,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":6,\"settling_indices\":[6,7,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0082","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[7,8,null],\"prefix_length\":7}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(7, [[0, 1/2, 7, 是, 是], [1, 1/2, 8, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(7, [[0, 1/2, 7, 是, 是], [1, 1/2, 8, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014082,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[7,8,null],"prefix_length":7,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":7,\"settling_indices\":[7,8,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0083","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[8,9,null],\"prefix_length\":8}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(8, [[0, 1/2, 8, 是, 是], [1, 1/2, 9, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(8, [[0, 1/2, 8, 是, 是], [1, 1/2, 9, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014083,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[8,9,null],"prefix_length":8,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":8,\"settling_indices\":[8,9,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0084","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[9,10,null],\"prefix_length\":9}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(9, [[0, 1/2, 9, 是, 是], [1, 1/2, 10, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(9, [[0, 1/2, 9, 是, 是], [1, 1/2, 10, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014084,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[9,10,null],"prefix_length":9,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":9,\"settling_indices\":[9,10,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0085","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[10,11,null],\"prefix_length\":10}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(10, [[0, 1/2, 10, 是, 是], [1, 1/2, 11, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(10, [[0, 1/2, 10, 是, 是], [1, 1/2, 11, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014085,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[10,11,null],"prefix_length":10,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":10,\"settling_indices\":[10,11,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0086","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[11,12,null],\"prefix_length\":11}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(11, [[0, 1/2, 11, 是, 是], [1, 1/2, 12, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(11, [[0, 1/2, 11, 是, 是], [1, 1/2, 12, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014086,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[11,12,null],"prefix_length":11,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":11,\"settling_indices\":[11,12,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0087","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[12,13,null],\"prefix_length\":12}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(12, [[0, 1/2, 12, 是, 是], [1, 1/2, 13, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(12, [[0, 1/2, 12, 是, 是], [1, 1/2, 13, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014087,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[12,13,null],"prefix_length":12,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":12,\"settling_indices\":[12,13,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0088","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[13,14,null],\"prefix_length\":13}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(13, [[0, 1/2, 13, 是, 是], [1, 1/2, 14, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(13, [[0, 1/2, 13, 是, 是], [1, 1/2, 14, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014088,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[13,14,null],"prefix_length":13,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":13,\"settling_indices\":[13,14,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0089","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[14,15,null],\"prefix_length\":14}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(14, [[0, 1/2, 14, 是, 是], [1, 1/2, 15, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(14, [[0, 1/2, 14, 是, 是], [1, 1/2, 15, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014089,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[14,15,null],"prefix_length":14,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":14,\"settling_indices\":[14,15,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0090","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[15,16,null],\"prefix_length\":15}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(15, [[0, 1/2, 15, 是, 是], [1, 1/2, 16, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(15, [[0, 1/2, 15, 是, 是], [1, 1/2, 16, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014090,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[15,16,null],"prefix_length":15,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":15,\"settling_indices\":[15,16,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0091","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[16,17,null],\"prefix_length\":16}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(16, [[0, 1/2, 16, 是, 是], [1, 1/2, 17, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(16, [[0, 1/2, 16, 是, 是], [1, 1/2, 17, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014091,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[16,17,null],"prefix_length":16,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":16,\"settling_indices\":[16,17,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0092","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[17,18,null],\"prefix_length\":17}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(17, [[0, 1/2, 17, 是, 是], [1, 1/2, 18, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(17, [[0, 1/2, 17, 是, 是], [1, 1/2, 18, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014092,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[17,18,null],"prefix_length":17,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":17,\"settling_indices\":[17,18,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0093","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[18,19,null],\"prefix_length\":18}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(18, [[0, 1/2, 18, 是, 是], [1, 1/2, 19, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(18, [[0, 1/2, 18, 是, 是], [1, 1/2, 19, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014093,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[18,19,null],"prefix_length":18,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":18,\"settling_indices\":[18,19,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0094","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[19,20,null],\"prefix_length\":19}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(19, [[0, 1/2, 19, 是, 是], [1, 1/2, 20, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(19, [[0, 1/2, 19, 是, 是], [1, 1/2, 20, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014094,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[19,20,null],"prefix_length":19,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":19,\"settling_indices\":[19,20,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0095","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[20,21,null],\"prefix_length\":20}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(20, [[0, 1/2, 20, 是, 是], [1, 1/2, 21, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(20, [[0, 1/2, 20, 是, 是], [1, 1/2, 21, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014095,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[20,21,null],"prefix_length":20,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":20,\"settling_indices\":[20,21,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0096","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[21,22,null],\"prefix_length\":21}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(21, [[0, 1/2, 21, 是, 是], [1, 1/2, 22, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(21, [[0, 1/2, 21, 是, 是], [1, 1/2, 22, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014096,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[21,22,null],"prefix_length":21,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":21,\"settling_indices\":[21,22,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0097","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[22,23,null],\"prefix_length\":22}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(22, [[0, 1/2, 22, 是, 是], [1, 1/2, 23, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(22, [[0, 1/2, 22, 是, 是], [1, 1/2, 23, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014097,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[22,23,null],"prefix_length":22,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":22,\"settling_indices\":[22,23,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0098","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[23,24,null],\"prefix_length\":23}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(23, [[0, 1/2, 23, 是, 是], [1, 1/2, 24, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(23, [[0, 1/2, 23, 是, 是], [1, 1/2, 24, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014098,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[23,24,null],"prefix_length":23,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":23,\"settling_indices\":[23,24,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0099","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[24,25,null],\"prefix_length\":24}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(24, [[0, 1/2, 24, 是, 是], [1, 1/2, 25, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(24, [[0, 1/2, 24, 是, 是], [1, 1/2, 25, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014099,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[24,25,null],"prefix_length":24,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":24,\"settling_indices\":[24,25,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r04-almost-sure-convergence-0100","batch_id":"batch-20261014-advance-20261101-r04-almost-sure-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-almost-sure-convergence"],"title_zh":"幾乎必然收斂","stem_zh":"同一完整有限原子機率空間與明示尾端證書。操作=asconv-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2],[0,1]],\"settling_indices\":[25,26,null],\"prefix_length\":25}。請依 [prefix_length,atom_rows,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(25, [[0, 1/2, 25, 是, 是], [1, 1/2, 26, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)","explanation_zh":"Wave5根節點核對=(25, [[0, 1/2, 25, 是, 是], [1, 1/2, 26, 是, 是], [2, 0, null, 否, 是]], 否, finite_prefix_not_almost_sure_convergence_certificate)；依完整明示資料重算；每個正質量原子須收斂；零質量失敗可忽略；有限prefix與依機率收斂本身不足以推出幾乎必然收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["幾乎必然收斂"]},"variant":{"family_id":"qf-mod32-asconv-finite-prefix-boundary","seed":202611014100,"parameters":{"masses":[[1,2],[1,2],[0,1]],"settling_indices":[25,26,null],"prefix_length":25,"domain":"Exact_finite_atomic_almost_sure_tail","operation":"asconv-finite-prefix-boundary","semantic_template":"qf-mod32-asconv-finite-prefix-boundary/{\"masses\":[[1,2],[1,2],[0,1]],\"prefix_length\":25,\"settling_indices\":[25,26,null]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}