{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GDJO4I7GBXC6KANOFLHQCYWAZB","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":"d0943be86af5cb1f4587a1f033c0abfec32e0b4c25e21bd983674f0d33ed6e51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-14T04:56:16Z","title_canon_sha256":"74c364bc11a3868d69a50adc521c2d6805056f8ef3ba96bce3ca65f6bc60e3b0"},"schema_version":"1.0","source":{"id":"1305.3019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3019","created_at":"2026-05-18T03:25:45Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3019v1","created_at":"2026-05-18T03:25:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3019","created_at":"2026-05-18T03:25:45Z"},{"alias_kind":"pith_short_12","alias_value":"GDJO4I7GBXC6","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GDJO4I7GBXC6KANO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GDJO4I7G","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:8381d013f2212f2f5454130fbf45fa4bf438857b4dca9f3c6b4d27aaf5a17dba","target":"graph","created_at":"2026-05-18T03:25:45Z","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":"Bicovering arcs in Galois affine planes of odd order are a powerful tool for constructing complete caps in spaces of higher dimensions. In this paper we investigate whether some arcs contained in nodal cubic curves are bicovering. For $m_1$, $m_2$ coprime divisors of $q-1$, bicovering arcs in $AG(2,q)$ of size $k\\le (q-1)\\frac{m_1+m_2}{m_1m_2}$ are obtained, provided that $(m_1m_2,6)=1$ and $m_1m_2<\\sqrt[4]{q}/3.5$. Such arcs produce complete caps of size $kq^{(N-2)/2}$ in affine spaces of dimension $N\\equiv 0 \\pmod 4$. For infinitely many $q$'s these caps are the smallest known complete caps ","authors_text":"Daniele Bartoli, Irene Platoni, Massimo Giulietti, Nurdagul Anbar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-14T04:56:16Z","title":"Small complete caps from nodal cubics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3019","kind":"arxiv","version":1},"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:d2b1fd434817ad7c5f13bdee3d4c9b6838dd011cdd822797bb11ba652854f2b4","target":"record","created_at":"2026-05-18T03:25:45Z","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":"d0943be86af5cb1f4587a1f033c0abfec32e0b4c25e21bd983674f0d33ed6e51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-14T04:56:16Z","title_canon_sha256":"74c364bc11a3868d69a50adc521c2d6805056f8ef3ba96bce3ca65f6bc60e3b0"},"schema_version":"1.0","source":{"id":"1305.3019","kind":"arxiv","version":1}},"canonical_sha256":"30d2ee23e60dc5e501ae2acf0162c0c8458c6ed9ea7fef6f3f244cb1754f834b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30d2ee23e60dc5e501ae2acf0162c0c8458c6ed9ea7fef6f3f244cb1754f834b","first_computed_at":"2026-05-18T03:25:45.096457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:45.096457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jnKs3eNsHNaSLxLZVT9lkO0SkvibX8JE8P5Kk2o3+x0BTi+YUp5ItDDbfr9nDvWD61ntPqZmPL8Qt5l3GCosCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:45.097242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2b1fd434817ad7c5f13bdee3d4c9b6838dd011cdd822797bb11ba652854f2b4","sha256:8381d013f2212f2f5454130fbf45fa4bf438857b4dca9f3c6b4d27aaf5a17dba"],"state_sha256":"cdd84f31c23661198a5d94517f7e55f636ccbae512503ad83df717cf88961d2b"}