{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0001","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[-2,-1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-2, 1/2], [-1, 1/2]], -3/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[-2, 1/2], [-1, 1/2]], -3/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182001,"parameters":{"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[-1,[1,2]],[-2,[1,2]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0002","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[-1,0],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-1, 1/2], [0, 1/2]], -1/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[-1, 1/2], [0, 1/2]], -1/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182002,"parameters":{"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[-1,[1,2]],[0,[1,2]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0003","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[0,1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2], [1, 1/2]], 1/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[0, 1/2], [1, 1/2]], 1/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182003,"parameters":{"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[0,[1,2]],[1,[1,2]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0004","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[1,2],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[1, 1/2], [2, 1/2]], 3/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[1, 1/2], [2, 1/2]], 3/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182004,"parameters":{"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[1,[1,2]],[2,[1,2]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0005","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[2,3],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[2, 1/2], [3, 1/2]], 5/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[2, 1/2], [3, 1/2]], 5/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182005,"parameters":{"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[2,[1,2]],[3,[1,2]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0006","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[-2,-1],\"probabilities\":[[1,3],[2,3]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-2, 1/3], [-1, 2/3]], -4/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[-2, 1/3], [-1, 2/3]], -4/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182006,"parameters":{"values":[-2,-1],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[-1,[2,3]],[-2,[1,3]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0007","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[-1,0],\"probabilities\":[[1,3],[2,3]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-1, 1/3], [0, 2/3]], -1/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[-1, 1/3], [0, 2/3]], -1/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182007,"parameters":{"values":[-1,0],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[-1,[1,3]],[0,[2,3]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0008","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[0,1],\"probabilities\":[[1,3],[2,3]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/3], [1, 2/3]], 2/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[0, 1/3], [1, 2/3]], 2/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182008,"parameters":{"values":[0,1],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[0,[1,3]],[1,[2,3]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0009","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[1,2],\"probabilities\":[[1,3],[2,3]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[1, 1/3], [2, 2/3]], 5/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[1, 1/3], [2, 2/3]], 5/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182009,"parameters":{"values":[1,2],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[1,[1,3]],[2,[2,3]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0010","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[2,3],\"probabilities\":[[1,3],[2,3]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[2, 1/3], [3, 2/3]], 8/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[2, 1/3], [3, 2/3]], 8/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182010,"parameters":{"values":[2,3],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[2,[1,3]],[3,[2,3]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0011","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[-2,-1],\"probabilities\":[[1,4],[3,4]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-2, 1/4], [-1, 3/4]], -5/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[-2, 1/4], [-1, 3/4]], -5/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182011,"parameters":{"values":[-2,-1],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[-1,[3,4]],[-2,[1,4]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0012","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[-1,0],\"probabilities\":[[1,4],[3,4]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-1, 1/4], [0, 3/4]], -1/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[-1, 1/4], [0, 3/4]], -1/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182012,"parameters":{"values":[-1,0],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[-1,[1,4]],[0,[3,4]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0013","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[0,1],\"probabilities\":[[1,4],[3,4]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/4], [1, 3/4]], 3/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[0, 1/4], [1, 3/4]], 3/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182013,"parameters":{"values":[0,1],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[0,[1,4]],[1,[3,4]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0014","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[1,2],\"probabilities\":[[1,4],[3,4]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[1, 1/4], [2, 3/4]], 7/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[1, 1/4], [2, 3/4]], 7/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182014,"parameters":{"values":[1,2],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[1,[1,4]],[2,[3,4]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0015","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[2,3],\"probabilities\":[[1,4],[3,4]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[2, 1/4], [3, 3/4]], 11/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[2, 1/4], [3, 3/4]], 11/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182015,"parameters":{"values":[2,3],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[2,[1,4]],[3,[3,4]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0016","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[-2,-1],\"probabilities\":[[2,5],[3,5]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-2, 2/5], [-1, 3/5]], -7/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[-2, 2/5], [-1, 3/5]], -7/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182016,"parameters":{"values":[-2,-1],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[-1,[3,5]],[-2,[2,5]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0017","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[-1,0],\"probabilities\":[[2,5],[3,5]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-1, 