{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JPN6XAULBL776HS73NJ3Q6VF7F","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":"0b03449fabae1efe4bd6f5c0f8c8997f0f61eb9671c1b87c7a18cb0341b14984","cross_cats_sorted":["math.DG","math.GR","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-03T21:41:58Z","title_canon_sha256":"39ec10f2960b5403587473842beeb56462d960913ac9d3be8148c9f0d35e589f"},"schema_version":"1.0","source":{"id":"1308.0745","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0745","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0745v4","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0745","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"JPN6XAULBL77","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JPN6XAULBL776HS7","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JPN6XAUL","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:b1da026bdd4510d8bcd6280d937bc555563c6150d797e817f6c261113f6fab18","target":"graph","created_at":"2026-05-18T00:54:15Z","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":"Our main aim is to provide a uniform geometric characterization of the analogues over arbitrary fields of the four complex Severi varieties, i.e.~the quadric Veronese varieties in 5-dimensional projective spaces, the Segre varieties in 8-di\\-men\\-sional projective spaces, the line Grassmannians in 14-dimensional projective spaces, and the exceptional varieties of type $\\mathsf{E}_{6}$ in 26-dimensional projective space. Our theorem can be regarded as a far-reaching generalization of Mazzocca and Melone's approach to finite quadric Veronesean varieties. This approach takes projective properties","authors_text":"Hendrik Van Maldeghem, Jeroen Schillewaert","cross_cats":["math.DG","math.GR","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-03T21:41:58Z","title":"On the varieties of the second row of the split Freudenthal-Tits Magic Square"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0745","kind":"arxiv","version":4},"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:d18e52ef558fb1f180449cf87e74eb401bbc5b52216fc6eb984fe2d3d8380f8c","target":"record","created_at":"2026-05-18T00:54:15Z","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":"0b03449fabae1efe4bd6f5c0f8c8997f0f61eb9671c1b87c7a18cb0341b14984","cross_cats_sorted":["math.DG","math.GR","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-03T21:41:58Z","title_canon_sha256":"39ec10f2960b5403587473842beeb56462d960913ac9d3be8148c9f0d35e589f"},"schema_version":"1.0","source":{"id":"1308.0745","kind":"arxiv","version":4}},"canonical_sha256":"4bdbeb828b0affff1e5fdb53b87aa5f971b9aeadd7c37a18134896b2732700e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bdbeb828b0affff1e5fdb53b87aa5f971b9aeadd7c37a18134896b2732700e5","first_computed_at":"2026-05-18T00:54:15.970366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:15.970366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OI/HADx54R7o4vRl221ESFr6nJWfi6MyLgclXleYSyyfXxym54/uDy3pszml2nIYLhTZq+JneXFORP4eRlYoBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:15.970824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0745","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d18e52ef558fb1f180449cf87e74eb401bbc5b52216fc6eb984fe2d3d8380f8c","sha256:b1da026bdd4510d8bcd6280d937bc555563c6150d797e817f6c261113f6fab18"],"state_sha256":"7e72844c9a9300b7f54c4f70ddb60192f80828537de3b214842870148178b7f4"}