{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:OVFVQJXV5BYJO7LOZ3L7ZN423A","short_pith_number":"pith:OVFVQJXV","schema_version":"1.0","canonical_sha256":"754b5826f5e870977d6eced7fcb79ad83b7854e464c2eedef373f828e6f45098","source":{"kind":"arxiv","id":"1808.00576","version":2},"attestation_state":"computed","paper":{"title":"All $(96,20,4)$ difference sets and related structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dylan Peifer, Ken W. Smith, Omar A. AbuGhneim","submitted_at":"2018-08-01T21:54:04Z","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"},"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":"1808.00576","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-01T21:54:04Z","cross_cats_sorted":[],"title_canon_sha256":"fa5f2131addc34de816526641fa4b1564e844ee2ea55f0a3d4aaea2c16171db5","abstract_canon_sha256":"faa3da63a1223a33596fad3c916a66cf3deb43d302023d6cc1d1ce473a3a656b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:29.545922Z","signature_b64":"v6RJRoBvpreQcjCWnsJm4/sAN884Y421wu5yoy2v2D25IqgDv9j5UTgxyc8EN2PX1HiZd+7GIpwKj74qEa3cCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"754b5826f5e870977d6eced7fcb79ad83b7854e464c2eedef373f828e6f45098","last_reissued_at":"2026-05-17T23:56:29.545509Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:29.545509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"All $(96,20,4)$ difference sets and related structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dylan Peifer, Ken W. Smith, Omar A. AbuGhneim","submitted_at":"2018-08-01T21:54:04Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00576","kind":"arxiv","version":2},"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":"1808.00576","created_at":"2026-05-17T23:56:29.545569+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.00576v2","created_at":"2026-05-17T23:56:29.545569+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00576","created_at":"2026-05-17T23:56:29.545569+00:00"},{"alias_kind":"pith_short_12","alias_value":"OVFVQJXV5BYJ","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"OVFVQJXV5BYJO7LO","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"OVFVQJXV","created_at":"2026-05-18T12:32:43.782077+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/OVFVQJXV5BYJO7LOZ3L7ZN423A","json":"https://pith.science/pith/OVFVQJXV5BYJO7LOZ3L7ZN423A.json","graph_json":"https://pith.science/api/pith-number/OVFVQJXV5BYJO7LOZ3L7ZN423A/graph.json","events_json":"https://pith.science/api/pith-number/OVFVQJXV5BYJO7LOZ3L7ZN423A/events.json","paper":"https://pith.science/paper/OVFVQJXV"},"agent_actions":{"view_html":"https://pith.science/pith/OVFVQJXV5BYJO7LOZ3L7ZN423A","download_json":"https://pith.science/pith/OVFVQJXV5BYJO7LOZ3L7ZN423A.json","view_paper":"https://pith.science/paper/OVFVQJXV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.00576&json=true","fetch_graph":"https://pith.science/api/pith-number/OVFVQJXV5BYJO7LOZ3L7ZN423A/graph.json","fetch_events":"https://pith.science/api/pith-number/OVFVQJXV5BYJO7LOZ3L7ZN423A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OVFVQJXV5BYJO7LOZ3L7ZN423A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OVFVQJXV5BYJO7LOZ3L7ZN423A/action/storage_attestation","attest_author":"https://pith.science/pith/OVFVQJXV5BYJO7LOZ3L7ZN423A/action/author_attestation","sign_citation":"https://pith.science/pith/OVFVQJXV5BYJO7LOZ3L7ZN423A/action/citation_signature","submit_replication":"https://pith.science/pith/OVFVQJXV5BYJO7LOZ3L7ZN423A/action/replication_record"}},"created_at":"2026-05-17T23:56:29.545569+00:00","updated_at":"2026-05-17T23:56:29.545569+00:00"}