{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GHCFPCTESV4PXPL7YX6PNFNU4A","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":"e95def9e95e2b613d343d6ba0a05eaa79cab2b74c2dc680a8aee8afff05cff16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-01T18:09:19Z","title_canon_sha256":"c11fd6289c8e5fc77928a6543942453858ed1ce77da80883a3e1285634fa5cf9"},"schema_version":"1.0","source":{"id":"1806.00493","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00493","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00493v1","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00493","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"GHCFPCTESV4P","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GHCFPCTESV4PXPL7","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GHCFPCTE","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:d6afcffdd4beeafb28ece71527f1094277c921c5528aec272cfd969d3e7fccef","target":"graph","created_at":"2026-05-18T00:14:21Z","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":"We prove that, for any $t\\ge 3$, there exists a constant $c=c(t)>0$ such that any $d$-regular $n$-vertex graph with the second largest eigenvalue in absolute value~$\\lambda$ satisfying $\\lambda\\le c d^{t-1}/n^{t-2}$ contains vertex-disjoint copies of $K_t$ covering all but at most $n^{1-1/(8t^4)}$ vertices. This provides further support for the conjecture of Krivelevich, Sudakov and Sz\\'abo [\\emph{Triangle factors in sparse pseudo-random graphs}, Combinatorica \\textbf{24} (2004), pp.~403--426] that $(n,d,\\lambda)$-graphs with $n\\in 3\\mathbb{N}$ and $\\lambda\\leq cd^{2}/n$ for a suitably small a","authors_text":"Jie Han, Yoshiharu Kohayakawa, Yury Person","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-01T18:09:19Z","title":"Near-perfect clique-factors in sparse pseudorandom graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00493","kind":"arxiv","version":1},"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":"sha256:031991b7047740ef74cc4234636d58ebef13925739672175050131649a134781","target":"record","created_at":"2026-05-18T00:14:21Z","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":"e95def9e95e2b613d343d6ba0a05eaa79cab2b74c2dc680a8aee8afff05cff16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-01T18:09:19Z","title_canon_sha256":"c11fd6289c8e5fc77928a6543942453858ed1ce77da80883a3e1285634fa5cf9"},"schema_version":"1.0","source":{"id":"1806.00493","kind":"arxiv","version":1}},"canonical_sha256":"31c4578a649578fbbd7fc5fcf695b4e0278ad5af12c6b48362996231a6ab9afc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31c4578a649578fbbd7fc5fcf695b4e0278ad5af12c6b48362996231a6ab9afc","first_computed_at":"2026-05-18T00:14:21.075455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:21.075455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ib9AdpR9B2WOvg6qD1e3SVob8oAE+IQJ0u1N8HYIjtG3JossbNA6oT5Ky8S5qAZ6VKKecAESODW2M+m2TkevCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:21.076149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.00493","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:031991b7047740ef74cc4234636d58ebef13925739672175050131649a134781","sha256:d6afcffdd4beeafb28ece71527f1094277c921c5528aec272cfd969d3e7fccef"],"state_sha256":"c2e0c436cfc88207c874276987fc926622d69456fdbaab755642b52410072d89"}