{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2P7QWK5ZFK3ZWEDC3XX44ECORL","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":"c024425a68e578dfe105def349b041dc5b7d8c8364d322f9e961db9df9896734","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-02-01T16:07:27Z","title_canon_sha256":"0ca4aebc92c03a8a87dfa883cadb9e0d475900c91cf27990225db9d6199883f7"},"schema_version":"1.0","source":{"id":"2402.00713","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.00713","created_at":"2026-07-05T09:23:46Z"},{"alias_kind":"arxiv_version","alias_value":"2402.00713v2","created_at":"2026-07-05T09:23:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.00713","created_at":"2026-07-05T09:23:46Z"},{"alias_kind":"pith_short_12","alias_value":"2P7QWK5ZFK3Z","created_at":"2026-07-05T09:23:46Z"},{"alias_kind":"pith_short_16","alias_value":"2P7QWK5ZFK3ZWEDC","created_at":"2026-07-05T09:23:46Z"},{"alias_kind":"pith_short_8","alias_value":"2P7QWK5Z","created_at":"2026-07-05T09:23:46Z"}],"graph_snapshots":[{"event_id":"sha256:523f9f7e1637e5fa4a4d11997acaa376b14ac780ec81281acf84253d4be0ab46","target":"graph","created_at":"2026-07-05T09:23:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2402.00713/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We revisit the question of whether the strong law of large numbers (SLLN) holds uniformly in a rich family of distributions, culminating in a distribution-uniform generalization of the Marcinkiewicz-Zygmund SLLN. These results can be viewed as extensions of Chung's distribution-uniform SLLN to random variables with uniformly integrable $q^\\text{th}$ absolute central moments for $0 < q < 2$. Furthermore, we show that uniform integrability of the $q^\\text{th}$ moment is both sufficient and necessary for the SLLN to hold uniformly at the Marcinkiewicz-Zygmund rate of $n^{1/q - 1}$. These proofs c","authors_text":"Aaditya Ramdas, Ian Waudby-Smith, Martin Larsson","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-02-01T16:07:27Z","title":"Distribution-uniform strong laws of large numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.00713","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":"sha256:7a2a71dcb5e878bfe5ae69d42b08dc5da3daeb983cfcfc4efe734a05cdf13879","target":"record","created_at":"2026-07-05T09:23:46Z","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":"c024425a68e578dfe105def349b041dc5b7d8c8364d322f9e961db9df9896734","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-02-01T16:07:27Z","title_canon_sha256":"0ca4aebc92c03a8a87dfa883cadb9e0d475900c91cf27990225db9d6199883f7"},"schema_version":"1.0","source":{"id":"2402.00713","kind":"arxiv","version":2}},"canonical_sha256":"d3ff0b2bb92ab79b1062ddefce104e8afbec35ff78a43a4160a7f6c906725645","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3ff0b2bb92ab79b1062ddefce104e8afbec35ff78a43a4160a7f6c906725645","first_computed_at":"2026-07-05T09:23:46.792455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:23:46.792455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dNr4tlsA+J7Lkb/bzledIAAk1+TS66wzNQeT/hym2KPlc0bj2GMsaSpFG45u7xeDa//w+8fWidn1pUhdtLdFDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:23:46.792952Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.00713","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a2a71dcb5e878bfe5ae69d42b08dc5da3daeb983cfcfc4efe734a05cdf13879","sha256:523f9f7e1637e5fa4a4d11997acaa376b14ac780ec81281acf84253d4be0ab46"],"state_sha256":"7b3d546dcd2c5f720dad36da5b4b8844b8fee85e826705ff8829c851d115a7ef"}