{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:STUYNZFICEV537IU62AVU67TRZ","short_pith_number":"pith:STUYNZFI","canonical_record":{"source":{"id":"1803.07653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-03-20T21:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"c3ad18ad8a6b0f6f434bbb32ad53fcb2787c366fc2893db92691a0f4a6ef0496","abstract_canon_sha256":"56d767c815db53c41dffcc5b02ac9216ba3a054a6831adfded7e43a5785a4569"},"schema_version":"1.0"},"canonical_sha256":"94e986e4a8112bddfd14f6815a7bf38e5beb0fc2d33b017c4bc64b32302a37ef","source":{"kind":"arxiv","id":"1803.07653","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07653","created_at":"2026-05-18T00:08:20Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07653v1","created_at":"2026-05-18T00:08:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07653","created_at":"2026-05-18T00:08:20Z"},{"alias_kind":"pith_short_12","alias_value":"STUYNZFICEV5","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"STUYNZFICEV537IU","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"STUYNZFI","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:STUYNZFICEV537IU62AVU67TRZ","target":"record","payload":{"canonical_record":{"source":{"id":"1803.07653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-03-20T21:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"c3ad18ad8a6b0f6f434bbb32ad53fcb2787c366fc2893db92691a0f4a6ef0496","abstract_canon_sha256":"56d767c815db53c41dffcc5b02ac9216ba3a054a6831adfded7e43a5785a4569"},"schema_version":"1.0"},"canonical_sha256":"94e986e4a8112bddfd14f6815a7bf38e5beb0fc2d33b017c4bc64b32302a37ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:20.933120Z","signature_b64":"/2npLv0AX5fwiA6T579fB6sI4udqw+aSVU1p6xP2pn3v7BFCNgeI52sqE2Zdw1EX2gTSi/1xZYqA331XkHO3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94e986e4a8112bddfd14f6815a7bf38e5beb0fc2d33b017c4bc64b32302a37ef","last_reissued_at":"2026-05-18T00:08:20.932539Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:20.932539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.07653","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":"2026-05-18T00:08:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NOK4qQAt9cDcT67NrgeAOaoOAqj4gEAzvQtAzakxt5VH7Gk/3AoABVs5WzYuIILfMGI+lgacGHTiHoxBk4+zDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:12:12.390858Z"},"content_sha256":"7f89ebb3e8c098375142fbb98596b86c2abfbbb9b19e2347cf5ca85e40a28d19","schema_version":"1.0","event_id":"sha256:7f89ebb3e8c098375142fbb98596b86c2abfbbb9b19e2347cf5ca85e40a28d19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:STUYNZFICEV537IU62AVU67TRZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Webster scalar curvature and sharp upper and lower bounds for the first positive eigenvalue of the Kohn-Laplacian on real hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Duong Ngoc Son, Song-Ying Li","submitted_at":"2018-03-20T21:00:00Z","abstract_excerpt":"Let $(M,\\theta)$ be a compact strictly pseudoconvex pseudohermitian manifold which is CR embedded into a complex space. In an earlier paper, Lin and the authors gave several sharp upper bounds for the first positive eigenvalue $\\lambda_1$ of the Kohn-Laplacian $\\Box_b$ on $(M,\\theta)$. In the present paper, we give a sharp upper bound for $\\lambda_1$, generalizing and extending some previous results. As a corollary, we obtain a Reilly-type estimate when $M$ is embedded into the standard sphere. In another direction, using a Lichnerowicz-type estimate by Chanillo, Chiu, and Yang and an explicit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07653","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":"2026-05-18T00:08:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mSpMc21+jDHPzUF8P62JM18VVsb5YpnQ/BDFc9WB/8kHouUR7QCxt2dtmqLl92nPBeyqVNwAYBQkqnV385BGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:12:12.391545Z"},"content_sha256":"50a70ea10623327ddac1843e950b8aed1b183f658fdbc7c7b638731893250824","schema_version":"1.0","event_id":"sha256:50a70ea10623327ddac1843e950b8aed1b183f658fdbc7c7b638731893250824"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/STUYNZFICEV537IU62AVU67TRZ/bundle.json","state_url":"https://pith.science/pith/STUYNZFICEV537IU62AVU67TRZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/STUYNZFICEV537IU62AVU67TRZ/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":"2026-06-07T06:12:12Z","links":{"resolver":"https://pith.science/pith/STUYNZFICEV537IU62AVU67TRZ","bundle":"https://pith.science/pith/STUYNZFICEV537IU62AVU67TRZ/bundle.json","state":"https://pith.science/pith/STUYNZFICEV537IU62AVU67TRZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/STUYNZFICEV537IU62AVU67TRZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:STUYNZFICEV537IU62AVU67TRZ","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":"56d767c815db53c41dffcc5b02ac9216ba3a054a6831adfded7e43a5785a4569","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-03-20T21:00:00Z","title_canon_sha256":"c3ad18ad8a6b0f6f434bbb32ad53fcb2787c366fc2893db92691a0f4a6ef0496"},"schema_version":"1.0","source":{"id":"1803.07653","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07653","created_at":"2026-05-18T00:08:20Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07653v1","created_at":"2026-05-18T00:08:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07653","created_at":"2026-05-18T00:08:20Z"},{"alias_kind":"pith_short_12","alias_value":"STUYNZFICEV5","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"STUYNZFICEV537IU","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"STUYNZFI","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:50a70ea10623327ddac1843e950b8aed1b183f658fdbc7c7b638731893250824","target":"graph","created_at":"2026-05-18T00:08:20Z","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 $(M,\\theta)$ be a compact strictly pseudoconvex pseudohermitian manifold which is CR embedded into a complex space. In an earlier paper, Lin and the authors gave several sharp upper bounds for the first positive eigenvalue $\\lambda_1$ of the Kohn-Laplacian $\\Box_b$ on $(M,\\theta)$. In the present paper, we give a sharp upper bound for $\\lambda_1$, generalizing and extending some previous results. As a corollary, we obtain a Reilly-type estimate when $M$ is embedded into the standard sphere. In another direction, using a Lichnerowicz-type estimate by Chanillo, Chiu, and Yang and an explicit","authors_text":"Duong Ngoc Son, Song-Ying Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-03-20T21:00:00Z","title":"The Webster scalar curvature and sharp upper and lower bounds for the first positive eigenvalue of the Kohn-Laplacian on real hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07653","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":"sha256:7f89ebb3e8c098375142fbb98596b86c2abfbbb9b19e2347cf5ca85e40a28d19","target":"record","created_at":"2026-05-18T00:08:20Z","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":"56d767c815db53c41dffcc5b02ac9216ba3a054a6831adfded7e43a5785a4569","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-03-20T21:00:00Z","title_canon_sha256":"c3ad18ad8a6b0f6f434bbb32ad53fcb2787c366fc2893db92691a0f4a6ef0496"},"schema_version":"1.0","source":{"id":"1803.07653","kind":"arxiv","version":1}},"canonical_sha256":"94e986e4a8112bddfd14f6815a7bf38e5beb0fc2d33b017c4bc64b32302a37ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94e986e4a8112bddfd14f6815a7bf38e5beb0fc2d33b017c4bc64b32302a37ef","first_computed_at":"2026-05-18T00:08:20.932539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:20.932539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/2npLv0AX5fwiA6T579fB6sI4udqw+aSVU1p6xP2pn3v7BFCNgeI52sqE2Zdw1EX2gTSi/1xZYqA331XkHO3CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:20.933120Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07653","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f89ebb3e8c098375142fbb98596b86c2abfbbb9b19e2347cf5ca85e40a28d19","sha256:50a70ea10623327ddac1843e950b8aed1b183f658fdbc7c7b638731893250824"],"state_sha256":"7edb455c492f6d587b978916d708c8b393ee58f81d084ce8152651c1b27fca17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"de4YUqkr9xx+9xjr8xnaDB8ezZSfdftauwvWkGmalrGENg0AeiWp1aONNhl1ksT/MM2HfH/rF+K0uJdP4yuHDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:12:12.394968Z","bundle_sha256":"976865d1db0beed7784ee181588bf4461c8f9f1c438eddca6f7e68b743255283"}}