2/5], [0, 3/5]], -2/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[-1, 2/5], [0, 3/5]], -2/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182017,"parameters":{"values":[-1,0],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[-1,[2,5]],[0,[3,5]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0018","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[0,1],\"probabilities\":[[2,5],[3,5]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 2/5], [1, 3/5]], 3/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[0, 2/5], [1, 3/5]], 3/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182018,"parameters":{"values":[0,1],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[0,[2,5]],[1,[3,5]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0019","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[1,2],\"probabilities\":[[2,5],[3,5]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[1, 2/5], [2, 3/5]], 8/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[1, 2/5], [2, 3/5]], 8/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182019,"parameters":{"values":[1,2],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[1,[2,5]],[2,[3,5]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0020","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[2,3],\"probabilities\":[[2,5],[3,5]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[2, 2/5], [3, 3/5]], 13/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[2, 2/5], [3, 3/5]], 13/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182020,"parameters":{"values":[2,3],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[2,[2,5]],[3,[3,5]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0021","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[-2,-1],\"probabilities\":[[1,5],[4,5]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-2, 1/5], [-1, 4/5]], -6/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[-2, 1/5], [-1, 4/5]], -6/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182021,"parameters":{"values":[-2,-1],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[-1,[4,5]],[-2,[1,5]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0022","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[-1,0],\"probabilities\":[[1,5],[4,5]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-1, 1/5], [0, 4/5]], -1/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[-1, 1/5], [0, 4/5]], -1/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182022,"parameters":{"values":[-1,0],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[-1,[1,5]],[0,[4,5]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0023","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[0,1],\"probabilities\":[[1,5],[4,5]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/5], [1, 4/5]], 4/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[0, 1/5], [1, 4/5]], 4/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182023,"parameters":{"values":[0,1],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[0,[1,5]],[1,[4,5]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0024","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[1,2],\"probabilities\":[[1,5],[4,5]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[1, 1/5], [2, 4/5]], 9/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[1, 1/5], [2, 4/5]], 9/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182024,"parameters":{"values":[1,2],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[1,[1,5]],[2,[4,5]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0025","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={\"values\":[2,3],\"probabilities\":[[1,5],[4,5]],\"process_certificate\":\"infinite_iid\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[2, 1/5], [3, 4/5]], 14/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)","explanation_zh":"Wave6第十二層核對=([[2, 1/5], [3, 4/5]], 14/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-process-law-qualification","seed":202611182025,"parameters":{"values":[2,3],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-process-law-qualification","semantic_template":"slln-process-law-qualification|{law:[[2,[1,5]],[3,[4,5]]],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0026","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[-2,-1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"observations\":[-2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-2], -3/2, -2, 1/2, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([-2], -3/2, -2, 1/2, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182026,"parameters":{"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","observations":[-2],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[-1,[1,2]],[-2,[1,2]]],observations:[-2],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0027","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[-1,0],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"observations\":[0,-1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, -1], -1/2, -1/2, 0, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([0, -1], -1/2, -1/2, 0, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182027,"parameters":{"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","observations":[0,-1],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[-1,[1,2]],[0,[1,2]]],observations:[0,-1],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0028","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[0,1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"observations\":[0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0], 1/2, 1/3, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([0, 1, 0], 1/2, 1/3, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182028,"parameters":{"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","observations":[0,1,0],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[0,[1,2]],[1,[1,2]]],observations:[0,1,0],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0029","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[1,2],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"observations\":[2,1,2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 2, 1], 3/2, 3/2, 0, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([2, 1, 2, 1], 3/2, 3/2, 0, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182029,"parameters":{"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","observations":[2,1,2,1],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[1,[1,2]],[2,[1,2]]],observations:[2,1,2,1],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0030","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[2,3],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"observations\":[2,3,2,3,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 2, 3, 2], 5/2, 12/5, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([2, 3, 2, 3, 2], 5/2, 