{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HBC4HC5LB2WRLL2LE7DPS74QXH","short_pith_number":"pith:HBC4HC5L","canonical_record":{"source":{"id":"1808.01927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-27T06:33:18Z","cross_cats_sorted":[],"title_canon_sha256":"5773c80cb00a90eb1bf588d4aef1f9334e934c2f30741b70fd43230d4a838be5","abstract_canon_sha256":"ac217bfccc3d25c2f1a128e8850e06a42b4cf0a0cf5584ce4876578b0444f20b"},"schema_version":"1.0"},"canonical_sha256":"3845c38bab0ead15af4b27c6f97f90b9dc71ebfa19d2ba17c12c63cdadb060ad","source":{"kind":"arxiv","id":"1808.01927","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01927","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01927v1","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01927","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"HBC4HC5LB2WR","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HBC4HC5LB2WRLL2L","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HBC4HC5L","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HBC4HC5LB2WRLL2LE7DPS74QXH","target":"record","payload":{"canonical_record":{"source":{"id":"1808.01927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-27T06:33:18Z","cross_cats_sorted":[],"title_canon_sha256":"5773c80cb00a90eb1bf588d4aef1f9334e934c2f30741b70fd43230d4a838be5","abstract_canon_sha256":"ac217bfccc3d25c2f1a128e8850e06a42b4cf0a0cf5584ce4876578b0444f20b"},"schema_version":"1.0"},"canonical_sha256":"3845c38bab0ead15af4b27c6f97f90b9dc71ebfa19d2ba17c12c63cdadb060ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:49.198779Z","signature_b64":"tCW9h3XTMacXIhIQeqBuaQViZtaj0y4sMGgEoXxq+FPavloRPteMPxpm3Ej6vNAzHDrEjjaQLTbIhNZBhmr+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3845c38bab0ead15af4b27c6f97f90b9dc71ebfa19d2ba17c12c63cdadb060ad","last_reissued_at":"2026-05-18T00:08:49.198188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:49.198188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.01927","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7uQJSCimRSCzI7hCYqdntGPzJ3tmOKRZG68oXhuYa6EDRpzoqNVrqpiN2dhh9NlFVUz80on7TWO5vQ1v/kYbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T20:16:12.981257Z"},"content_sha256":"0a06a87047111c7e0b61d74bae8b01b0a9fe6bd2ba38badd34463ad38aa505ad","schema_version":"1.0","event_id":"sha256:0a06a87047111c7e0b61d74bae8b01b0a9fe6bd2ba38badd34463ad38aa505ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HBC4HC5LB2WRLL2LE7DPS74QXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Torus equivariant Szeg\\H{o} kernel asymptotics on strongly pseudoconvex CR manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Chin-Yu Hsiao, Hendrik Herrmann, Xiaoshan Li","submitted_at":"2018-07-27T06:33:18Z","abstract_excerpt":"Let $(X, T^{1,0}X)$ be a compact strongly pseudoconvex CR manifold of dimension $2n+1$. Assume that $X$ admits a Torus action $T^d$. In this work, we study the behavior of torus equivariant Szeg\\H{o} kernels and prove that the weighted torus equivariant Szeg\\H{o} kernels admit asymptotic expansions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01927","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DVo/AamGevAw+Biokf4VrbcoACSEHeVle7RfaHXtg+QKUHC1UseHXaszupmqUAsOFgI4Iab4Nfm+82kSsIYTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T20:16:12.981617Z"},"content_sha256":"79d15982bf0bc1303a0504d5a2836915095017a04986ca30629276cf2bb0b61b","schema_version":"1.0","event_id":"sha256:79d15982bf0bc1303a0504d5a2836915095017a04986ca30629276cf2bb0b61b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HBC4HC5LB2WRLL2LE7DPS74QXH/bundle.json","state_url":"https://pith.science/pith/HBC4HC5LB2WRLL2LE7DPS74QXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HBC4HC5LB2WRLL2LE7DPS74QXH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-21T20:16:12Z","links":{"resolver":"https://pith.science/pith/HBC4HC5LB2WRLL2LE7DPS74QXH","bundle":"https://pith.science/pith/HBC4HC5LB2WRLL2LE7DPS74QXH/bundle.json","state":"https://pith.science/pith/HBC4HC5LB2WRLL2LE7DPS74QXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HBC4HC5LB2WRLL2LE7DPS74QXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HBC4HC5LB2WRLL2LE7DPS74QXH","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":"ac217bfccc3d25c2f1a128e8850e06a42b4cf0a0cf5584ce4876578b0444f20b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-27T06:33:18Z","title_canon_sha256":"5773c80cb00a90eb1bf588d4aef1f9334e934c2f30741b70fd43230d4a838be5"},"schema_version":"1.0","source":{"id":"1808.01927","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01927","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01927v1","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01927","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"HBC4HC5LB2WR","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HBC4HC5LB2WRLL2L","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HBC4HC5L","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:79d15982bf0bc1303a0504d5a2836915095017a04986ca30629276cf2bb0b61b","target":"graph","created_at":"2026-05-18T00:08:49Z","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 $(X, T^{1,0}X)$ be a compact strongly pseudoconvex CR manifold of dimension $2n+1$. Assume that $X$ admits a Torus action $T^d$. In this work, we study the behavior of torus equivariant Szeg\\H{o} kernels and prove that the weighted torus equivariant Szeg\\H{o} kernels admit asymptotic expansions.","authors_text":"Chin-Yu Hsiao, Hendrik Herrmann, Xiaoshan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-27T06:33:18Z","title":"Torus equivariant Szeg\\H{o} kernel asymptotics on strongly pseudoconvex CR manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01927","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":"sha256:0a06a87047111c7e0b61d74bae8b01b0a9fe6bd2ba38badd34463ad38aa505ad","target":"record","created_at":"2026-05-18T00:08:49Z","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":"ac217bfccc3d25c2f1a128e8850e06a42b4cf0a0cf5584ce4876578b0444f20b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-27T06:33:18Z","title_canon_sha256":"5773c80cb00a90eb1bf588d4aef1f9334e934c2f30741b70fd43230d4a838be5"},"schema_version":"1.0","source":{"id":"1808.01927","kind":"arxiv","version":1}},"canonical_sha256":"3845c38bab0ead15af4b27c6f97f90b9dc71ebfa19d2ba17c12c63cdadb060ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3845c38bab0ead15af4b27c6f97f90b9dc71ebfa19d2ba17c12c63cdadb060ad","first_computed_at":"2026-05-18T00:08:49.198188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:49.198188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tCW9h3XTMacXIhIQeqBuaQViZtaj0y4sMGgEoXxq+FPavloRPteMPxpm3Ej6vNAzHDrEjjaQLTbIhNZBhmr+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:49.198779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01927","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a06a87047111c7e0b61d74bae8b01b0a9fe6bd2ba38badd34463ad38aa505ad","sha256:79d15982bf0bc1303a0504d5a2836915095017a04986ca30629276cf2bb0b61b"],"state_sha256":"d04b5ed61af97a47eb369013324faf9a9bb28f09946f41321d31bcecdd6bae04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1/WUUfBBKu2OfOA7r9s/niNKw7VT8IyETtyvwnlIuQsC1qsnKUQfeNYXFfACB8I+aLT7hD1IECI8w7ikttwiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T20:16:12.983912Z","bundle_sha256":"0e4608c3a98758f3b60dd5ed65d03c6042e1ae6317b57fdc9c62146853fe225b"}}