{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OVFVQJXV5BYJO7LOZ3L7ZN423A","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":"faa3da63a1223a33596fad3c916a66cf3deb43d302023d6cc1d1ce473a3a656b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-01T21:54:04Z","title_canon_sha256":"fa5f2131addc34de816526641fa4b1564e844ee2ea55f0a3d4aaea2c16171db5"},"schema_version":"1.0","source":{"id":"1808.00576","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.00576","created_at":"2026-05-17T23:56:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.00576v2","created_at":"2026-05-17T23:56:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00576","created_at":"2026-05-17T23:56:29Z"},{"alias_kind":"pith_short_12","alias_value":"OVFVQJXV5BYJ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OVFVQJXV5BYJO7LO","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OVFVQJXV","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:0eb05ea323b030c64a96356800028a5fb340ee860d94b12dbe52f1b596f6c0b6","target":"graph","created_at":"2026-05-17T23:56:29Z","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":"In 1978, Robert Kibler at the National Security Agency in Fort Meade, Maryland published a description of all noncyclic difference sets with $k < 20$. Kibler's decision to stop his extensive computer search for difference sets at block size 19 was motivated partly by the difficult barrier at $k=20$, the difference sets with parameters $(96,20,4)$. In this paper, we announce the completion of the search for all $(96,20,4)$ difference sets, relying on the computer software GAP and the work of numerous authors over the last few decades. The difference sets and the symmetric designs they create ar","authors_text":"Dylan Peifer, Ken W. Smith, Omar A. AbuGhneim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-01T21:54:04Z","title":"All $(96,20,4)$ difference sets and related structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00576","kind":"arxiv","version":2},"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:e0200b4b41ecf3f49d61589a56c4bdbb07ca0076e460fa2963af5577e0f6c646","target":"record","created_at":"2026-05-17T23:56:29Z","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":"faa3da63a1223a33596fad3c916a66cf3deb43d302023d6cc1d1ce473a3a656b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-01T21:54:04Z","title_canon_sha256":"fa5f2131addc34de816526641fa4b1564e844ee2ea55f0a3d4aaea2c16171db5"},"schema_version":"1.0","source":{"id":"1808.00576","kind":"arxiv","version":2}},"canonical_sha256":"754b5826f5e870977d6eced7fcb79ad83b7854e464c2eedef373f828e6f45098","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"754b5826f5e870977d6eced7fcb79ad83b7854e464c2eedef373f828e6f45098","first_computed_at":"2026-05-17T23:56:29.545509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:29.545509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v6RJRoBvpreQcjCWnsJm4/sAN884Y421wu5yoy2v2D25IqgDv9j5UTgxyc8EN2PX1HiZd+7GIpwKj74qEa3cCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:29.545922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.00576","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0200b4b41ecf3f49d61589a56c4bdbb07ca0076e460fa2963af5577e0f6c646","sha256:0eb05ea323b030c64a96356800028a5fb340ee860d94b12dbe52f1b596f6c0b6"],"state_sha256":"0d90f6196c397324413d1e69ce165caca6daf92e4fc210b7ffa40779049796a1"}