{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:65YDSJOSUXTS52KDIYPF33PSLV","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":"3fdfc4d4cb9e9adcdc025b4bf6da2351cdbd36e07779eb159c585038d063c7b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-09-02T00:54:39Z","title_canon_sha256":"c96f895e3b2e32624b4a13c6821ef97cf9c56e6f981e3f22ddec157abb04ead0"},"schema_version":"1.0","source":{"id":"1309.0279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0279","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0279v1","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0279","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"pith_short_12","alias_value":"65YDSJOSUXTS","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"65YDSJOSUXTS52KD","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"65YDSJOS","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:557283eef1a23a38d855e364b157c97fb9147d3bec5385928b18d673dac3684d","target":"graph","created_at":"2026-05-18T03:14:27Z","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 discuss a family $M_t^n$, with $n\\ge 2$, $t>1$, of real hypersurfaces in a complex affine $n$-dimensional quadric arising in connection with the classification of homogeneous compact simply-connected real-analytic hypersurfaces in ${\\mathbb C}^n$ due to Morimoto and Nagano. To finalize their classification, one needs to resolve the problem of the embeddability of $M_t^n$ in ${\\mathbb C}^n$ for $n=3,7$. We show that $M_t^7$ is not embeddable in ${\\mathbb C}^7$ for every $t$ and that $M_t^3$ is embeddable in ${\\mathbb C}^3$ for all $1<t<1+10^{-6}$. As a consequence of our analysis of a map co","authors_text":"Alexander Isaev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-09-02T00:54:39Z","title":"On the Classification of Homogeneous Hypersurfaces in Complex Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0279","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":"sha256:0708311226ad317e613aaba7e65711566f64eab80c4cc3e86701f9b4d1f2c0a2","target":"record","created_at":"2026-05-18T03:14:27Z","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":"3fdfc4d4cb9e9adcdc025b4bf6da2351cdbd36e07779eb159c585038d063c7b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-09-02T00:54:39Z","title_canon_sha256":"c96f895e3b2e32624b4a13c6821ef97cf9c56e6f981e3f22ddec157abb04ead0"},"schema_version":"1.0","source":{"id":"1309.0279","kind":"arxiv","version":1}},"canonical_sha256":"f7703925d2a5e72ee943461e5dedf25d71b7c23cf43f6c38e3f000895268864c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7703925d2a5e72ee943461e5dedf25d71b7c23cf43f6c38e3f000895268864c","first_computed_at":"2026-05-18T03:14:27.664201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:27.664201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ky80iS7W5XUfXDppUWOq7mA735T7aNImOJ22esXLvMS5Piv6n7IaDJl7MitwU4xvQ7M66HxXt7M3CZb3f+zABw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:27.664621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0708311226ad317e613aaba7e65711566f64eab80c4cc3e86701f9b4d1f2c0a2","sha256:557283eef1a23a38d855e364b157c97fb9147d3bec5385928b18d673dac3684d"],"state_sha256":"f21af26b58b4b8fa94799caf4d0ad1aa34b043105de4c4c0e7af952e5610d7e5"}