{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XGYF73PBEPZJHPATPX2WFLJR3X","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":"c92e96c73ee7186e45cf5bfe2f0f99ef04e05778150ff6be645a9b99a53f6465","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-09-12T21:08:01Z","title_canon_sha256":"ef0b3af90df2025f9141c40e122b800a58bf4bad93fe013b8e63983a360ea4bc"},"schema_version":"1.0","source":{"id":"1309.3304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3304","created_at":"2026-05-18T03:13:22Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3304v1","created_at":"2026-05-18T03:13:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3304","created_at":"2026-05-18T03:13:22Z"},{"alias_kind":"pith_short_12","alias_value":"XGYF73PBEPZJ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XGYF73PBEPZJHPAT","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XGYF73PB","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:61fdc2bace0efbbda8b50446fcc61a57a459fc59717eb9d2dd765488b396deb2","target":"graph","created_at":"2026-05-18T03:13:22Z","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":"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,","authors_text":"Hendrik Van Maldeghem, Jeroen Schillewaert","cross_cats":["math.CO","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-09-12T21:08:01Z","title":"Imbrex geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3304","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:b3c6dddba92301877a36f4db5166aec009b12878daf1e9c10fe134774ee65037","target":"record","created_at":"2026-05-18T03:13:22Z","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":"c92e96c73ee7186e45cf5bfe2f0f99ef04e05778150ff6be645a9b99a53f6465","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-09-12T21:08:01Z","title_canon_sha256":"ef0b3af90df2025f9141c40e122b800a58bf4bad93fe013b8e63983a360ea4bc"},"schema_version":"1.0","source":{"id":"1309.3304","kind":"arxiv","version":1}},"canonical_sha256":"b9b05fede123f293bc137df562ad31ddcd464462161f43812e9805d7d4e3365c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9b05fede123f293bc137df562ad31ddcd464462161f43812e9805d7d4e3365c","first_computed_at":"2026-05-18T03:13:22.996213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:22.996213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eXQr7V7UFjIER3chtKx7P2D9oDPOvJhhhZqyj13HaP5T1t2SRHUGilQmTpsEwQaz79Z+dozGyl9oPjBUnSLLCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:22.996875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3304","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3c6dddba92301877a36f4db5166aec009b12878daf1e9c10fe134774ee65037","sha256:61fdc2bace0efbbda8b50446fcc61a57a459fc59717eb9d2dd765488b396deb2"],"state_sha256":"ba61b9d3d6710e10175dbf8e7abaa67e3b5f9ad3e7b538193d795029a77f5ea3"}