{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZNB7ZEDWHXOAMKEANAB2TEMGAX","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":"2d830af7e6eeec4d79117fbb9a9c5d9a192a1f7408cd15b5369486318b7a8857","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-05T22:39:30Z","title_canon_sha256":"d0b2a2f24def6c89bb0268b0f77ab438c0a089c16d554af79640396076d6ac87"},"schema_version":"1.0","source":{"id":"1507.01289","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01289","created_at":"2026-05-18T01:30:01Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01289v2","created_at":"2026-05-18T01:30:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01289","created_at":"2026-05-18T01:30:01Z"},{"alias_kind":"pith_short_12","alias_value":"ZNB7ZEDWHXOA","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZNB7ZEDWHXOAMKEA","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZNB7ZEDW","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:fbc56d857272732a425ce37ba53962217531e46e82b06a11504532493be0b268","target":"graph","created_at":"2026-05-18T01:30:01Z","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":"Fix positive integers $p,q,$ and $r$ so that $p$ is prime, $q=p^r$, and $q\\equiv 1$ (mod $4$). Fix a graph $G$ as follows: If $r$ is odd or $p\\not\\equiv 3$ (mod $4$), let $G$ be the $q$-vertex Paley graph; if $r$ is even and $p\\equiv 3$ (mod $4$), let $G$ be either the $q$-vertex Paley graph or the $q$-vertex Peisert graph. We use the subgraph structure of $G$ to construct four sequences of $2$-designs, and we compute their parameters. Letting $k_4$ denote the number of $4$-vertex cliques in $G$, we create $62$ additional sequences of $2$-designs from $G$, and show how to express their paramet","authors_text":"James Alexander","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-05T22:39:30Z","title":"Designs from Paley graphs and Peisert graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01289","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:d1f4dabba3c264d6ac72b1fd6bc85f381c4cb8c01ed7fd76126b37e06a6459c1","target":"record","created_at":"2026-05-18T01:30:01Z","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":"2d830af7e6eeec4d79117fbb9a9c5d9a192a1f7408cd15b5369486318b7a8857","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-05T22:39:30Z","title_canon_sha256":"d0b2a2f24def6c89bb0268b0f77ab438c0a089c16d554af79640396076d6ac87"},"schema_version":"1.0","source":{"id":"1507.01289","kind":"arxiv","version":2}},"canonical_sha256":"cb43fc90763ddc0628806803a9918605c5c82fc44bc7f68a30efa9239bdbb100","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb43fc90763ddc0628806803a9918605c5c82fc44bc7f68a30efa9239bdbb100","first_computed_at":"2026-05-18T01:30:01.780295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:01.780295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FgapKbiVfaTP1rr70OD+l9/oueM6VZr8TT7kQwB5ZHsk3luYJGTop8j4ZQi79zyCxQrgXASsewZGB0+tDvzECg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:01.780797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01289","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1f4dabba3c264d6ac72b1fd6bc85f381c4cb8c01ed7fd76126b37e06a6459c1","sha256:fbc56d857272732a425ce37ba53962217531e46e82b06a11504532493be0b268"],"state_sha256":"fde75016969d664d6b251039383bf87ef538241422bea0caa373bf5d65cfaa84"}