12/5, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182030,"parameters":{"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","observations":[2,3,2,3,2],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[2,[1,2]],[3,[1,2]]],observations:[2,3,2,3,2],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0031","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[-2,-1],\"probabilities\":[[1,3],[2,3]],\"process_certificate\":\"infinite_iid\",\"observations\":[-1,-2,-1,-2,-1,-2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-1, -2, -1, -2, -1, -2], -4/3, -3/2, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([-1, -2, -1, -2, -1, -2], -4/3, -3/2, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182031,"parameters":{"values":[-2,-1],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","observations":[-1,-2,-1,-2,-1,-2],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[-1,[2,3]],[-2,[1,3]]],observations:[-1,-2,-1,-2,-1,-2],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0032","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[-1,0],\"probabilities\":[[1,3],[2,3]],\"process_certificate\":\"infinite_iid\",\"observations\":[-1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-1], -1/3, -1, 2/3, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([-1], -1/3, -1, 2/3, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182032,"parameters":{"values":[-1,0],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","observations":[-1],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[-1,[1,3]],[0,[2,3]]],observations:[-1],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0033","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[0,1],\"probabilities\":[[1,3],[2,3]],\"process_certificate\":\"infinite_iid\",\"observations\":[1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 0], 2/3, 1/2, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([1, 0], 2/3, 1/2, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182033,"parameters":{"values":[0,1],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","observations":[1,0],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[0,[1,3]],[1,[2,3]]],observations:[1,0],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0034","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[1,2],\"probabilities\":[[1,3],[2,3]],\"process_certificate\":\"infinite_iid\",\"observations\":[1,2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 1], 5/3, 4/3, 1/3, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([1, 2, 1], 5/3, 4/3, 1/3, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182034,"parameters":{"values":[1,2],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","observations":[1,2,1],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[1,[1,3]],[2,[2,3]]],observations:[1,2,1],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0035","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[2,3],\"probabilities\":[[1,3],[2,3]],\"process_certificate\":\"infinite_iid\",\"observations\":[3,2,3,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 3, 2], 8/3, 5/2, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([3, 2, 3, 2], 8/3, 5/2, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182035,"parameters":{"values":[2,3],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","observations":[3,2,3,2],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[2,[1,3]],[3,[2,3]]],observations:[3,2,3,2],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0036","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[-2,-1],\"probabilities\":[[1,4],[3,4]],\"process_certificate\":\"infinite_iid\",\"observations\":[-2,-1,-2,-1,-2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-2, -1, -2, -1, -2], -5/4, -8/5, 7/20, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([-2, -1, -2, -1, -2], -5/4, -8/5, 7/20, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182036,"parameters":{"values":[-2,-1],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","observations":[-2,-1,-2,-1,-2],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[-1,[3,4]],[-2,[1,4]]],observations:[-2,-1,-2,-1,-2],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0037","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[-1,0],\"probabilities\":[[1,4],[3,4]],\"process_certificate\":\"infinite_iid\",\"observations\":[0,-1,0,-1,0,-1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, -1, 0, -1, 0, -1], -1/4, -1/2, 1/4, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([0, -1, 0, -1, 0, -1], -1/4, -1/2, 1/4, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182037,"parameters":{"values":[-1,0],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","observations":[0,-1,0,-1,0,-1],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[-1,[1,4]],[0,[3,4]]],observations:[0,-1,0,-1,0,-1],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0038","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[0,1],\"probabilities\":[[1,4],[3,4]],\"process_certificate\":\"infinite_iid\",\"observations\":[0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0], 3/4, 0, 3/4, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([0], 3/4, 0, 3/4, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182038,"parameters":{"values":[0,1],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","observations":[0],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[0,[1,4]],[1,[3,4]]],observations:[0],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0039","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[1,2],\"probabilities\":[[1,4],[3,4]],\"process_certificate\":\"infinite_iid\",\"observations\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 1], 7/4, 3/2, 1/4, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([2, 1], 7/4, 3/2, 1/4, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182039,"parameters":{"values":[1,2],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","observations":[2,1],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[1,[1,4]],[2,[3,4]]],observations:[2,1],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0040","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[2,3],\"probabilities\":[[1,4],[3,4]],\"process_certificate\":\"infinite_iid\",\"observations\":[2,3,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 2], 11/4, 7/3, 5/12, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([2, 3, 2], 11/4, 7/3, 5/12, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182040,"parameters":{"values":[2,3],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","observations":[2,3,2],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[2,[1,4]],[3,[3,4]]],observations:[2,3,2],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0041","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[-2,-1],\"probabilities\":[[2,5],[3,5]],\"process_certificate\":\"infinite_iid\",\"observations\":[-1,-2,-1,-2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-1, -2, -1, -2], -7/5, -3/2, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([-1, -2, -1, -2], -7/5, -3/2, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182041,"parameters":{"values":[-2,-1],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","observations":[-1,-2,-1,-2],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[-1,[3,5]],[-2,[2,5]]],observations:[-1,-2,-1,-2],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0042","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[-1,0],\"probabilities\":[[2,5],[3,5]],\"process_certificate\":\"infinite_iid\",\"observations\":[-1,0,-1,0,-1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-1, 0, -1, 0, -1], -2/5, -3/5, 1/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([-1, 0, -1, 0, -1], -2/5, -3/5, 