{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TXY2BSP3ZHJFTNGWSE5O2PQBNI","short_pith_number":"pith:TXY2BSP3","schema_version":"1.0","canonical_sha256":"9df1a0c9fbc9d259b4d6913aed3e016a1c3a1b46c4489c6694fa35839c112771","source":{"kind":"arxiv","id":"1612.05246","version":2},"attestation_state":"computed","paper":{"title":"Counting Arcs in Projective Planes via Glynn's Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luke Peilen, Max Weinreich, Nathan Kaplan, Rachel Lawrence, Susie Kimport","submitted_at":"2016-12-15T20:51:43Z","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"},"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":"1612.05246","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-15T20:51:43Z","cross_cats_sorted":[],"title_canon_sha256":"e29d86faa4f1aa0a8b29416a3509d93342f7a11671e1c44359b5888167a81b31","abstract_canon_sha256":"cc113b27c3b6066e846e81299b5e47cfdc00db66cc00dd50de089ede5aab0fa2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:39.196445Z","signature_b64":"W2pkodHIygoNzj/lkWvT3NLWgJ0H+i0x8n4/gIwNK6tW9zPvKR/MmnMeoiY6DAe9hw0D3YpOpnZLzffzzXMKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9df1a0c9fbc9d259b4d6913aed3e016a1c3a1b46c4489c6694fa35839c112771","last_reissued_at":"2026-05-18T00:42:39.195736Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:39.195736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting Arcs in Projective Planes via Glynn's Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luke Peilen, Max Weinreich, Nathan Kaplan, Rachel Lawrence, Susie Kimport","submitted_at":"2016-12-15T20:51:43Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05246","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":"1612.05246","created_at":"2026-05-18T00:42:39.195856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.05246v2","created_at":"2026-05-18T00:42:39.195856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05246","created_at":"2026-05-18T00:42:39.195856+00:00"},{"alias_kind":"pith_short_12","alias_value":"TXY2BSP3ZHJF","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"TXY2BSP3ZHJFTNGW","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"TXY2BSP3","created_at":"2026-05-18T12:30:46.583412+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/TXY2BSP3ZHJFTNGWSE5O2PQBNI","json":"https://pith.science/pith/TXY2BSP3ZHJFTNGWSE5O2PQBNI.json","graph_json":"https://pith.science/api/pith-number/TXY2BSP3ZHJFTNGWSE5O2PQBNI/graph.json","events_json":"https://pith.science/api/pith-number/TXY2BSP3ZHJFTNGWSE5O2PQBNI/events.json","paper":"https://pith.science/paper/TXY2BSP3"},"agent_actions":{"view_html":"https://pith.science/pith/TXY2BSP3ZHJFTNGWSE5O2PQBNI","download_json":"https://pith.science/pith/TXY2BSP3ZHJFTNGWSE5O2PQBNI.json","view_paper":"https://pith.science/paper/TXY2BSP3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.05246&json=true","fetch_graph":"https://pith.science/api/pith-number/TXY2BSP3ZHJFTNGWSE5O2PQBNI/graph.json","fetch_events":"https://pith.science/api/pith-number/TXY2BSP3ZHJFTNGWSE5O2PQBNI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TXY2BSP3ZHJFTNGWSE5O2PQBNI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TXY2BSP3ZHJFTNGWSE5O2PQBNI/action/storage_attestation","attest_author":"https://pith.science/pith/TXY2BSP3ZHJFTNGWSE5O2PQBNI/action/author_attestation","sign_citation":"https://pith.science/pith/TXY2BSP3ZHJFTNGWSE5O2PQBNI/action/citation_signature","submit_replication":"https://pith.science/pith/TXY2BSP3ZHJFTNGWSE5O2PQBNI/action/replication_record"}},"created_at":"2026-05-18T00:42:39.195856+00:00","updated_at":"2026-05-18T00:42:39.195856+00:00"}