{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IIJ5IEQVG7DEMNR6KX7WVSLRZP","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":"30f446108901bf73b870c2f5cb33879bfa3c9b0543202e273652fb2af4344e54","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-07T09:20:30Z","title_canon_sha256":"e15622d8cdc1e6804f42e5bbbc17253bd9c280ab81af12c0180fd6f266cf316b"},"schema_version":"1.0","source":{"id":"1301.1133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1133","created_at":"2026-05-18T03:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1133v1","created_at":"2026-05-18T03:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1133","created_at":"2026-05-18T03:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"IIJ5IEQVG7DE","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IIJ5IEQVG7DEMNR6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IIJ5IEQV","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:409e002829d73aa5a0cd039aafc56d4b6d67095ac80e766f438af6d4953503f6","target":"graph","created_at":"2026-05-18T03:37:06Z","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":"Let $M$ be a closed (compact with no boundary) spherical $CR$ manifold of dimension $2n+1$. Let $\\widetilde{M}$ be the universal covering of $M.$ Let $% \\Phi $ denote a $CR$ developing map {equation*} \\Phi :\\widetilde{M}\\rightarrow S^{2n+1} {equation*}% where $S^{2n+1}$ is the standard unit sphere in complex $n+1$-space $C^{n+1}$% . Suppose that the $CR$ Yamabe invariant of $M$ is positive. Then we show that $\\Phi $ is injective for $n\\geq 3$. In the case $n=2$, we also show that $\\Phi $ is injective under the condition: $s(M)<1$. It then follows that $M$ is uniformizable.","authors_text":"Hung-Lin Chiu, Jih-Hsin Cheng, Paul Yang","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-07T09:20:30Z","title":"Uniformization of spherical CR manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1133","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":"sha256:82551b571dd8a73147c9c4778c1a46a75dca5777b790d4e821b403156f939ce3","target":"record","created_at":"2026-05-18T03:37:06Z","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":"30f446108901bf73b870c2f5cb33879bfa3c9b0543202e273652fb2af4344e54","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-07T09:20:30Z","title_canon_sha256":"e15622d8cdc1e6804f42e5bbbc17253bd9c280ab81af12c0180fd6f266cf316b"},"schema_version":"1.0","source":{"id":"1301.1133","kind":"arxiv","version":1}},"canonical_sha256":"4213d4121537c646363e55ff6ac971cbdb044a2b5e63cd77f9be0445e7e9aa1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4213d4121537c646363e55ff6ac971cbdb044a2b5e63cd77f9be0445e7e9aa1b","first_computed_at":"2026-05-18T03:37:06.764963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:06.764963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bBtgZ42A14ZXhyUW3S5S3bjnDjjlu6qWLND1TDUaz/zRMW0ONCaGuFTa/1dIzxezmvV3PocSFhNK8LcB5DDSBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:06.765781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82551b571dd8a73147c9c4778c1a46a75dca5777b790d4e821b403156f939ce3","sha256:409e002829d73aa5a0cd039aafc56d4b6d67095ac80e766f438af6d4953503f6"],"state_sha256":"46b7e4ad6e875542c448f1420755a0a06047c65600868acfeafa907d757f2a4f"}