1/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182042,"parameters":{"values":[-1,0],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","observations":[-1,0,-1,0,-1],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[-1,[2,5]],[0,[3,5]]],observations:[-1,0,-1,0,-1],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0043","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[0,1],\"probabilities\":[[2,5],[3,5]],\"process_certificate\":\"infinite_iid\",\"observations\":[1,0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 1, 0], 3/5, 1/2, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([1, 0, 1, 0, 1, 0], 3/5, 1/2, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182043,"parameters":{"values":[0,1],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","observations":[1,0,1,0,1,0],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[0,[2,5]],[1,[3,5]]],observations:[1,0,1,0,1,0],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0044","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[1,2],\"probabilities\":[[2,5],[3,5]],\"process_certificate\":\"infinite_iid\",\"observations\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], 8/5, 1, 3/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([1], 8/5, 1, 3/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182044,"parameters":{"values":[1,2],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","observations":[1],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[1,[2,5]],[2,[3,5]]],observations:[1],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0045","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[2,3],\"probabilities\":[[2,5],[3,5]],\"process_certificate\":\"infinite_iid\",\"observations\":[3,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3, 2], 13/5, 5/2, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([3, 2], 13/5, 5/2, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182045,"parameters":{"values":[2,3],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","observations":[3,2],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[2,[2,5]],[3,[3,5]]],observations:[3,2],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0046","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[-2,-1],\"probabilities\":[[1,5],[4,5]],\"process_certificate\":\"infinite_iid\",\"observations\":[-2,-1,-2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-2, -1, -2], -6/5, -5/3, 7/15, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([-2, -1, -2], -6/5, -5/3, 7/15, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182046,"parameters":{"values":[-2,-1],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","observations":[-2,-1,-2],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[-1,[4,5]],[-2,[1,5]]],observations:[-2,-1,-2],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0047","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[-1,0],\"probabilities\":[[1,5],[4,5]],\"process_certificate\":\"infinite_iid\",\"observations\":[0,-1,0,-1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, -1, 0, -1], -1/5, -1/2, 3/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([0, -1, 0, -1], -1/5, -1/2, 3/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182047,"parameters":{"values":[-1,0],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","observations":[0,-1,0,-1],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[-1,[1,5]],[0,[4,5]]],observations:[0,-1,0,-1],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0048","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[0,1],\"probabilities\":[[1,5],[4,5]],\"process_certificate\":\"infinite_iid\",\"observations\":[0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0, 1, 0], 4/5, 2/5, 2/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([0, 1, 0, 1, 0], 4/5, 2/5, 2/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182048,"parameters":{"values":[0,1],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","observations":[0,1,0,1,0],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[0,[1,5]],[1,[4,5]]],observations:[0,1,0,1,0],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0049","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[1,2],\"probabilities\":[[1,5],[4,5]],\"process_certificate\":\"infinite_iid\",\"observations\":[2,1,2,1,2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 2, 1, 2, 1], 9/5, 3/2, 3/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([2, 1, 2, 1, 2, 1], 9/5, 3/2, 3/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182049,"parameters":{"values":[1,2],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","observations":[2,1,2,1,2,1],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[1,[1,5]],[2,[4,5]]],observations:[2,1,2,1,2,1],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0050","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={\"values\":[2,3],\"probabilities\":[[1,5],[4,5]],\"process_certificate\":\"infinite_iid\",\"observations\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], 14/5, 2, 4/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)","explanation_zh":"Wave6第十二層核對=([2], 14/5, 2, 4/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-prefix-sample-mean","seed":202611182050,"parameters":{"values":[2,3],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","observations":[2],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-prefix-sample-mean","semantic_template":"slln-prefix-sample-mean|{law:[[2,[1,5]],[3,[4,5]]],observations:[2],process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0051","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[-2,-1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":1,\"epsilon\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, -3/2, 1/3, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(1, -3/2, 1/3, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182051,"parameters":{"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":1,"epsilon":[1,3],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,3],law:[[-1,[1,2]],[-2,[1,2]]],n:1,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0052","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[-1,0],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":1,\"epsilon\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, -1/2, 1/2, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(1, -1/2, 1/2, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182052,"parameters":{"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":1,"epsilon":[2,4],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,2],law:[[-1,[1,2]],[0,[1,2]]],n:1,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0053","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[0,1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":1,\"epsilon\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(1, 1/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182053,"parameters":{"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":1,"epsilon":[3,5],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[3,5],law:[[0,[1,2]],[1,[1,2]]],n:1,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0054","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[1,2],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":1,\"epsilon\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 3/2, 