{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KGH2JA6RPGYZP5AO4XP7FGENRQ","short_pith_number":"pith:KGH2JA6R","schema_version":"1.0","canonical_sha256":"518fa483d179b197f40ee5dff2988d8c2adb02f4fe9a44ec386b237554d95e5d","source":{"kind":"arxiv","id":"1503.06286","version":2},"attestation_state":"computed","paper":{"title":"Maximizing the order of a regular graph of given valency and second eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Hiroshi Nozaki, Jack H. Koolen, Jason R. Vermette, Sebastian M. Cioab\\u{a}","submitted_at":"2015-03-21T11:13:58Z","abstract_excerpt":"From Alon and Boppana, and Serre, we know that for any given integer $k\\geq 3$ and real number $\\lambda<2\\sqrt{k-1}$, there are finitely many $k$-regular graphs whose second largest eigenvalue is at most $\\lambda$. In this paper, we investigate the largest number of vertices of such graphs."},"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":"1503.06286","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-21T11:13:58Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"fa0c7b47c3826eb68f17879b35f06dba2d521b4938b99a33931a90be3a9ec2a2","abstract_canon_sha256":"c6ef9d733554d62c3586b9d1f83b53d2c795dee3038e1fb01eaf35088b5ad55b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:02.361188Z","signature_b64":"u1hk2/VVQGfHNTc2ZQ2xWgI6Tj39N7tn1GS/rkPrN9Hzy/w1bg8zUa88iCeawVlXfzSMfNg+p6Vy1VxOdAJcDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"518fa483d179b197f40ee5dff2988d8c2adb02f4fe9a44ec386b237554d95e5d","last_reissued_at":"2026-05-18T00:52:02.360554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:02.360554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximizing the order of a regular graph of given valency and second eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Hiroshi Nozaki, Jack H. Koolen, Jason R. Vermette, Sebastian M. Cioab\\u{a}","submitted_at":"2015-03-21T11:13:58Z","abstract_excerpt":"From Alon and Boppana, and Serre, we know that for any given integer $k\\geq 3$ and real number $\\lambda<2\\sqrt{k-1}$, there are finitely many $k$-regular graphs whose second largest eigenvalue is at most $\\lambda$. In this paper, we investigate the largest number of vertices of such graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06286","kind":"arxiv","version":2},"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":"1503.06286","created_at":"2026-05-18T00:52:02.360654+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.06286v2","created_at":"2026-05-18T00:52:02.360654+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06286","created_at":"2026-05-18T00:52:02.360654+00:00"},{"alias_kind":"pith_short_12","alias_value":"KGH2JA6RPGYZ","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"KGH2JA6RPGYZP5AO","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"KGH2JA6R","created_at":"2026-05-18T12:29:27.538025+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/KGH2JA6RPGYZP5AO4XP7FGENRQ","json":"https://pith.science/pith/KGH2JA6RPGYZP5AO4XP7FGENRQ.json","graph_json":"https://pith.science/api/pith-number/KGH2JA6RPGYZP5AO4XP7FGENRQ/graph.json","events_json":"https://pith.science/api/pith-number/KGH2JA6RPGYZP5AO4XP7FGENRQ/events.json","paper":"https://pith.science/paper/KGH2JA6R"},"agent_actions":{"view_html":"https://pith.science/pith/KGH2JA6RPGYZP5AO4XP7FGENRQ","download_json":"https://pith.science/pith/KGH2JA6RPGYZP5AO4XP7FGENRQ.json","view_paper":"https://pith.science/paper/KGH2JA6R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.06286&json=true","fetch_graph":"https://pith.science/api/pith-number/KGH2JA6RPGYZP5AO4XP7FGENRQ/graph.json","fetch_events":"https://pith.science/api/pith-number/KGH2JA6RPGYZP5AO4XP7FGENRQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KGH2JA6RPGYZP5AO4XP7FGENRQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KGH2JA6RPGYZP5AO4XP7FGENRQ/action/storage_attestation","attest_author":"https://pith.science/pith/KGH2JA6RPGYZP5AO4XP7FGENRQ/action/author_attestation","sign_citation":"https://pith.science/pith/KGH2JA6RPGYZP5AO4XP7FGENRQ/action/citation_signature","submit_replication":"https://pith.science/pith/KGH2JA6RPGYZP5AO4XP7FGENRQ/action/replication_record"}},"created_at":"2026-05-18T00:52:02.360654+00:00","updated_at":"2026-05-18T00:52:02.360654+00:00"}