{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XGYF73PBEPZJHPATPX2WFLJR3X","short_pith_number":"pith:XGYF73PB","schema_version":"1.0","canonical_sha256":"b9b05fede123f293bc137df562ad31ddcd464462161f43812e9805d7d4e3365c","source":{"kind":"arxiv","id":"1309.3304","version":1},"attestation_state":"computed","paper":{"title":"Imbrex geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.MG","authors_text":"Hendrik Van Maldeghem, Jeroen Schillewaert","submitted_at":"2013-09-12T21:08:01Z","abstract_excerpt":"We introduce an axiom on strong parapolar spaces of diameter 2, which arises naturally in the framework of Hjelmslev geometries. This way, we characterize the Hjelmslev-Moufang plane and its relatives (line Grassmannians, certain half-spin geometries and Segre geometries). At the same time we provide a more general framework for a Lemma of Cohen, which is widely used to study parapolar spaces. As an application, if the geometries are embedded in projective space, we provide a common characterization of (projections of) Segre varieties, line Grassmann varieties, half-spin varieties of low rank,"},"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":"1309.3304","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-09-12T21:08:01Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"ef0b3af90df2025f9141c40e122b800a58bf4bad93fe013b8e63983a360ea4bc","abstract_canon_sha256":"c92e96c73ee7186e45cf5bfe2f0f99ef04e05778150ff6be645a9b99a53f6465"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:22.996875Z","signature_b64":"eXQr7V7UFjIER3chtKx7P2D9oDPOvJhhhZqyj13HaP5T1t2SRHUGilQmTpsEwQaz79Z+dozGyl9oPjBUnSLLCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9b05fede123f293bc137df562ad31ddcd464462161f43812e9805d7d4e3365c","last_reissued_at":"2026-05-18T03:13:22.996213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:22.996213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Imbrex geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.MG","authors_text":"Hendrik Van Maldeghem, Jeroen Schillewaert","submitted_at":"2013-09-12T21:08:01Z","abstract_excerpt":"We introduce an axiom on strong parapolar spaces of diameter 2, which arises naturally in the framework of Hjelmslev geometries. This way, we characterize the Hjelmslev-Moufang plane and its relatives (line Grassmannians, certain half-spin geometries and Segre geometries). At the same time we provide a more general framework for a Lemma of Cohen, which is widely used to study parapolar spaces. As an application, if the geometries are embedded in projective space, we provide a common characterization of (projections of) Segre varieties, line Grassmann varieties, half-spin varieties of low rank,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3304","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":"1309.3304","created_at":"2026-05-18T03:13:22.996312+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.3304v1","created_at":"2026-05-18T03:13:22.996312+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3304","created_at":"2026-05-18T03:13:22.996312+00:00"},{"alias_kind":"pith_short_12","alias_value":"XGYF73PBEPZJ","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XGYF73PBEPZJHPAT","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XGYF73PB","created_at":"2026-05-18T12:28:06.772260+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/XGYF73PBEPZJHPATPX2WFLJR3X","json":"https://pith.science/pith/XGYF73PBEPZJHPATPX2WFLJR3X.json","graph_json":"https://pith.science/api/pith-number/XGYF73PBEPZJHPATPX2WFLJR3X/graph.json","events_json":"https://pith.science/api/pith-number/XGYF73PBEPZJHPATPX2WFLJR3X/events.json","paper":"https://pith.science/paper/XGYF73PB"},"agent_actions":{"view_html":"https://pith.science/pith/XGYF73PBEPZJHPATPX2WFLJR3X","download_json":"https://pith.science/pith/XGYF73PBEPZJHPATPX2WFLJR3X.json","view_paper":"https://pith.science/paper/XGYF73PB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.3304&json=true","fetch_graph":"https://pith.science/api/pith-number/XGYF73PBEPZJHPATPX2WFLJR3X/graph.json","fetch_events":"https://pith.science/api/pith-number/XGYF73PBEPZJHPATPX2WFLJR3X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XGYF73PBEPZJHPATPX2WFLJR3X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XGYF73PBEPZJHPATPX2WFLJR3X/action/storage_attestation","attest_author":"https://pith.science/pith/XGYF73PBEPZJHPATPX2WFLJR3X/action/author_attestation","sign_citation":"https://pith.science/pith/XGYF73PBEPZJHPATPX2WFLJR3X/action/citation_signature","submit_replication":"https://pith.science/pith/XGYF73PBEPZJHPATPX2WFLJR3X/action/replication_record"}},"created_at":"2026-05-18T03:13:22.996312+00:00","updated_at":"2026-05-18T03:13:22.996312+00:00"}