{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:S4TLP5HRIBGHDIVTLNGGD5RQ2Y","short_pith_number":"pith:S4TLP5HR","schema_version":"1.0","canonical_sha256":"9726b7f4f1404c71a2b35b4c61f630d638f549fea65ba19ebcd65635500b5657","source":{"kind":"arxiv","id":"1402.0620","version":1},"attestation_state":"computed","paper":{"title":"Almost-Ramanujan Graphs and Prime Gaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Adrian Dudek","submitted_at":"2014-02-04T05:37:01Z","abstract_excerpt":"The method of Murty and Cioab\\u{a} shows how one can use results about gaps between primes to construct families of almost-Ramanujan graphs. In this paper we give a simpler construction which avoids the search for perfect matchings and thus eliminates the need for computation. A couple of recent explicit bounds on the gap between consecutive primes are then used to give the construction of $k$-regular families with explicit lower bounds on the spectral gaps. We then show that a result of Ben-Aroya and Ta-Shma can be improved using our simpler construction on the assumption of the Riemann Hypot"},"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":"1402.0620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-04T05:37:01Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4f8a3bb686a5d75090ba0798015ba19452878094067821663ffdf445cc2ce2da","abstract_canon_sha256":"06b083c46b1e21bd438f40a54d61d3a06ea1c7034362b6a5d94bc998a57e66f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:13.516044Z","signature_b64":"2mlh4UQRTbD2OdACGcS0TdCsgZQ6/8Lx9Mvsxb2BtyklA0r7pyru0rWQ5wZF4j01xyWt8x/cyqQEFlOayQzPDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9726b7f4f1404c71a2b35b4c61f630d638f549fea65ba19ebcd65635500b5657","last_reissued_at":"2026-05-18T03:00:13.515130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:13.515130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost-Ramanujan Graphs and Prime Gaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Adrian Dudek","submitted_at":"2014-02-04T05:37:01Z","abstract_excerpt":"The method of Murty and Cioab\\u{a} shows how one can use results about gaps between primes to construct families of almost-Ramanujan graphs. In this paper we give a simpler construction which avoids the search for perfect matchings and thus eliminates the need for computation. A couple of recent explicit bounds on the gap between consecutive primes are then used to give the construction of $k$-regular families with explicit lower bounds on the spectral gaps. We then show that a result of Ben-Aroya and Ta-Shma can be improved using our simpler construction on the assumption of the Riemann Hypot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0620","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":"1402.0620","created_at":"2026-05-18T03:00:13.515286+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.0620v1","created_at":"2026-05-18T03:00:13.515286+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0620","created_at":"2026-05-18T03:00:13.515286+00:00"},{"alias_kind":"pith_short_12","alias_value":"S4TLP5HRIBGH","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"S4TLP5HRIBGHDIVT","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"S4TLP5HR","created_at":"2026-05-18T12:28:49.207871+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/S4TLP5HRIBGHDIVTLNGGD5RQ2Y","json":"https://pith.science/pith/S4TLP5HRIBGHDIVTLNGGD5RQ2Y.json","graph_json":"https://pith.science/api/pith-number/S4TLP5HRIBGHDIVTLNGGD5RQ2Y/graph.json","events_json":"https://pith.science/api/pith-number/S4TLP5HRIBGHDIVTLNGGD5RQ2Y/events.json","paper":"https://pith.science/paper/S4TLP5HR"},"agent_actions":{"view_html":"https://pith.science/pith/S4TLP5HRIBGHDIVTLNGGD5RQ2Y","download_json":"https://pith.science/pith/S4TLP5HRIBGHDIVTLNGGD5RQ2Y.json","view_paper":"https://pith.science/paper/S4TLP5HR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.0620&json=true","fetch_graph":"https://pith.science/api/pith-number/S4TLP5HRIBGHDIVTLNGGD5RQ2Y/graph.json","fetch_events":"https://pith.science/api/pith-number/S4TLP5HRIBGHDIVTLNGGD5RQ2Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S4TLP5HRIBGHDIVTLNGGD5RQ2Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S4TLP5HRIBGHDIVTLNGGD5RQ2Y/action/storage_attestation","attest_author":"https://pith.science/pith/S4TLP5HRIBGHDIVTLNGGD5RQ2Y/action/author_attestation","sign_citation":"https://pith.science/pith/S4TLP5HRIBGHDIVTLNGGD5RQ2Y/action/citation_signature","submit_replication":"https://pith.science/pith/S4TLP5HRIBGHDIVTLNGGD5RQ2Y/action/replication_record"}},"created_at":"2026-05-18T03:00:13.515286+00:00","updated_at":"2026-05-18T03:00:13.515286+00:00"}