{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ELZ3Y43H56TSJ2NDIBERPBDHSO","short_pith_number":"pith:ELZ3Y43H","schema_version":"1.0","canonical_sha256":"22f3bc7367efa724e9a340491784679389bc40479a8959b4800350b5381f4f3a","source":{"kind":"arxiv","id":"1512.05976","version":1},"attestation_state":"computed","paper":{"title":"The uniqueness of a distance-regular graph with intersection array {32,27,8,1;1,4,27,32} and related results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Leonard H. Soicher","submitted_at":"2015-12-18T14:44:43Z","abstract_excerpt":"It is known that, up to isomorphism, there is a unique distance-regular graph $\\Delta$ with intersection array {32,27;1,12} (equivalently, $\\Delta$ is the unique strongly regular graph with parameters (105,32,4,12)). Here we investigate the distance-regular antipodal covers of $\\Delta$. We show that, up to isomorphism, there is just one distance-regular antipodal triple cover of $\\Delta$ (a graph $\\hat\\Delta$ discovered by the author over twenty years ago), proving that there is a unique distance-regular graph with intersection array {32,27,8,1;1,4,27,32}. In the process, we confirm an unpubli"},"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":"1512.05976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-18T14:44:43Z","cross_cats_sorted":[],"title_canon_sha256":"99f386b9a55f29e100bab222069edc37e34340d15c4a617413cb241d77f336c6","abstract_canon_sha256":"895aea485522499f19130d449bc770d4cc405a610e5b29f51d8051ee3a5fdb70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:05.747602Z","signature_b64":"ozLMJPPpn0+AdwrtN/nRecon6EtAAZ1Y5ZHCQbWgnLySKSao3DskoNqFsFqm/OcoBeDMWVtgVOGorT2/mXJWCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22f3bc7367efa724e9a340491784679389bc40479a8959b4800350b5381f4f3a","last_reissued_at":"2026-05-18T01:24:05.747069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:05.747069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The uniqueness of a distance-regular graph with intersection array {32,27,8,1;1,4,27,32} and related results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Leonard H. Soicher","submitted_at":"2015-12-18T14:44:43Z","abstract_excerpt":"It is known that, up to isomorphism, there is a unique distance-regular graph $\\Delta$ with intersection array {32,27;1,12} (equivalently, $\\Delta$ is the unique strongly regular graph with parameters (105,32,4,12)). Here we investigate the distance-regular antipodal covers of $\\Delta$. We show that, up to isomorphism, there is just one distance-regular antipodal triple cover of $\\Delta$ (a graph $\\hat\\Delta$ discovered by the author over twenty years ago), proving that there is a unique distance-regular graph with intersection array {32,27,8,1;1,4,27,32}. In the process, we confirm an unpubli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05976","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":"1512.05976","created_at":"2026-05-18T01:24:05.747159+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.05976v1","created_at":"2026-05-18T01:24:05.747159+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05976","created_at":"2026-05-18T01:24:05.747159+00:00"},{"alias_kind":"pith_short_12","alias_value":"ELZ3Y43H56TS","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"ELZ3Y43H56TSJ2ND","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"ELZ3Y43H","created_at":"2026-05-18T12:29:19.899920+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/ELZ3Y43H56TSJ2NDIBERPBDHSO","json":"https://pith.science/pith/ELZ3Y43H56TSJ2NDIBERPBDHSO.json","graph_json":"https://pith.science/api/pith-number/ELZ3Y43H56TSJ2NDIBERPBDHSO/graph.json","events_json":"https://pith.science/api/pith-number/ELZ3Y43H56TSJ2NDIBERPBDHSO/events.json","paper":"https://pith.science/paper/ELZ3Y43H"},"agent_actions":{"view_html":"https://pith.science/pith/ELZ3Y43H56TSJ2NDIBERPBDHSO","download_json":"https://pith.science/pith/ELZ3Y43H56TSJ2NDIBERPBDHSO.json","view_paper":"https://pith.science/paper/ELZ3Y43H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.05976&json=true","fetch_graph":"https://pith.science/api/pith-number/ELZ3Y43H56TSJ2NDIBERPBDHSO/graph.json","fetch_events":"https://pith.science/api/pith-number/ELZ3Y43H56TSJ2NDIBERPBDHSO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ELZ3Y43H56TSJ2NDIBERPBDHSO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ELZ3Y43H56TSJ2NDIBERPBDHSO/action/storage_attestation","attest_author":"https://pith.science/pith/ELZ3Y43H56TSJ2NDIBERPBDHSO/action/author_attestation","sign_citation":"https://pith.science/pith/ELZ3Y43H56TSJ2NDIBERPBDHSO/action/citation_signature","submit_replication":"https://pith.science/pith/ELZ3Y43H56TSJ2NDIBERPBDHSO/action/replication_record"}},"created_at":"2026-05-18T01:24:05.747159+00:00","updated_at":"2026-05-18T01:24:05.747159+00:00"}