{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5KAYHTLF6M556JFSRAV76SYL72","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":"6b577764c21b78bc0773f626d0ff051a712376745e0c001a46a7eba95ef6681e","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-14T18:20:00Z","title_canon_sha256":"83848cce43e609b2641d929064ad4d4ab7f567373bde398a1d12f37e6a5e2252"},"schema_version":"1.0","source":{"id":"1106.2779","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2779","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2779v1","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2779","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"pith_short_12","alias_value":"5KAYHTLF6M55","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5KAYHTLF6M556JFS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5KAYHTLF","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:27a8b474de0627872c5dd30bd739b6bfbfaf80660749fbfeb971111b77e921e8","target":"graph","created_at":"2026-05-18T04:20:04Z","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 consider a class of compact homogeneous CR manifolds, that we call $\\mathfrak n$-reductive, which includes the orbits of minimal dimension of a compact Lie group $K_0$ in an algebraic homogeneous variety of its complexification $K$. For these manifolds we define canonical equivariant fibrations onto complex flag manifolds. The simplest example is the Hopf fibration $S^3\\to\\mathbb{CP}^1$.\n  In general these fibrations are not $CR$ submersions, however they satisfy a weaker condition that we introduce here, namely they are CR-deployments.","authors_text":"Andrea Altomani, Costantino Medori, Mauro Nacinovich","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-14T18:20:00Z","title":"Reductive compact homogeneous CR manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2779","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:b2ba60a24ce88eca58d3b1c1fcd00bed5fd34a294186a6984ec1113927237567","target":"record","created_at":"2026-05-18T04:20:04Z","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":"6b577764c21b78bc0773f626d0ff051a712376745e0c001a46a7eba95ef6681e","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-14T18:20:00Z","title_canon_sha256":"83848cce43e609b2641d929064ad4d4ab7f567373bde398a1d12f37e6a5e2252"},"schema_version":"1.0","source":{"id":"1106.2779","kind":"arxiv","version":1}},"canonical_sha256":"ea8183cd65f33bdf24b2882bff4b0bfe9834eeea4efdaa126e27d7af75e99b11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea8183cd65f33bdf24b2882bff4b0bfe9834eeea4efdaa126e27d7af75e99b11","first_computed_at":"2026-05-18T04:20:04.162970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:04.162970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rsptOHyvL2RXQlLPCnaQyvOT5E76rMXWcE2paHKi3yFt0SFa2xIoO9fSqNmRDXY3WshXzynfj1ZQB2QWQnyoAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:04.163432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.2779","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2ba60a24ce88eca58d3b1c1fcd00bed5fd34a294186a6984ec1113927237567","sha256:27a8b474de0627872c5dd30bd739b6bfbfaf80660749fbfeb971111b77e921e8"],"state_sha256":"50a7353bc61a6c8f0533e969d3e27d7070d237a007d66f072ebac47af9f71732"}