{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:KTKFNEHK2RY42IVIXH55VPH2PC","short_pith_number":"pith:KTKFNEHK","schema_version":"1.0","canonical_sha256":"54d45690ead471cd22a8b9fbdabcfa78b2f3822d86d1677a858cb9aa1aee0292","source":{"kind":"arxiv","id":"1809.10029","version":1},"attestation_state":"computed","paper":{"title":"There does not exist a distance-regular graph with intersection array $\\{80, 54,12; 1, 6, 60\\}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jack H. Koolen, Jongyook Park, Masood Ur Rehman, Quaid Iqbal","submitted_at":"2018-09-26T14:37:49Z","abstract_excerpt":"In this paper we will show that there does not exist a distance-regular graph $\\Gamma$ with intersection array $\\{80, 54,12; 1, 6, 60\\}$. We first show that a local graph $\\Delta$ of $\\Gamma$ does not contain a coclique with 5 vertices, and then we prove that the graph $\\Gamma$ is geometric by showing that $\\Delta$ consists of 4 disjoint cliques with 20 vertices. Then we apply a result of Koolen and Bang to the graph $\\Gamma$, and we could obtain that there is no such a distance-regular graph."},"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":"1809.10029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-26T14:37:49Z","cross_cats_sorted":[],"title_canon_sha256":"bde3377fca39cd9c57629e5a3743485c700dc060291ba69dd578110176ef9dac","abstract_canon_sha256":"c128896ec4fc72e5c80e0fbbf03922a11132e51c179b9c6faa5fd3a616b42ca6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:42.818526Z","signature_b64":"5Fl32Re2Oo1ipkqD7+y7GzJSMvVLOCZNBgs33Khka2EQKG7UUByqEb+h/weUy0faJz0BXPmAIJsqHuKNqgZIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54d45690ead471cd22a8b9fbdabcfa78b2f3822d86d1677a858cb9aa1aee0292","last_reissued_at":"2026-05-18T00:04:42.817463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:42.817463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"There does not exist a distance-regular graph with intersection array $\\{80, 54,12; 1, 6, 60\\}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jack H. Koolen, Jongyook Park, Masood Ur Rehman, Quaid Iqbal","submitted_at":"2018-09-26T14:37:49Z","abstract_excerpt":"In this paper we will show that there does not exist a distance-regular graph $\\Gamma$ with intersection array $\\{80, 54,12; 1, 6, 60\\}$. We first show that a local graph $\\Delta$ of $\\Gamma$ does not contain a coclique with 5 vertices, and then we prove that the graph $\\Gamma$ is geometric by showing that $\\Delta$ consists of 4 disjoint cliques with 20 vertices. Then we apply a result of Koolen and Bang to the graph $\\Gamma$, and we could obtain that there is no such a distance-regular graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10029","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":"1809.10029","created_at":"2026-05-18T00:04:42.817567+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.10029v1","created_at":"2026-05-18T00:04:42.817567+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10029","created_at":"2026-05-18T00:04:42.817567+00:00"},{"alias_kind":"pith_short_12","alias_value":"KTKFNEHK2RY4","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"KTKFNEHK2RY42IVI","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"KTKFNEHK","created_at":"2026-05-18T12:32:33.847187+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/KTKFNEHK2RY42IVIXH55VPH2PC","json":"https://pith.science/pith/KTKFNEHK2RY42IVIXH55VPH2PC.json","graph_json":"https://pith.science/api/pith-number/KTKFNEHK2RY42IVIXH55VPH2PC/graph.json","events_json":"https://pith.science/api/pith-number/KTKFNEHK2RY42IVIXH55VPH2PC/events.json","paper":"https://pith.science/paper/KTKFNEHK"},"agent_actions":{"view_html":"https://pith.science/pith/KTKFNEHK2RY42IVIXH55VPH2PC","download_json":"https://pith.science/pith/KTKFNEHK2RY42IVIXH55VPH2PC.json","view_paper":"https://pith.science/paper/KTKFNEHK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.10029&json=true","fetch_graph":"https://pith.science/api/pith-number/KTKFNEHK2RY42IVIXH55VPH2PC/graph.json","fetch_events":"https://pith.science/api/pith-number/KTKFNEHK2RY42IVIXH55VPH2PC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KTKFNEHK2RY42IVIXH55VPH2PC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KTKFNEHK2RY42IVIXH55VPH2PC/action/storage_attestation","attest_author":"https://pith.science/pith/KTKFNEHK2RY42IVIXH55VPH2PC/action/author_attestation","sign_citation":"https://pith.science/pith/KTKFNEHK2RY42IVIXH55VPH2PC/action/citation_signature","submit_replication":"https://pith.science/pith/KTKFNEHK2RY42IVIXH55VPH2PC/action/replication_record"}},"created_at":"2026-05-18T00:04:42.817567+00:00","updated_at":"2026-05-18T00:04:42.817567+00:00"}