{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7NA6QBGW3QUB7PREMRVML24XKQ","short_pith_number":"pith:7NA6QBGW","schema_version":"1.0","canonical_sha256":"fb41e804d6dc281fbe24646ac5eb9754378f23ae792a0ce3b91cb6874aaa94c2","source":{"kind":"arxiv","id":"1410.6748","version":3},"attestation_state":"computed","paper":{"title":"Non-existence of (76,30,8,14) strongly regular graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Prymak, A. V. Bondarenko, D. Radchenko","submitted_at":"2014-10-24T17:25:50Z","abstract_excerpt":"We prove the non-existence of strongly regular graph with parameters $(76,30,8,14)$. We use Euclidean representation of a strongly regular graph together with a new lower bound on the number of 4-cliques to derive strong structural properties of the graph, and then use these properties to show that the graph cannot exist."},"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":"1410.6748","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-24T17:25:50Z","cross_cats_sorted":[],"title_canon_sha256":"aa6e09a35443f5e4da3eee30edfb4e0e33fbe7272e097205c845bc1a9addb2d2","abstract_canon_sha256":"675e85e0de8f2af420f27b176fc57c141a5c7323b3cb473d48a46fd7dc34f23a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:08.525034Z","signature_b64":"Q+6uLRLeFY9VKKuKgKTmYv8eFH0Ez4yrvdDQc4pm6PBQSEgJIWtwV85dJ6Yuvp1lobnCST4Op9YLnQAZDtu8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb41e804d6dc281fbe24646ac5eb9754378f23ae792a0ce3b91cb6874aaa94c2","last_reissued_at":"2026-05-18T00:46:08.524461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:08.524461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-existence of (76,30,8,14) strongly regular graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Prymak, A. V. Bondarenko, D. Radchenko","submitted_at":"2014-10-24T17:25:50Z","abstract_excerpt":"We prove the non-existence of strongly regular graph with parameters $(76,30,8,14)$. We use Euclidean representation of a strongly regular graph together with a new lower bound on the number of 4-cliques to derive strong structural properties of the graph, and then use these properties to show that the graph cannot exist."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6748","kind":"arxiv","version":3},"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":"1410.6748","created_at":"2026-05-18T00:46:08.524554+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.6748v3","created_at":"2026-05-18T00:46:08.524554+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6748","created_at":"2026-05-18T00:46:08.524554+00:00"},{"alias_kind":"pith_short_12","alias_value":"7NA6QBGW3QUB","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"7NA6QBGW3QUB7PRE","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"7NA6QBGW","created_at":"2026-05-18T12:28:19.803747+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/7NA6QBGW3QUB7PREMRVML24XKQ","json":"https://pith.science/pith/7NA6QBGW3QUB7PREMRVML24XKQ.json","graph_json":"https://pith.science/api/pith-number/7NA6QBGW3QUB7PREMRVML24XKQ/graph.json","events_json":"https://pith.science/api/pith-number/7NA6QBGW3QUB7PREMRVML24XKQ/events.json","paper":"https://pith.science/paper/7NA6QBGW"},"agent_actions":{"view_html":"https://pith.science/pith/7NA6QBGW3QUB7PREMRVML24XKQ","download_json":"https://pith.science/pith/7NA6QBGW3QUB7PREMRVML24XKQ.json","view_paper":"https://pith.science/paper/7NA6QBGW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.6748&json=true","fetch_graph":"https://pith.science/api/pith-number/7NA6QBGW3QUB7PREMRVML24XKQ/graph.json","fetch_events":"https://pith.science/api/pith-number/7NA6QBGW3QUB7PREMRVML24XKQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7NA6QBGW3QUB7PREMRVML24XKQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7NA6QBGW3QUB7PREMRVML24XKQ/action/storage_attestation","attest_author":"https://pith.science/pith/7NA6QBGW3QUB7PREMRVML24XKQ/action/author_attestation","sign_citation":"https://pith.science/pith/7NA6QBGW3QUB7PREMRVML24XKQ/action/citation_signature","submit_replication":"https://pith.science/pith/7NA6QBGW3QUB7PREMRVML24XKQ/action/replication_record"}},"created_at":"2026-05-18T00:46:08.524554+00:00","updated_at":"2026-05-18T00:46:08.524554+00:00"}