{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TXY2BSP3ZHJFTNGWSE5O2PQBNI","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":"cc113b27c3b6066e846e81299b5e47cfdc00db66cc00dd50de089ede5aab0fa2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-15T20:51:43Z","title_canon_sha256":"e29d86faa4f1aa0a8b29416a3509d93342f7a11671e1c44359b5888167a81b31"},"schema_version":"1.0","source":{"id":"1612.05246","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05246","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05246v2","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05246","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"TXY2BSP3ZHJF","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TXY2BSP3ZHJFTNGW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TXY2BSP3","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:790da9ab0452173f1c1f308db3e32bd25ec048a08d320bdd768efd3d73aa8dec","target":"graph","created_at":"2026-05-18T00:42:39Z","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":"An $n$-arc in a projective plane is a collection of $n$ distinct points in the plane, no three of which lie on a line. Formulas counting the number of $n$-arcs in any finite projective plane of order $q$ are known for $n \\le 8$. In 1995, Iampolskaia, Skorobogatov, and Sorokin counted $9$-arcs in the projective plane over a finite field of order $q$ and showed that this count is a quasipolynomial function of $q$. We present a formula for the number of $9$-arcs in any projective plane of order $q$, even those that are non-Desarguesian, deriving Iampolskaia, Skorobogatov, and Sorokin's formula as","authors_text":"Luke Peilen, Max Weinreich, Nathan Kaplan, Rachel Lawrence, Susie Kimport","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-15T20:51:43Z","title":"Counting Arcs in Projective Planes via Glynn's Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05246","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:a9b8bb1610fd63b7e9b2b273a5ed89b7b30cb4b06bde8f3bf69e9ca87ee84916","target":"record","created_at":"2026-05-18T00:42:39Z","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":"cc113b27c3b6066e846e81299b5e47cfdc00db66cc00dd50de089ede5aab0fa2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-15T20:51:43Z","title_canon_sha256":"e29d86faa4f1aa0a8b29416a3509d93342f7a11671e1c44359b5888167a81b31"},"schema_version":"1.0","source":{"id":"1612.05246","kind":"arxiv","version":2}},"canonical_sha256":"9df1a0c9fbc9d259b4d6913aed3e016a1c3a1b46c4489c6694fa35839c112771","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9df1a0c9fbc9d259b4d6913aed3e016a1c3a1b46c4489c6694fa35839c112771","first_computed_at":"2026-05-18T00:42:39.195736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:39.195736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W2pkodHIygoNzj/lkWvT3NLWgJ0H+i0x8n4/gIwNK6tW9zPvKR/MmnMeoiY6DAe9hw0D3YpOpnZLzffzzXMKCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:39.196445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05246","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9b8bb1610fd63b7e9b2b273a5ed89b7b30cb4b06bde8f3bf69e9ca87ee84916","sha256:790da9ab0452173f1c1f308db3e32bd25ec048a08d320bdd768efd3d73aa8dec"],"state_sha256":"4852535fe5495fa808be6d6b949a812ebec3257b710e79899d847d5d6cd51169"}