{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DWKSGLWIUDSESNVFA6CWQCAY4J","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":"4134764aa6bf4e815a5efd2b78d9c96c440c7040327b9267ea68cbb45150ffe7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-18T00:28:22Z","title_canon_sha256":"39d2b82155c3dccfc9532c773c91799fb2f40f406a3b961f9196755f4f9287fb"},"schema_version":"1.0","source":{"id":"1003.3498","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3498","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3498v3","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3498","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"DWKSGLWIUDSE","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DWKSGLWIUDSESNVF","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DWKSGLWI","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:50dc7bb72825547191e4c932b9b6a07a0296be96ce211c7956938fc9e793eb33","target":"graph","created_at":"2026-05-18T04:24:36Z","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":"This paper solves the problem of sharp large deviation estimates for the upper tail of the number of triangles in an Erdos-Renyi random graph, by establishing a logarithmic factor in the exponent that was missing till now. It is possible that the method of proof may extend to general subgraph counts.","authors_text":"Sourav Chatterjee","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-18T00:28:22Z","title":"The missing log in large deviations for triangle counts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3498","kind":"arxiv","version":3},"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:e1dc7d04c5d091109a265958b503256f9808a94218ce9c9d7987f98e346d7d64","target":"record","created_at":"2026-05-18T04:24:36Z","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":"4134764aa6bf4e815a5efd2b78d9c96c440c7040327b9267ea68cbb45150ffe7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-18T00:28:22Z","title_canon_sha256":"39d2b82155c3dccfc9532c773c91799fb2f40f406a3b961f9196755f4f9287fb"},"schema_version":"1.0","source":{"id":"1003.3498","kind":"arxiv","version":3}},"canonical_sha256":"1d95232ec8a0e44936a50785680818e27e045c2981fc599531a554ddd7d78f72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d95232ec8a0e44936a50785680818e27e045c2981fc599531a554ddd7d78f72","first_computed_at":"2026-05-18T04:24:36.321531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:36.321531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uq2pBu5YS+kldexJDSKycclXwfm5VADOa7HR1RWIBnBdr63M/WnaE64SCmA3YoANBCNDabcqX4Icp38tDIkjDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:36.321998Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.3498","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1dc7d04c5d091109a265958b503256f9808a94218ce9c9d7987f98e346d7d64","sha256:50dc7bb72825547191e4c932b9b6a07a0296be96ce211c7956938fc9e793eb33"],"state_sha256":"af40874cf9d83ce2f31250ecb06705d35425b0a169a1a9abe44b3c3862ccaaab"}