{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OGIXNM2AQ6DWFALTRT3UQMFK25","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5f23a3779542fc9f94a4ab0054d8efacdb5d275390c95111a3d96e15a47b9778","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-15T17:21:35Z","title_canon_sha256":"5cffa236115f7a96befa6ab1ce0e46d566f1c86a75eb3baf2ac4b49278b658f7"},"schema_version":"1.0","source":{"id":"1103.2965","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2965","created_at":"2026-05-18T00:50:36Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2965v2","created_at":"2026-05-18T00:50:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2965","created_at":"2026-05-18T00:50:36Z"},{"alias_kind":"pith_short_12","alias_value":"OGIXNM2AQ6DW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OGIXNM2AQ6DWFALT","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OGIXNM2A","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:29b247fdc06bf5351e57cc77772e4c8c0c584a12d41879e3f1c78288658ee7c0","target":"graph","created_at":"2026-05-18T00:50:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, motivated by the notion of independent identically distributed (IID) random variables under sub-linear expectations initiated by Peng, we investigate a law of the iterated logarithm for capacities. It turns out that our theorem is a natural extension of the Kolmogorov and the Hartman-Wintner laws of the iterated logarithm.","authors_text":"Feng Hu, Zengjing Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-15T17:21:35Z","title":"A law of the iterated logarithm sublinear expectations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2965","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:03741e2e825f53fb2d5dc8584840c190ff341ea2f49167bbf21bf041259adf75","target":"record","created_at":"2026-05-18T00:50:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5f23a3779542fc9f94a4ab0054d8efacdb5d275390c95111a3d96e15a47b9778","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-15T17:21:35Z","title_canon_sha256":"5cffa236115f7a96befa6ab1ce0e46d566f1c86a75eb3baf2ac4b49278b658f7"},"schema_version":"1.0","source":{"id":"1103.2965","kind":"arxiv","version":2}},"canonical_sha256":"719176b34087876281738cf74830aad771573e9ecea7fa8617243d0e79e8c181","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"719176b34087876281738cf74830aad771573e9ecea7fa8617243d0e79e8c181","first_computed_at":"2026-05-18T00:50:36.220149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:36.220149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b04rCA+T+tpiHT8EhA9JjWbMjaE74GuO+ZG3SwhRdxlFRAaPeSvqAMveejJjSIWfnqkXYVUyhsPfXA3VWgZXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:36.220813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2965","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03741e2e825f53fb2d5dc8584840c190ff341ea2f49167bbf21bf041259adf75","sha256:29b247fdc06bf5351e57cc77772e4c8c0c584a12d41879e3f1c78288658ee7c0"],"state_sha256":"b0372f2e40681a9d6edfb9143aca8484f58bc1f95fc014f1380fc9138ca1a0eb"}