{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:X4NEGIT42DSFVX6HTTSXMWMKMQ","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":"70c72f724162b8615f6cbde735d7556c3ed41a25fac2413d987607bcca63896d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-10-12T14:56:57Z","title_canon_sha256":"dd4c22af09b686793e3c9413fb2bfedea6ff9a279800aa239ef3946607e9efdb"},"schema_version":"1.0","source":{"id":"1510.03323","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03323","created_at":"2026-05-18T01:11:54Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03323v2","created_at":"2026-05-18T01:11:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03323","created_at":"2026-05-18T01:11:54Z"},{"alias_kind":"pith_short_12","alias_value":"X4NEGIT42DSF","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"X4NEGIT42DSFVX6H","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"X4NEGIT4","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:6af99ca4275eec0c8c01cd27a229795f5212ad8df773430573709dfd95b0c36b","target":"graph","created_at":"2026-05-18T01:11:54Z","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":"In this work, we obtain an unexpected geometric characterization of sphericity of a real-analytic Levi-nondegenerate hypersurface $M\\subset\\mathbb C^{2}$. We prove that $M$ is spherical if and only if its Segre\\,(-Webster) varieties satisfy an elementary combinatorial property, identical to a property of straight lines on the plane and known in Projective Geometry as the {\\em Desargues Theorem}.","authors_text":"Ilya Kossovskiy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-10-12T14:56:57Z","title":"Sphericity of a real hypersurface via projective geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03323","kind":"arxiv","version":2},"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:d634a3b9720e80e17452a17340dcd2d96ab7444b4d1eff1f226b171c10279ed9","target":"record","created_at":"2026-05-18T01:11:54Z","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":"70c72f724162b8615f6cbde735d7556c3ed41a25fac2413d987607bcca63896d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-10-12T14:56:57Z","title_canon_sha256":"dd4c22af09b686793e3c9413fb2bfedea6ff9a279800aa239ef3946607e9efdb"},"schema_version":"1.0","source":{"id":"1510.03323","kind":"arxiv","version":2}},"canonical_sha256":"bf1a43227cd0e45adfc79ce576598a642cfe5d2f49bc2a0795e3592351b607de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf1a43227cd0e45adfc79ce576598a642cfe5d2f49bc2a0795e3592351b607de","first_computed_at":"2026-05-18T01:11:54.981963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:54.981963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F5Vxl9HaPt4DvCAFYxmMqJaHCHRDRHrFcLhmBEtYpfqTe8YWOw5/plFoTNwfPlPePS10tv2HUPD+17RyjAeeCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:54.982326Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03323","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d634a3b9720e80e17452a17340dcd2d96ab7444b4d1eff1f226b171c10279ed9","sha256:6af99ca4275eec0c8c01cd27a229795f5212ad8df773430573709dfd95b0c36b"],"state_sha256":"cc458e3c31b8aa0a9b708045147eb08063d5578976c2290ad9c03af8cd0b2025"}