{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YY66MLM5W7LO4QZIJNUMTURJH4","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":"3977254ed5bc99f946a0764f6bb0fe5f5c33b7c3d4dc00dea22cb35834998008","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-16T11:17:51Z","title_canon_sha256":"6b87d088cd3e6ea0cf636903bb214dffd9f87ca5eae7f3d1d88e88f9a3c0dd0f"},"schema_version":"1.0","source":{"id":"1004.2817","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2817","created_at":"2026-05-18T04:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2817v5","created_at":"2026-05-18T04:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2817","created_at":"2026-05-18T04:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"YY66MLM5W7LO","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YY66MLM5W7LO4QZI","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YY66MLM5","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:55717db84d82cf0d7ed145495e337b9efc2457740741391486eac0f25277da59","target":"graph","created_at":"2026-05-18T04:41:43Z","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":"New upper bounds on the smallest size t_{2}(2,q) of a complete arc in the projective plane PG(2,q) are obtained for 853<= q<= 2879 and q=3511,4096, 4523,5003,5347,5641,5843,6011. For q<= 2377 and q=2401,2417,2437, the relation t_{2}(2,q)<4.5\\sqrt{q} holds. The bounds are obtained by finding of new small complete arcs with the help of computer search using randomized greedy algorithms. Also new sizes of complete arcs are presented.","authors_text":"Alexander A. Davydov, Fernanda Pambianco, Giorgio Faina, Stefano Marcugini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-16T11:17:51Z","title":"New sizes of complete arcs in PG(2,q)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2817","kind":"arxiv","version":5},"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":"sha256:6d8794fd60c348681427fad86bf8d0a5b10ce3f13006143e3134b2125b3ebf7d","target":"record","created_at":"2026-05-18T04:41:43Z","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":"3977254ed5bc99f946a0764f6bb0fe5f5c33b7c3d4dc00dea22cb35834998008","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-16T11:17:51Z","title_canon_sha256":"6b87d088cd3e6ea0cf636903bb214dffd9f87ca5eae7f3d1d88e88f9a3c0dd0f"},"schema_version":"1.0","source":{"id":"1004.2817","kind":"arxiv","version":5}},"canonical_sha256":"c63de62d9db7d6ee43284b68c9d2293f1e789e808f4e97929ba60aa82c2991f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c63de62d9db7d6ee43284b68c9d2293f1e789e808f4e97929ba60aa82c2991f4","first_computed_at":"2026-05-18T04:41:43.901815Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:43.901815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bQ95kGAQqNi5iyO/tzPuxHdTfnM+QqC/2Y49+ZNtvNlcjkiaYkUNds+oI0MIL89K7wDuk0OJ5NoOVVEn4b3MCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:43.902209Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.2817","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d8794fd60c348681427fad86bf8d0a5b10ce3f13006143e3134b2125b3ebf7d","sha256:55717db84d82cf0d7ed145495e337b9efc2457740741391486eac0f25277da59"],"state_sha256":"2d780160a28cb144f9c5827c16ff35f0b80579a7b513e0d8f83433143c6f3c1d"}