1/3, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(1, 3/2, 1/3, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182054,"parameters":{"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":1,"epsilon":[1,3],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,3],law:[[1,[1,2]],[2,[1,2]]],n:1,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0055","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[2,3],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":1,\"epsilon\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 5/2, 1/2, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(1, 5/2, 1/2, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182055,"parameters":{"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":1,"epsilon":[2,4],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,2],law:[[2,[1,2]],[3,[1,2]]],n:1,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0056","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[-2,-1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":2,\"epsilon\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, -3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(2, -3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182056,"parameters":{"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":2,"epsilon":[3,5],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[3,5],law:[[-1,[1,2]],[-2,[1,2]]],n:2,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0057","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[-1,0],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":2,\"epsilon\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, -1/2, 1/3, 2, 1/2, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(2, -1/2, 1/3, 2, 1/2, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182057,"parameters":{"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":2,"epsilon":[1,3],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,3],law:[[-1,[1,2]],[0,[1,2]]],n:2,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0058","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[0,1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":2,\"epsilon\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 1/2, 1/2, 2, 1/2, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(2, 1/2, 1/2, 2, 1/2, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182058,"parameters":{"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":2,"epsilon":[2,4],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,2],law:[[0,[1,2]],[1,[1,2]]],n:2,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0059","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[1,2],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":2,\"epsilon\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(2, 3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182059,"parameters":{"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":2,"epsilon":[3,5],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[3,5],law:[[1,[1,2]],[2,[1,2]]],n:2,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0060","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[2,3],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":2,\"epsilon\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 5/2, 1/3, 2, 1/2, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(2, 5/2, 1/3, 2, 1/2, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182060,"parameters":{"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":2,"epsilon":[1,3],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,3],law:[[2,[1,2]],[3,[1,2]]],n:2,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0061","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[-2,-1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":3,\"epsilon\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, -3/2, 1/2, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(3, -3/2, 1/2, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182061,"parameters":{"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":3,"epsilon":[2,4],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,2],law:[[-1,[1,2]],[-2,[1,2]]],n:3,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0062","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[-1,0],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":3,\"epsilon\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, -1/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(3, -1/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182062,"parameters":{"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":3,"epsilon":[3,5],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[3,5],law:[[-1,[1,2]],[0,[1,2]]],n:3,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0063","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[0,1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":3,\"epsilon\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 1/2, 1/3, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(3, 1/2, 1/3, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182063,"parameters":{"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":3,"epsilon":[1,3],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,3],law:[[0,[1,2]],[1,[1,2]]],n:3,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0064","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[1,2],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":3,\"epsilon\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 3/2, 1/2, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(3, 3/2, 1/2, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182064,"parameters":{"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":3,"epsilon":[2,4],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,2],law:[[1,[1,2]],[2,[1,2]]],n:3,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0065","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[2,3],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":3,\"epsilon\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 5/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(3, 5/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182065,"parameters":{"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":3,"epsilon":[3,5],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[3,5],law:[[2,[1,2]],[3,[1,2]]],n:3,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0066","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[-2,-1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":4,\"epsilon\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, -3/2, 1/3, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(4, -3/2, 1/3, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182066,"parameters":{"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":4,"epsilon":[1,3],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,3],law:[[-1,[1,2]],[-2,[1,2]]],n:4,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0067","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[-1,0],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":4,\"epsilon\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, -1/2, 1/2, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(4, -1/2, 