{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KRNGJ6Q4DBWMD5TDVC4JPTECP3","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":"998f8f6ec0f35c2a58a36e74ae5a1b28b80caae997a96f5c4e203250eb0f07d9","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-12-12T19:32:54Z","title_canon_sha256":"9f02c2c5606f3cf4efd1f515580122734c6457e348f3d42935f63642dc2739ce"},"schema_version":"1.0","source":{"id":"1512.03952","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03952","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03952v3","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03952","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"KRNGJ6Q4DBWM","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KRNGJ6Q4DBWMD5TD","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KRNGJ6Q4","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:ddde38081fa191dd191de96ea5046d99f8ef7ca48d7278c437d501f824b9e3a9","target":"graph","created_at":"2026-05-18T00:13:38Z","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 $X$ be a compact strongly pseudoconvex CR manifold with a transversal CR $S^1$-action. In this paper, we establish the asymptotic expansion of Szeg\\H{o} kernels of positive Fourier components and by using the asymptotics, we show that $X$ can be equivariant CR embedded into some $\\mathbb C^N$ equipped with a simple $S^1$-action. An equivariant embedding of quasi-regular Sasakian manifold is also derived.","authors_text":"Chin-Yu Hsiao, Hendrik Herrmann, Xiaoshan Li","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-12-12T19:32:54Z","title":"Szeg\\H{o} kernel expansion and equivariant embedding of CR manifolds with circle action"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03952","kind":"arxiv","version":3},"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":"sha256:03e0c3fd53ab3692920ebb808d5235aa45a6aebf8870f458d7997b17cb50b82c","target":"record","created_at":"2026-05-18T00:13:38Z","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":"998f8f6ec0f35c2a58a36e74ae5a1b28b80caae997a96f5c4e203250eb0f07d9","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-12-12T19:32:54Z","title_canon_sha256":"9f02c2c5606f3cf4efd1f515580122734c6457e348f3d42935f63642dc2739ce"},"schema_version":"1.0","source":{"id":"1512.03952","kind":"arxiv","version":3}},"canonical_sha256":"545a64fa1c186cc1f663a8b897cc827eef89724718fbf567a13637c6f0e92f0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"545a64fa1c186cc1f663a8b897cc827eef89724718fbf567a13637c6f0e92f0e","first_computed_at":"2026-05-18T00:13:38.268137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:38.268137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g4NkN2ONYurfnUejCi1i2Jt4XBReY8oR2gWCstHSq1gtt3NU4wXTifzpPVYBLnIh1h1yPl1FGxFjztjqyFEGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:38.268860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03952","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03e0c3fd53ab3692920ebb808d5235aa45a6aebf8870f458d7997b17cb50b82c","sha256:ddde38081fa191dd191de96ea5046d99f8ef7ca48d7278c437d501f824b9e3a9"],"state_sha256":"2fee705b359170f3ad903dcc4f98eb2fe65265f23347a9cdeb555d4cc276175d"}