{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:QHQICJYKBGTQGX2Y6AYNBYVRXK","short_pith_number":"pith:QHQICJYK","schema_version":"1.0","canonical_sha256":"81e081270a09a7035f58f030d0e2b1ba835dc9b556f0af48a457ddb0318610c6","source":{"kind":"arxiv","id":"1211.2672","version":1},"attestation_state":"computed","paper":{"title":"Families of small regular graphs of girth 7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Balbuena, D. Labbate, G. Araujo-Pardo, J. Salas, M.Abreu","submitted_at":"2012-11-12T16:03:49Z","abstract_excerpt":"The first known families of cages arised from the incidence graphs of generalized polygons of order $q$, $q$ a prime power. In particular, $(q+1,6)$--cages have been obtained from the projective planes of order $q$. Morever, infinite families of small regular graphs of girth 5 have been constructed performing algebraic operations on $\\mathbb{F}_q$.\n  In this paper, we introduce some combinatorial operations to construct new infinite families of small regular graphs of girth 7 from the $(q+1,8)$--cages arising from the generalized quadrangles of order $q$, $q$ a prime power."},"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":"1211.2672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-12T16:03:49Z","cross_cats_sorted":[],"title_canon_sha256":"1fd7ecc51093bda6f50b799c6a3453581d422f118ad53e6fb045283ff1bc8252","abstract_canon_sha256":"c74a742caf1d01a259741ac66dc0978f7534b093bc08e119de6750bbca699a28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:02.117987Z","signature_b64":"jyFlnVj8ZukFJyHGtmkxhbv3TqqrkhBlelvMuAFi2YYKeLrZTcuKOyMzBiMa5Tg5RwgSI8caOlu9bZCt/TODAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81e081270a09a7035f58f030d0e2b1ba835dc9b556f0af48a457ddb0318610c6","last_reissued_at":"2026-05-18T03:41:02.117251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:02.117251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Families of small regular graphs of girth 7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Balbuena, D. Labbate, G. Araujo-Pardo, J. Salas, M.Abreu","submitted_at":"2012-11-12T16:03:49Z","abstract_excerpt":"The first known families of cages arised from the incidence graphs of generalized polygons of order $q$, $q$ a prime power. In particular, $(q+1,6)$--cages have been obtained from the projective planes of order $q$. Morever, infinite families of small regular graphs of girth 5 have been constructed performing algebraic operations on $\\mathbb{F}_q$.\n  In this paper, we introduce some combinatorial operations to construct new infinite families of small regular graphs of girth 7 from the $(q+1,8)$--cages arising from the generalized quadrangles of order $q$, $q$ a prime power."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2672","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":"1211.2672","created_at":"2026-05-18T03:41:02.117377+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.2672v1","created_at":"2026-05-18T03:41:02.117377+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2672","created_at":"2026-05-18T03:41:02.117377+00:00"},{"alias_kind":"pith_short_12","alias_value":"QHQICJYKBGTQ","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QHQICJYKBGTQGX2Y","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QHQICJYK","created_at":"2026-05-18T12:27:18.751474+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/QHQICJYKBGTQGX2Y6AYNBYVRXK","json":"https://pith.science/pith/QHQICJYKBGTQGX2Y6AYNBYVRXK.json","graph_json":"https://pith.science/api/pith-number/QHQICJYKBGTQGX2Y6AYNBYVRXK/graph.json","events_json":"https://pith.science/api/pith-number/QHQICJYKBGTQGX2Y6AYNBYVRXK/events.json","paper":"https://pith.science/paper/QHQICJYK"},"agent_actions":{"view_html":"https://pith.science/pith/QHQICJYKBGTQGX2Y6AYNBYVRXK","download_json":"https://pith.science/pith/QHQICJYKBGTQGX2Y6AYNBYVRXK.json","view_paper":"https://pith.science/paper/QHQICJYK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.2672&json=true","fetch_graph":"https://pith.science/api/pith-number/QHQICJYKBGTQGX2Y6AYNBYVRXK/graph.json","fetch_events":"https://pith.science/api/pith-number/QHQICJYKBGTQGX2Y6AYNBYVRXK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QHQICJYKBGTQGX2Y6AYNBYVRXK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QHQICJYKBGTQGX2Y6AYNBYVRXK/action/storage_attestation","attest_author":"https://pith.science/pith/QHQICJYKBGTQGX2Y6AYNBYVRXK/action/author_attestation","sign_citation":"https://pith.science/pith/QHQICJYKBGTQGX2Y6AYNBYVRXK/action/citation_signature","submit_replication":"https://pith.science/pith/QHQICJYKBGTQGX2Y6AYNBYVRXK/action/replication_record"}},"created_at":"2026-05-18T03:41:02.117377+00:00","updated_at":"2026-05-18T03:41:02.117377+00:00"}