{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JMBYLUPZEB4LRPCHMW72GTXQ52","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":"ca6e79ea4d39b62e845d1394c0d4f1f5839e15ef46a5f9e33304ea63d60ec27e","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-14T23:55:23Z","title_canon_sha256":"d8b8b15e6f1ca5166fd6e11dd22693a676ab9c2830fd51ae6a082051fa8e3bf4"},"schema_version":"1.0","source":{"id":"1610.04669","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04669","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04669v2","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04669","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"JMBYLUPZEB4L","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JMBYLUPZEB4LRPCH","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JMBYLUPZ","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:83ff48b12a758899e918102392c266fc4ef595427e3037c8298ebb64c48fd707","target":"graph","created_at":"2026-05-18T00:06:21Z","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 connected strongly pseudoconvex CR manifold of dimension $2n+1, n \\ge 1$ with a transversal CR $S^1$ action on $X$. We establish an asymptotic expansion for the $m$-th Fourier component of the Szeg\\H{o} kernel function as $m\\rightarrow\\infty$, where the expansion involves a contribution in terms of a distance function from lower dimensional strata of the $S^1$ action. We also obtain explicit formulas for the first three coefficients of the expansion.","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":"2016-10-14T23:55:23Z","title":"Szeg\\H{o} kernel asymptotic expansion on CR manifolds with $S^1$ action"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04669","kind":"arxiv","version":2},"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:fbc56f2af16f34da9adc2e12aff71e78614a381cc7f18da42e2eaaa464480d7e","target":"record","created_at":"2026-05-18T00:06:21Z","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":"ca6e79ea4d39b62e845d1394c0d4f1f5839e15ef46a5f9e33304ea63d60ec27e","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-14T23:55:23Z","title_canon_sha256":"d8b8b15e6f1ca5166fd6e11dd22693a676ab9c2830fd51ae6a082051fa8e3bf4"},"schema_version":"1.0","source":{"id":"1610.04669","kind":"arxiv","version":2}},"canonical_sha256":"4b0385d1f92078b8bc4765bfa34ef0ee89980d86d976b325886835028b463136","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b0385d1f92078b8bc4765bfa34ef0ee89980d86d976b325886835028b463136","first_computed_at":"2026-05-18T00:06:21.043447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:21.043447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EfGrXYDWVKmi4XXGoL6k9e/NSzstU3MhCXACm0ZR/air0H13cxXYR1UjFnpR+RQf1kaVfYZ8yiLSvFpMrxPcBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:21.043890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04669","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbc56f2af16f34da9adc2e12aff71e78614a381cc7f18da42e2eaaa464480d7e","sha256:83ff48b12a758899e918102392c266fc4ef595427e3037c8298ebb64c48fd707"],"state_sha256":"077bf88e2dd7d882232cebeea006e293563dc7d5af3252a520f5707668333ed5"}