{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EGDQLN2S5IEAOTHKAUZETH7HPG","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":"1fbdf3657418a98ecdf022b197244422cb68c8a8aba636047ec9ecb5315fc199","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-20T12:38:49Z","title_canon_sha256":"b6120f71e2d4647fc775799c2d6e7814b8017e9d1cb4ceb2f53555add247d56a"},"schema_version":"1.0","source":{"id":"1802.07087","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07087","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07087v1","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07087","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"EGDQLN2S5IEA","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EGDQLN2S5IEAOTHK","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EGDQLN2S","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:460df5aec2eb548a448953a02d62efb85c178a27427064f6d4db9ed2d4ae6088","target":"graph","created_at":"2026-05-18T00:22:53Z","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":"Based on uniform CR Sobolev inequality and Moser iteration, this paper investigates the convergence of closed pseudo-Hermitian manifolds. In terms of the subelliptic inequality, the set of closed normalized pseudo-Einstein manifolds with some uniform geometric conditions is compact. Moreover, the set of closed normalized Sasakian $\\eta$-Einstein $(2n+1)$-manifolds with Carnot-Carath\\'eodory distance bounded from above, volume bounded from below and $L^{n + \\frac{1}{2}}$ norm of pseudo-Hermitian curvature bounded is $C^\\infty$ compact. As an application, we will deduce some pointed convergence ","authors_text":"Shu-Cheng Chang, Yibin Ren, Yuxin Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-20T12:38:49Z","title":"Convergence of Closed Pseudo-Hermitian Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07087","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":"sha256:7ee4c6dbd6a3cbb15b82db834754c9569e49b9d75b8a5ae58ce436c7efc1adc3","target":"record","created_at":"2026-05-18T00:22:53Z","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":"1fbdf3657418a98ecdf022b197244422cb68c8a8aba636047ec9ecb5315fc199","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-20T12:38:49Z","title_canon_sha256":"b6120f71e2d4647fc775799c2d6e7814b8017e9d1cb4ceb2f53555add247d56a"},"schema_version":"1.0","source":{"id":"1802.07087","kind":"arxiv","version":1}},"canonical_sha256":"218705b752ea08074cea0532499fe7799550e95e8494f3517b320a7a7873de31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"218705b752ea08074cea0532499fe7799550e95e8494f3517b320a7a7873de31","first_computed_at":"2026-05-18T00:22:53.586001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:53.586001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dS9XWlRFUzgznglqhUsWddxPzt8AObU4TZTvfFSC0MW8gGVfTlZDjgApN4YwFYRXyVRjtwvk1dfq1sakTcydBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:53.586423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07087","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ee4c6dbd6a3cbb15b82db834754c9569e49b9d75b8a5ae58ce436c7efc1adc3","sha256:460df5aec2eb548a448953a02d62efb85c178a27427064f6d4db9ed2d4ae6088"],"state_sha256":"681f99f9f29b9683265ebf98111992a1c8de46135f6b862564194d0bde15feb3"}