{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4MH5T47TJN2SG5EWYX5E2WPIT7","short_pith_number":"pith:4MH5T47T","schema_version":"1.0","canonical_sha256":"e30fd9f3f34b75237496c5fa4d59e89fe3e60350afb0253e5b224696c95afc31","source":{"kind":"arxiv","id":"1407.4285","version":1},"attestation_state":"computed","paper":{"title":"Spectral radius minus average degree: a better bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Felix Goldberg","submitted_at":"2014-07-16T12:44:34Z","abstract_excerpt":"Collatz and Sinogowitz had proposed to measure the departure of a graph $G$ from regularity by the difference of the (adjacency) spectral radius and the average degree: $\\epsilon(G)=\\rho(G)-\\frac{2m}{n}$. We give here new lower bounds on this quantity, which improve upon the currently known ones."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.4285","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-16T12:44:34Z","cross_cats_sorted":[],"title_canon_sha256":"ed28005831de57fbc15989c82f9869381d6b8513e781af41cf7f6541f3bdac0d","abstract_canon_sha256":"6470120dc15f6e9ae3d57c6449375c685f48a35af7ba2165a08456aa0ee92f95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:30.751848Z","signature_b64":"Q6POmVSlRUQOHFxOAwynx7c8fPmXVs55tPMYMQWS1b0UnMxC5zIbZXBHMavxnGRWKtrVcfwBtxu4nuHswq/qDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e30fd9f3f34b75237496c5fa4d59e89fe3e60350afb0253e5b224696c95afc31","last_reissued_at":"2026-05-18T02:47:30.751330Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:30.751330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral radius minus average degree: a better bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Felix Goldberg","submitted_at":"2014-07-16T12:44:34Z","abstract_excerpt":"Collatz and Sinogowitz had proposed to measure the departure of a graph $G$ from regularity by the difference of the (adjacency) spectral radius and the average degree: $\\epsilon(G)=\\rho(G)-\\frac{2m}{n}$. We give here new lower bounds on this quantity, which improve upon the currently known ones."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4285","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.4285","created_at":"2026-05-18T02:47:30.751393+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.4285v1","created_at":"2026-05-18T02:47:30.751393+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4285","created_at":"2026-05-18T02:47:30.751393+00:00"},{"alias_kind":"pith_short_12","alias_value":"4MH5T47TJN2S","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4MH5T47TJN2SG5EW","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4MH5T47T","created_at":"2026-05-18T12:28:14.216126+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4MH5T47TJN2SG5EWYX5E2WPIT7","json":"https://pith.science/pith/4MH5T47TJN2SG5EWYX5E2WPIT7.json","graph_json":"https://pith.science/api/pith-number/4MH5T47TJN2SG5EWYX5E2WPIT7/graph.json","events_json":"https://pith.science/api/pith-number/4MH5T47TJN2SG5EWYX5E2WPIT7/events.json","paper":"https://pith.science/paper/4MH5T47T"},"agent_actions":{"view_html":"https://pith.science/pith/4MH5T47TJN2SG5EWYX5E2WPIT7","download_json":"https://pith.science/pith/4MH5T47TJN2SG5EWYX5E2WPIT7.json","view_paper":"https://pith.science/paper/4MH5T47T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.4285&json=true","fetch_graph":"https://pith.science/api/pith-number/4MH5T47TJN2SG5EWYX5E2WPIT7/graph.json","fetch_events":"https://pith.science/api/pith-number/4MH5T47TJN2SG5EWYX5E2WPIT7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4MH5T47TJN2SG5EWYX5E2WPIT7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4MH5T47TJN2SG5EWYX5E2WPIT7/action/storage_attestation","attest_author":"https://pith.science/pith/4MH5T47TJN2SG5EWYX5E2WPIT7/action/author_attestation","sign_citation":"https://pith.science/pith/4MH5T47TJN2SG5EWYX5E2WPIT7/action/citation_signature","submit_replication":"https://pith.science/pith/4MH5T47TJN2SG5EWYX5E2WPIT7/action/replication_record"}},"created_at":"2026-05-18T02:47:30.751393+00:00","updated_at":"2026-05-18T02:47:30.751393+00:00"}