1/2, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182067,"parameters":{"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":4,"epsilon":[2,4],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,2],law:[[-1,[1,2]],[0,[1,2]]],n:4,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0068","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[0,1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":4,\"epsilon\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 1/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(4, 1/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182068,"parameters":{"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":4,"epsilon":[3,5],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[3,5],law:[[0,[1,2]],[1,[1,2]]],n:4,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0069","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[1,2],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":4,\"epsilon\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 3/2, 1/3, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(4, 3/2, 1/3, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182069,"parameters":{"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":4,"epsilon":[1,3],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,3],law:[[1,[1,2]],[2,[1,2]]],n:4,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0070","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[2,3],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":4,\"epsilon\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 5/2, 1/2, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(4, 5/2, 1/2, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182070,"parameters":{"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":4,"epsilon":[2,4],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,2],law:[[2,[1,2]],[3,[1,2]]],n:4,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0071","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[-2,-1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":5,\"epsilon\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, -3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(5, -3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182071,"parameters":{"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5,"epsilon":[3,5],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[3,5],law:[[-1,[1,2]],[-2,[1,2]]],n:5,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0072","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[-1,0],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":5,\"epsilon\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, -1/2, 1/3, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(5, -1/2, 1/3, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182072,"parameters":{"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5,"epsilon":[1,3],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,3],law:[[-1,[1,2]],[0,[1,2]]],n:5,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0073","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[0,1],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":5,\"epsilon\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 1/2, 1/2, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(5, 1/2, 1/2, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182073,"parameters":{"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5,"epsilon":[2,4],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,2],law:[[0,[1,2]],[1,[1,2]]],n:5,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0074","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[1,2],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":5,\"epsilon\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(5, 3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182074,"parameters":{"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5,"epsilon":[3,5],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[3,5],law:[[1,[1,2]],[2,[1,2]]],n:5,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0075","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={\"values\":[2,3],\"probabilities\":[[1,2],[1,2]],\"process_certificate\":\"infinite_iid\",\"n\":5,\"epsilon\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 5/2, 1/3, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)","explanation_zh":"Wave6第十二層核對=(5, 5/2, 1/3, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-fixed-n-deviation","seed":202611182075,"parameters":{"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5,"epsilon":[1,3],"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-fixed-n-deviation","semantic_template":"slln-fixed-n-deviation|{epsilon:[1,3],law:[[2,[1,2]],[3,[1,2]]],n:5,process_certificate:\"infinite_iid\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0076","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"nonfinite_support\",\"model\":{\"support_kind\":\"countably_infinite\",\"moment_status\":\"integrable\"}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(nonfinite_support, countably_infinite, integrable, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)","explanation_zh":"Wave6第十二層核對=(nonfinite_support, countably_infinite, integrable, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182076,"parameters":{"mode":"nonfinite_support","model":{"support_kind":"countably_infinite","moment_status":"integrable"},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"nonfinite_support\",model:{moment_status:\"integrable\",support_kind:\"countably_infinite\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0077","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"nonfinite_support\",\"model\":{\"support_kind\":\"countably_infinite\",\"moment_status\":\"unknown\"}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(nonfinite_support, countably_infinite, unknown, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)","explanation_zh":"Wave6第十二層核對=(nonfinite_support, countably_infinite, unknown, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182077,"parameters":{"mode":"nonfinite_support","model":{"support_kind":"countably_infinite","moment_status":"unknown"},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"nonfinite_support\",model:{moment_status:\"unknown\",support_kind:\"countably_infinite\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0078","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"nonfinite_support\",\"model\":{\"support_kind\":\"continuous\",\"moment_status\":\"integrable\"}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(nonfinite_support, continuous, integrable, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)","explanation_zh":"Wave6第十二層核對=(nonfinite_support, continuous, integrable, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182078,"parameters":{"mode":"nonfinite_support","model":{"support_kind":"continuous","moment_status":"integrable"},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"nonfinite_support\",model:{moment_status:\"integrable\",support_kind:\"continuous\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0079","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"nonfinite_support\",\"model\":{\"support_kind\":\"continuous\",\"moment_status\":\"unknown\"}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(nonfinite_support, continuous, unknown, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)","explanation_zh":"Wave6第十二層核對=(nonfinite_support, continuous, unknown, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182079