{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YW7JDDMPSPE44UH74HK57DGOFX","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":"ec8f7ca536e15fac3ed4e10ff50185ed30127aee55a01226c21a6e02309a6c61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-20T01:57:10Z","title_canon_sha256":"985dcce09e9c92d7aea450be0bc6dfe88df351c564c578a30681a153824c7dac"},"schema_version":"1.0","source":{"id":"1310.5292","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5292","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5292v1","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5292","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"YW7JDDMPSPE4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YW7JDDMPSPE44UH7","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YW7JDDMP","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:a7a73e87bf346b0795fcd20efd4097922c2c4dc013f90bbef858702874d72ac4","target":"graph","created_at":"2026-05-18T03:09:46Z","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"},"paper":{"abstract_excerpt":"In this paper, we give upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and characterize the equality cases. These bounds theoretically improve and generalize some known results of Duan et al.[X. Duan, B. Zhou, Sharp bounds on the spectral radius of a nonnegative matrix, Linear Algebra Appl. (2013), http://dx.doi.org/10.1016/j.laa.2013.08.026]. Finally, applying these bounds to various matrices associated with a graph, we obtain some new upper and lower bounds on various spectral radiuses of graphs, which generalize and improve some known results.","authors_text":"Gui-Xian Tian, Shu-Yu Cui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-20T01:57:10Z","title":"Bounds on the spectral radius of nonnegative matrices and applications in graph spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5292","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":"sha256:9044efa6926b59340ad0edc3bf97ff03318e5c59bb40db2af4eca50897844991","target":"record","created_at":"2026-05-18T03:09:46Z","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":"ec8f7ca536e15fac3ed4e10ff50185ed30127aee55a01226c21a6e02309a6c61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-20T01:57:10Z","title_canon_sha256":"985dcce09e9c92d7aea450be0bc6dfe88df351c564c578a30681a153824c7dac"},"schema_version":"1.0","source":{"id":"1310.5292","kind":"arxiv","version":1}},"canonical_sha256":"c5be918d8f93c9ce50ffe1d5df8cce2df012b361f43fbbb48a4ac61da2f014ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5be918d8f93c9ce50ffe1d5df8cce2df012b361f43fbbb48a4ac61da2f014ee","first_computed_at":"2026-05-18T03:09:46.051419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:46.051419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eoE73ZGkWrEdDI79ZEB6QZ1TSlJqREBAG+Iu2PgTUKetJq34v8aMyzrDO+L+X0ZDJM/3pwxZqqCHNn7zEK78Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:46.052291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5292","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9044efa6926b59340ad0edc3bf97ff03318e5c59bb40db2af4eca50897844991","sha256:a7a73e87bf346b0795fcd20efd4097922c2c4dc013f90bbef858702874d72ac4"],"state_sha256":"5823699eff57133bb58346006752ca9a6aee76ba0139b64dec1b8298a42bf615"}