{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UPXRDHKBA7MV2XV7DG3WNJZMBW","short_pith_number":"pith:UPXRDHKB","schema_version":"1.0","canonical_sha256":"a3ef119d4107d95d5ebf19b766a72c0da6e65478b9c1df37c50815aa1c4e62e5","source":{"kind":"arxiv","id":"1302.0489","version":2},"attestation_state":"computed","paper":{"title":"Q-prime curvature on CR manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Kengo Hirachi","submitted_at":"2013-02-03T13:40:06Z","abstract_excerpt":"Q-prime curvature, which was introduced by J. Case and P. Yang, is a local invariant of pseudo-hermitian structure on CR manifolds that can be defined only when the Q-curvature vanishes identically. It is considered as a secondary invariant on CR manifolds and, in 3-dimensions, its integral agrees with the Burns-Epstein invariant, a Chern-Simons type invariant in CR geometry. We give an ambient metric construction of the Q-prime curvature and study its basic properties. In particular, we show that, for the boundary of a strictly pseudoconvex domain in a Stein manifold, the integral of the Q-pr"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1302.0489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-03T13:40:06Z","cross_cats_sorted":[],"title_canon_sha256":"e5329bad3336aac2f69331d951037607451087ef6ab57a995f97c9585f0b5657","abstract_canon_sha256":"495b4fc6776ae0605227f38cfa4aa122d5593f59353f22835b28259570ff5e0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:26.513458Z","signature_b64":"ZM2CI1Mt/GUUAVy9FJAUYkGrb/xjHg0dCxxOEKOGh2RNUIVlif5+eTahCDz3LH/YjUyYtoS62U7v6sQdxgPiDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3ef119d4107d95d5ebf19b766a72c0da6e65478b9c1df37c50815aa1c4e62e5","last_reissued_at":"2026-05-18T03:00:26.512775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:26.512775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Q-prime curvature on CR manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Kengo Hirachi","submitted_at":"2013-02-03T13:40:06Z","abstract_excerpt":"Q-prime curvature, which was introduced by J. Case and P. Yang, is a local invariant of pseudo-hermitian structure on CR manifolds that can be defined only when the Q-curvature vanishes identically. It is considered as a secondary invariant on CR manifolds and, in 3-dimensions, its integral agrees with the Burns-Epstein invariant, a Chern-Simons type invariant in CR geometry. We give an ambient metric construction of the Q-prime curvature and study its basic properties. In particular, we show that, for the boundary of a strictly pseudoconvex domain in a Stein manifold, the integral of the Q-pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0489","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1302.0489","created_at":"2026-05-18T03:00:26.512872+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.0489v2","created_at":"2026-05-18T03:00:26.512872+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0489","created_at":"2026-05-18T03:00:26.512872+00:00"},{"alias_kind":"pith_short_12","alias_value":"UPXRDHKBA7MV","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UPXRDHKBA7MV2XV7","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UPXRDHKB","created_at":"2026-05-18T12:28:02.375192+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UPXRDHKBA7MV2XV7DG3WNJZMBW","json":"https://pith.science/pith/UPXRDHKBA7MV2XV7DG3WNJZMBW.json","graph_json":"https://pith.science/api/pith-number/UPXRDHKBA7MV2XV7DG3WNJZMBW/graph.json","events_json":"https://pith.science/api/pith-number/UPXRDHKBA7MV2XV7DG3WNJZMBW/events.json","paper":"https://pith.science/paper/UPXRDHKB"},"agent_actions":{"view_html":"https://pith.science/pith/UPXRDHKBA7MV2XV7DG3WNJZMBW","download_json":"https://pith.science/pith/UPXRDHKBA7MV2XV7DG3WNJZMBW.json","view_paper":"https://pith.science/paper/UPXRDHKB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.0489&json=true","fetch_graph":"https://pith.science/api/pith-number/UPXRDHKBA7MV2XV7DG3WNJZMBW/graph.json","fetch_events":"https://pith.science/api/pith-number/UPXRDHKBA7MV2XV7DG3WNJZMBW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UPXRDHKBA7MV2XV7DG3WNJZMBW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UPXRDHKBA7MV2XV7DG3WNJZMBW/action/storage_attestation","attest_author":"https://pith.science/pith/UPXRDHKBA7MV2XV7DG3WNJZMBW/action/author_attestation","sign_citation":"https://pith.science/pith/UPXRDHKBA7MV2XV7DG3WNJZMBW/action/citation_signature","submit_replication":"https://pith.science/pith/UPXRDHKBA7MV2XV7DG3WNJZMBW/action/replication_record"}},"created_at":"2026-05-18T03:00:26.512872+00:00","updated_at":"2026-05-18T03:00:26.512872+00:00"}