,"parameters":{"mode":"nonfinite_support","model":{"support_kind":"continuous","moment_status":"unknown"},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"nonfinite_support\",model:{moment_status:\"unknown\",support_kind:\"continuous\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0080","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"non_iid\",\"model\":{\"values_a\":[2,3],\"probabilities_a\":[[1,2],[1,2]],\"values_b\":[2,3],\"probabilities_b\":[[1,7],[6,7]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)","explanation_zh":"Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182080,"parameters":{"mode":"non_iid","model":{"values_a":[2,3],"probabilities_a":[[1,2],[1,2]],"values_b":[2,3],"probabilities_b":[[1,7],[6,7]]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"non_iid\",model:{law_a:[[2,[1,2]],[3,[1,2]]],law_b:[[2,[1,7]],[3,[6,7]]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0081","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"finite_prefix\",\"model\":{\"values\":[-2,-1],\"probabilities\":[[1,3],[2,3]],\"observations\":[-2,-1,-1]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_prefix, [-2, -1, -1], -4/3, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)","explanation_zh":"Wave6第十二層核對=(finite_prefix, [-2, -1, -1], -4/3, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182081,"parameters":{"mode":"finite_prefix","model":{"values":[-2,-1],"probabilities":[[1,3],[2,3]],"observations":[-2,-1,-1]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"finite_prefix\",model:{law:[[-1,[2,3]],[-2,[1,3]]],observations:[-2,-1,-1]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0082","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"wrong_target\",\"model\":{\"values\":[-1,0],\"probabilities\":[[1,3],[2,3]],\"target\":8}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(wrong_target, -1/3, 8, 否, 否, SLLN_target_is_common_expectation)","explanation_zh":"Wave6第十二層核對=(wrong_target, -1/3, 8, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182082,"parameters":{"mode":"wrong_target","model":{"values":[-1,0],"probabilities":[[1,3],[2,3]],"target":8},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"wrong_target\",model:{law:[[-1,[1,3]],[0,[2,3]]],target:[8,1]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0083","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"non_iid\",\"model\":{\"values_a\":[0,1],\"probabilities_a\":[[1,3],[2,3]],\"values_b\":[0,1],\"probabilities_b\":[[1,7],[6,7]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)","explanation_zh":"Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182083,"parameters":{"mode":"non_iid","model":{"values_a":[0,1],"probabilities_a":[[1,3],[2,3]],"values_b":[0,1],"probabilities_b":[[1,7],[6,7]]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"non_iid\",model:{law_a:[[0,[1,3]],[1,[2,3]]],law_b:[[0,[1,7]],[1,[6,7]]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0084","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"finite_prefix\",\"model\":{\"values\":[1,2],\"probabilities\":[[1,3],[2,3]],\"observations\":[1,2,1]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_prefix, [1, 2, 1], 5/3, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)","explanation_zh":"Wave6第十二層核對=(finite_prefix, [1, 2, 1], 5/3, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182084,"parameters":{"mode":"finite_prefix","model":{"values":[1,2],"probabilities":[[1,3],[2,3]],"observations":[1,2,1]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"finite_prefix\",model:{law:[[1,[1,3]],[2,[2,3]]],observations:[1,2,1]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0085","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"wrong_target\",\"model\":{\"values\":[2,3],\"probabilities\":[[1,3],[2,3]],\"target\":11}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(wrong_target, 8/3, 11, 否, 否, SLLN_target_is_common_expectation)","explanation_zh":"Wave6第十二層核對=(wrong_target, 8/3, 11, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182085,"parameters":{"mode":"wrong_target","model":{"values":[2,3],"probabilities":[[1,3],[2,3]],"target":11},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"wrong_target\",model:{law:[[2,[1,3]],[3,[2,3]]],target:[11,1]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0086","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"non_iid\",\"model\":{\"values_a\":[-2,-1],\"probabilities_a\":[[1,4],[3,4]],\"values_b\":[-2,-1],\"probabilities_b\":[[1,7],[6,7]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)","explanation_zh":"Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182086,"parameters":{"mode":"non_iid","model":{"values_a":[-2,-1],"probabilities_a":[[1,4],[3,4]],"values_b":[-2,-1],"probabilities_b":[[1,7],[6,7]]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"non_iid\",model:{law_a:[[-1,[3,4]],[-2,[1,4]]],law_b:[[-1,[6,7]],[-2,[1,7]]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0087","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"finite_prefix\",\"model\":{\"values\":[-1,0],\"probabilities\":[[1,4],[3,4]],\"observations\":[-1,0,0]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_prefix, [-1, 0, 0], -1/4, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)","explanation_zh":"Wave6第十二層核對=(finite_prefix, [-1, 0, 0], -1/4, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182087,"parameters":{"mode":"finite_prefix","model":{"values":[-1,0],"probabilities":[[1,4],[3,4]],"observations":[-1,0,0]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"finite_prefix\",model:{law:[[-1,[1,4]],[0,[3,4]]],observations:[-1,0,0]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0088","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"wrong_target\",\"model\":{\"values\":[0,1],\"probabilities\":[[1,4],[3,4]],\"target\":14}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(wrong_target, 3/4, 14, 否, 否, SLLN_target_is_common_expectation)","explanation_zh":"Wave6第十二層核對=(wrong_target, 3/4, 14, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182088,"parameters":{"mode":"wrong_target","model":{"values":[0,1],"probabilities":[[1,4],[3,4]],"target":14},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"wrong_target\",model:{law:[[0,[1,4]],[1,[3,4]]],target:[14,1]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0089","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"non_iid\",\"model\":{\"values_a\":[1,2],\"probabilities_a\":[[1,4],[3,4]],\"values_b\":[1,2],\"probabilities_b\":[[1,7],[6,7]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)","explanation_zh":"Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182089,"parameters":{"mode":"non_iid","model":{"values_a":[1,2],"probabilities_a":[[1,4],[3,4]],"values_b":[1,2],"probabilities_b":[[1,7],[6,7]]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"non_iid\",model:{law_a:[[1,[1,4]],[2,[3,4]]],law_b:[[1,[1,7]],[2,[6,7]]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0090","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"finite_prefix\",\"model\":{\"values\":[2,3],\"probabilities\":[[1,4],[3,4]],\"observations\":[2,3,2]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_prefix, [2, 3, 2], 11/4, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)","explanation_zh":"Wave6第十二層核對=(finite_prefix, [2, 3, 2], 