{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LICRBD7MC5I3JFJXXKERQB5EQT","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":"e970ac686d71f3e3a26df76c833eef769fc5202fb4b21cb37a63e515878bceb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-08T12:13:40Z","title_canon_sha256":"b2e90519d3fdd3b52a571e7699cbce7cf585949100d1cf484a79e1c82a4c8616"},"schema_version":"1.0","source":{"id":"1203.1766","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1766","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1766v1","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1766","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"LICRBD7MC5I3","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LICRBD7MC5I3JFJX","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LICRBD7M","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:0938903b2f92a4880ade76a27b541e0710e81448cb895199b9344528b26fbd62","target":"graph","created_at":"2026-05-18T04:00:37Z","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":"A unital in PG(2,q^2) is a set U of q^3+1 points such that each line meets U in 1 or q+1 points. The well known example is the classical unital consisting of all absolute points of a non-degenerate unitary polarity of PG(2,q^2). Unitals other than the classical one also exist in PG(2,q^2) for every q>2. Actually, all known unitals are of Buekenhout-Metz type and they can be obtained by a construction due to Buekenhout. The unitals constructed by Baker-Ebert, and independently by Hirschfeld-Szonyi, are the union of q conics. Our Theorem 1.1 shows that this geometric property characterizes the B","authors_text":"A. Siciliano, N. Durante","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-08T12:13:40Z","title":"Unitals of PG(2,q^2) containing conics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1766","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:a0bebfd98fe81f86f115977df0471309bc108971936729f30e4b626aaae3693d","target":"record","created_at":"2026-05-18T04:00:37Z","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":"e970ac686d71f3e3a26df76c833eef769fc5202fb4b21cb37a63e515878bceb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-08T12:13:40Z","title_canon_sha256":"b2e90519d3fdd3b52a571e7699cbce7cf585949100d1cf484a79e1c82a4c8616"},"schema_version":"1.0","source":{"id":"1203.1766","kind":"arxiv","version":1}},"canonical_sha256":"5a05108fec1751b49537ba891807a484db0ea7e6d46b8b7a1a1eace0ec0443ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a05108fec1751b49537ba891807a484db0ea7e6d46b8b7a1a1eace0ec0443ed","first_computed_at":"2026-05-18T04:00:37.035627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:37.035627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j4wG9wkEXwo3yXv7a1x9n1/LS47yW0iPkILOSx3BAHm6OlP5CMsybpDsSV+zlYYVPInDNKDNpnL+ZFxCT7ioCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:37.036455Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1766","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0bebfd98fe81f86f115977df0471309bc108971936729f30e4b626aaae3693d","sha256:0938903b2f92a4880ade76a27b541e0710e81448cb895199b9344528b26fbd62"],"state_sha256":"e1810f04c3d676dfc6561b0c64aa031b7e4fb5338e7558a90bdb2e2d64c14810"}