{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:SI3QYI3UTGRLISVO5GUVNH73QI","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":"5d9e5bf4ea29d4902505f327a22cf3ea24151402297ecab055c5ae2e9c78fa8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-08T09:19:32Z","title_canon_sha256":"626d45ce8daac2003ac726b259783e82175367f229e143be360bae63386418f1"},"schema_version":"1.0","source":{"id":"2310.05085","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.05085","created_at":"2026-07-05T07:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"2310.05085v3","created_at":"2026-07-05T07:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.05085","created_at":"2026-07-05T07:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"SI3QYI3UTGRL","created_at":"2026-07-05T07:25:25Z"},{"alias_kind":"pith_short_16","alias_value":"SI3QYI3UTGRLISVO","created_at":"2026-07-05T07:25:25Z"},{"alias_kind":"pith_short_8","alias_value":"SI3QYI3U","created_at":"2026-07-05T07:25:25Z"}],"graph_snapshots":[{"event_id":"sha256:fcc17617d35c7e2a210a3b7b90318ea22b3e03d6ec23fe0b3f6192e83182cc88","target":"graph","created_at":"2026-07-05T07:25:25Z","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/2310.05085/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let ${\\rm ex}(n,F)$ and ${\\rm spex}(n,F)$ be the maximum size and maximum spectral radius of an $F$-free graph of order $n$, respectively. The value ${\\rm spex}(n,F)$ is called the spectral extremal value of $F$. Nikiforov [J. Graph Theory 62 (2009) 362--368] gave the spectral Stability Lemma, which implies that for every $\\varepsilon>0$, sufficiently large $n$ and a non-bipartite graph $H$ with chromatic number $\\chi(H)$, the extremal graph for ${\\rm spex}(n,H)$ can be obtained from the Tur\\'{a}n graph $T_{\\chi(H)-1}(n)$ by adding and deleting at most $\\varepsilon n^2$ edges. It is still a ch","authors_text":"Huiqiu Lin, Longfei Fang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-08T09:19:32Z","title":"Spectral extremal results on edge blow-up of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.05085","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":"sha256:23eba0fc08257606a6c71588ad07451749c9747f7f78d05fd7b93040261138de","target":"record","created_at":"2026-07-05T07:25:25Z","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":"5d9e5bf4ea29d4902505f327a22cf3ea24151402297ecab055c5ae2e9c78fa8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-08T09:19:32Z","title_canon_sha256":"626d45ce8daac2003ac726b259783e82175367f229e143be360bae63386418f1"},"schema_version":"1.0","source":{"id":"2310.05085","kind":"arxiv","version":3}},"canonical_sha256":"92370c237499a2b44aaee9a9569ffb82379ae5c0178e33478359d449cf70eb68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92370c237499a2b44aaee9a9569ffb82379ae5c0178e33478359d449cf70eb68","first_computed_at":"2026-07-05T07:25:25.492602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:25:25.492602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yj/1zvoIgL+m1OskxfA0tg+mrrfHstYvPASdHlIGFJwDSRoGmwJGKcotkRIMUw7wHc/BkE1bOacR58pDhPizAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:25:25.493019Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.05085","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23eba0fc08257606a6c71588ad07451749c9747f7f78d05fd7b93040261138de","sha256:fcc17617d35c7e2a210a3b7b90318ea22b3e03d6ec23fe0b3f6192e83182cc88"],"state_sha256":"5621295391c68f1d919bb7a0881091abcd1f9ce2078ecc1ca46c0a1f5b6307d0"}