11/4, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182090,"parameters":{"mode":"finite_prefix","model":{"values":[2,3],"probabilities":[[1,4],[3,4]],"observations":[2,3,2]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"finite_prefix\",model:{law:[[2,[1,4]],[3,[3,4]]],observations:[2,3,2]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0091","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"wrong_target\",\"model\":{\"values\":[-2,-1],\"probabilities\":[[2,5],[3,5]],\"target\":17}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(wrong_target, -7/5, 17, 否, 否, SLLN_target_is_common_expectation)","explanation_zh":"Wave6第十二層核對=(wrong_target, -7/5, 17, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182091,"parameters":{"mode":"wrong_target","model":{"values":[-2,-1],"probabilities":[[2,5],[3,5]],"target":17},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"wrong_target\",model:{law:[[-1,[3,5]],[-2,[2,5]]],target:[17,1]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0092","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"non_iid\",\"model\":{\"values_a\":[-1,0],\"probabilities_a\":[[2,5],[3,5]],\"values_b\":[-1,0],\"probabilities_b\":[[1,7],[6,7]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)","explanation_zh":"Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182092,"parameters":{"mode":"non_iid","model":{"values_a":[-1,0],"probabilities_a":[[2,5],[3,5]],"values_b":[-1,0],"probabilities_b":[[1,7],[6,7]]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"non_iid\",model:{law_a:[[-1,[2,5]],[0,[3,5]]],law_b:[[-1,[1,7]],[0,[6,7]]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0093","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"finite_prefix\",\"model\":{\"values\":[0,1],\"probabilities\":[[2,5],[3,5]],\"observations\":[0,1,1]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_prefix, [0, 1, 1], 3/5, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)","explanation_zh":"Wave6第十二層核對=(finite_prefix, [0, 1, 1], 3/5, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182093,"parameters":{"mode":"finite_prefix","model":{"values":[0,1],"probabilities":[[2,5],[3,5]],"observations":[0,1,1]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"finite_prefix\",model:{law:[[0,[2,5]],[1,[3,5]]],observations:[0,1,1]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0094","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"wrong_target\",\"model\":{\"values\":[1,2],\"probabilities\":[[2,5],[3,5]],\"target\":20}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(wrong_target, 8/5, 20, 否, 否, SLLN_target_is_common_expectation)","explanation_zh":"Wave6第十二層核對=(wrong_target, 8/5, 20, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182094,"parameters":{"mode":"wrong_target","model":{"values":[1,2],"probabilities":[[2,5],[3,5]],"target":20},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"wrong_target\",model:{law:[[1,[2,5]],[2,[3,5]]],target:[20,1]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0095","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"non_iid\",\"model\":{\"values_a\":[2,3],\"probabilities_a\":[[2,5],[3,5]],\"values_b\":[2,3],\"probabilities_b\":[[1,7],[6,7]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)","explanation_zh":"Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182095,"parameters":{"mode":"non_iid","model":{"values_a":[2,3],"probabilities_a":[[2,5],[3,5]],"values_b":[2,3],"probabilities_b":[[1,7],[6,7]]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"non_iid\",model:{law_a:[[2,[2,5]],[3,[3,5]]],law_b:[[2,[1,7]],[3,[6,7]]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0096","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"finite_prefix\",\"model\":{\"values\":[-2,-1],\"probabilities\":[[1,5],[4,5]],\"observations\":[-2,-1,-2]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_prefix, [-2, -1, -2], -6/5, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)","explanation_zh":"Wave6第十二層核對=(finite_prefix, [-2, -1, -2], -6/5, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182096,"parameters":{"mode":"finite_prefix","model":{"values":[-2,-1],"probabilities":[[1,5],[4,5]],"observations":[-2,-1,-2]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"finite_prefix\",model:{law:[[-1,[4,5]],[-2,[1,5]]],observations:[-2,-1,-2]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0097","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"wrong_target\",\"model\":{\"values\":[-1,0],\"probabilities\":[[1,5],[4,5]],\"target\":23}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(wrong_target, -1/5, 23, 否, 否, SLLN_target_is_common_expectation)","explanation_zh":"Wave6第十二層核對=(wrong_target, -1/5, 23, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182097,"parameters":{"mode":"wrong_target","model":{"values":[-1,0],"probabilities":[[1,5],[4,5]],"target":23},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"wrong_target\",model:{law:[[-1,[1,5]],[0,[4,5]]],target:[23,1]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0098","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"non_iid\",\"model\":{\"values_a\":[0,1],\"probabilities_a\":[[1,5],[4,5]],\"values_b\":[0,1],\"probabilities_b\":[[1,7],[6,7]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)","explanation_zh":"Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182098,"parameters":{"mode":"non_iid","model":{"values_a":[0,1],"probabilities_a":[[1,5],[4,5]],"values_b":[0,1],"probabilities_b":[[1,7],[6,7]]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"non_iid\",model:{law_a:[[0,[1,5]],[1,[4,5]]],law_b:[[0,[1,7]],[1,[6,7]]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0099","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"finite_prefix\",\"model\":{\"values\":[1,2],\"probabilities\":[[1,5],[4,5]],\"observations\":[1,2,2]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_prefix, [1, 2, 2], 9/5, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)","explanation_zh":"Wave6第十二層核對=(finite_prefix, [1, 2, 2], 9/5, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182099,"parameters":{"mode":"finite_prefix","model":{"values":[1,2],"probabilities":[[1,5],[4,5]],"observations":[1,2,2]},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"finite_prefix\",model:{law:[[1,[1,5]],[2,[4,5]]],observations:[1,2,2]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0100","batch_id":"batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations","language":"zh-Hant","source_mko_ids":["mko-strong-law-large-numbers-finite-valued-iid"],"title_zh":"有限值IID強大數律","stem_zh":"無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"wrong_target\",\"model\":{\"values\":[2,3],\"probabilities\":[[1,5],[4,5]],\"target\":26}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(wrong_target, 14/5, 26, 否, 否, SLLN_target_is_common_expectation)","explanation_zh":"Wave6第十二層核對=(wrong_target, 14/5, 26, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限值IID強大數律"]},"variant":{"family_id":"qf-mod49-slln-scope-boundary","seed":202611182100,"parameters":{"mode":"wrong_target","model":{"values":[2,3],"probabilities":[[1,5],[4,5]],"target":26},"domain":"Exact_finite_valued_SLLN_boundary","operation":"slln-scope-boundary","semantic_template":"slln-scope-boundary|{mode:\"wrong_target\",model:{law:[[2,[1,5]],[3,[4,5]]],target:[26,1]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}