{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7NA6QBGW3QUB7PREMRVML24XKQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"675e85e0de8f2af420f27b176fc57c141a5c7323b3cb473d48a46fd7dc34f23a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-24T17:25:50Z","title_canon_sha256":"aa6e09a35443f5e4da3eee30edfb4e0e33fbe7272e097205c845bc1a9addb2d2"},"schema_version":"1.0","source":{"id":"1410.6748","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6748","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6748v3","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6748","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"pith_short_12","alias_value":"7NA6QBGW3QUB","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7NA6QBGW3QUB7PRE","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7NA6QBGW","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:f54daf347879c5dc53e6df6cb8eed098caa07d624f61751d0dccfbe61a7e464b","target":"graph","created_at":"2026-05-18T00:46:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"A. Prymak, A. V. Bondarenko, D. Radchenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-24T17:25:50Z","title":"Non-existence of (76,30,8,14) strongly regular graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6748","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:569086588bf70337e13a9e400af6a12fbc12b2a545875243f62a9349e59c4fff","target":"record","created_at":"2026-05-18T00:46:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"675e85e0de8f2af420f27b176fc57c141a5c7323b3cb473d48a46fd7dc34f23a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-24T17:25:50Z","title_canon_sha256":"aa6e09a35443f5e4da3eee30edfb4e0e33fbe7272e097205c845bc1a9addb2d2"},"schema_version":"1.0","source":{"id":"1410.6748","kind":"arxiv","version":3}},"canonical_sha256":"fb41e804d6dc281fbe24646ac5eb9754378f23ae792a0ce3b91cb6874aaa94c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb41e804d6dc281fbe24646ac5eb9754378f23ae792a0ce3b91cb6874aaa94c2","first_computed_at":"2026-05-18T00:46:08.524461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:08.524461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q+6uLRLeFY9VKKuKgKTmYv8eFH0Ez4yrvdDQc4pm6PBQSEgJIWtwV85dJ6Yuvp1lobnCST4Op9YLnQAZDtu8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:08.525034Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6748","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:569086588bf70337e13a9e400af6a12fbc12b2a545875243f62a9349e59c4fff","sha256:f54daf347879c5dc53e6df6cb8eed098caa07d624f61751d0dccfbe61a7e464b"],"state_sha256":"194176dff508d81f6573d716ea7468078133d9e8f7ab53826a2a41ebe5fcd643"}