{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FB3GRN6IGJOXNKKL6DVLUD7IUL","short_pith_number":"pith:FB3GRN6I","schema_version":"1.0","canonical_sha256":"287668b7c8325d76a94bf0eaba0fe8a2f770e2539d67204029faa323729b3c65","source":{"kind":"arxiv","id":"1706.06578","version":1},"attestation_state":"computed","paper":{"title":"A characterization of Hermitian varieties as codewords","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Aguglia, D. Bartoli, L. Storme, Zs. Weiner","submitted_at":"2017-06-19T18:20:59Z","abstract_excerpt":"It is known that the Hermitian varieties are codewords in the code defined by the points and hyperplanes of the projective spaces $PG(r,q^2)$. In finite geometry, also quasi-Hermitian varieties are defined. These are sets of points of $PG(r,q^2)$ of the same size as a non-singular Hermitian variety of $PG(r,q^2)$, having the same intersection sizes with the hyperplanes of $PG(r,q^2)$. In the planar case, this reduces to the definition of a unital. A famous result of Blokhuis, Brouwer, and Wilbrink states that every unital in the code of the points and lines of $PG(2,q^2)$ is a Hermitian curve."},"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":"1706.06578","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-19T18:20:59Z","cross_cats_sorted":[],"title_canon_sha256":"5a6f9bf46ccd1f2f0c83c708e24b163010d4add488bfb1f4d563019a47807c8e","abstract_canon_sha256":"928aac6b08bb2c0b35affe1639630bc05725d29d396a1cc5d9ba32fee4c2d23f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:57.469232Z","signature_b64":"DBpO9C+ARf0DVdq7U08i5Tk++9kGhcL6YnU84qvC9fsRaUMsB9kvFsYMSnrmR4GEqwhXjiF4bkhpuEp9fHwFDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"287668b7c8325d76a94bf0eaba0fe8a2f770e2539d67204029faa323729b3c65","last_reissued_at":"2026-05-18T00:41:57.468700Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:57.468700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characterization of Hermitian varieties as codewords","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Aguglia, D. Bartoli, L. Storme, Zs. Weiner","submitted_at":"2017-06-19T18:20:59Z","abstract_excerpt":"It is known that the Hermitian varieties are codewords in the code defined by the points and hyperplanes of the projective spaces $PG(r,q^2)$. In finite geometry, also quasi-Hermitian varieties are defined. These are sets of points of $PG(r,q^2)$ of the same size as a non-singular Hermitian variety of $PG(r,q^2)$, having the same intersection sizes with the hyperplanes of $PG(r,q^2)$. In the planar case, this reduces to the definition of a unital. A famous result of Blokhuis, Brouwer, and Wilbrink states that every unital in the code of the points and lines of $PG(2,q^2)$ is a Hermitian curve."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06578","kind":"arxiv","version":1},"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":"1706.06578","created_at":"2026-05-18T00:41:57.468791+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.06578v1","created_at":"2026-05-18T00:41:57.468791+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06578","created_at":"2026-05-18T00:41:57.468791+00:00"},{"alias_kind":"pith_short_12","alias_value":"FB3GRN6IGJOX","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FB3GRN6IGJOXNKKL","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FB3GRN6I","created_at":"2026-05-18T12:31:15.632608+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/FB3GRN6IGJOXNKKL6DVLUD7IUL","json":"https://pith.science/pith/FB3GRN6IGJOXNKKL6DVLUD7IUL.json","graph_json":"https://pith.science/api/pith-number/FB3GRN6IGJOXNKKL6DVLUD7IUL/graph.json","events_json":"https://pith.science/api/pith-number/FB3GRN6IGJOXNKKL6DVLUD7IUL/events.json","paper":"https://pith.science/paper/FB3GRN6I"},"agent_actions":{"view_html":"https://pith.science/pith/FB3GRN6IGJOXNKKL6DVLUD7IUL","download_json":"https://pith.science/pith/FB3GRN6IGJOXNKKL6DVLUD7IUL.json","view_paper":"https://pith.science/paper/FB3GRN6I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.06578&json=true","fetch_graph":"https://pith.science/api/pith-number/FB3GRN6IGJOXNKKL6DVLUD7IUL/graph.json","fetch_events":"https://pith.science/api/pith-number/FB3GRN6IGJOXNKKL6DVLUD7IUL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FB3GRN6IGJOXNKKL6DVLUD7IUL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FB3GRN6IGJOXNKKL6DVLUD7IUL/action/storage_attestation","attest_author":"https://pith.science/pith/FB3GRN6IGJOXNKKL6DVLUD7IUL/action/author_attestation","sign_citation":"https://pith.science/pith/FB3GRN6IGJOXNKKL6DVLUD7IUL/action/citation_signature","submit_replication":"https://pith.science/pith/FB3GRN6IGJOXNKKL6DVLUD7IUL/action/replication_record"}},"created_at":"2026-05-18T00:41:57.468791+00:00","updated_at":"2026-05-18T00:41:57.468791+00:00"}