{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FTCRX64XLT3M2CAG4H75LU7FXR","short_pith_number":"pith:FTCRX64X","schema_version":"1.0","canonical_sha256":"2cc51bfb975cf6cd0806e1ffd5d3e5bc73f145aff659e8859fc4d645ec82a30a","source":{"kind":"arxiv","id":"1610.07016","version":3},"attestation_state":"computed","paper":{"title":"Bergman kernel and hyperconvexity index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bo-Yong Chen","submitted_at":"2016-10-22T08:49:55Z","abstract_excerpt":"Let $\\Omega\\subset {\\mathbb C}^n$ be a bounded domain with the hyperconvexity index $\\alpha(\\Omega)>0$. Let $\\varrho$ be the relative extremal function of a fixed closed ball in $\\Omega$ and set $\\mu:=|\\varrho|(1+|\\log|\\varrho||)^{-1}$, $\\nu:=|\\varrho|(1+|\\log|\\varrho||)^n$. We obtain the following estimates for the Bergman kernel: (1) For every $0<\\alpha<\\alpha(\\Omega)$ and $2\\le p<2+\\frac{2\\alpha(\\Omega)}{2n-\\alpha(\\Omega)}$, there exists a constant $C>0$ such that $\\int_\\Omega |\\frac{K_\\Omega(\\cdot,w)}{\\sqrt{K_\\Omega(w)}}|^{p}\\le C |\\mu(w)|^{-\\frac{(p-2) n}\\alpha}$ for all $w\\in \\Omega$. (2"},"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":"1610.07016","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-22T08:49:55Z","cross_cats_sorted":[],"title_canon_sha256":"fc4158bba4dfb6f0169ece28a17fc42eb98bc2f6a3d41a66a119f0fc2379089a","abstract_canon_sha256":"562155185d05f78605495fb4b6bc76d2d2f36a80633fc10a17036d403099e299"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:57.091617Z","signature_b64":"xgRggOifrZGVzlgmCy5RCbAAEUK8tnYeffWa3pRMwDzSiVVpmZfbd9e+QsIrIgTKdBWyMcDAvDERxND576u/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cc51bfb975cf6cd0806e1ffd5d3e5bc73f145aff659e8859fc4d645ec82a30a","last_reissued_at":"2026-05-18T00:20:57.091058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:57.091058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bergman kernel and hyperconvexity index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bo-Yong Chen","submitted_at":"2016-10-22T08:49:55Z","abstract_excerpt":"Let $\\Omega\\subset {\\mathbb C}^n$ be a bounded domain with the hyperconvexity index $\\alpha(\\Omega)>0$. Let $\\varrho$ be the relative extremal function of a fixed closed ball in $\\Omega$ and set $\\mu:=|\\varrho|(1+|\\log|\\varrho||)^{-1}$, $\\nu:=|\\varrho|(1+|\\log|\\varrho||)^n$. We obtain the following estimates for the Bergman kernel: (1) For every $0<\\alpha<\\alpha(\\Omega)$ and $2\\le p<2+\\frac{2\\alpha(\\Omega)}{2n-\\alpha(\\Omega)}$, there exists a constant $C>0$ such that $\\int_\\Omega |\\frac{K_\\Omega(\\cdot,w)}{\\sqrt{K_\\Omega(w)}}|^{p}\\le C |\\mu(w)|^{-\\frac{(p-2) n}\\alpha}$ for all $w\\in \\Omega$. (2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07016","kind":"arxiv","version":3},"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":"1610.07016","created_at":"2026-05-18T00:20:57.091154+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.07016v3","created_at":"2026-05-18T00:20:57.091154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07016","created_at":"2026-05-18T00:20:57.091154+00:00"},{"alias_kind":"pith_short_12","alias_value":"FTCRX64XLT3M","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FTCRX64XLT3M2CAG","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FTCRX64X","created_at":"2026-05-18T12:30:15.759754+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/FTCRX64XLT3M2CAG4H75LU7FXR","json":"https://pith.science/pith/FTCRX64XLT3M2CAG4H75LU7FXR.json","graph_json":"https://pith.science/api/pith-number/FTCRX64XLT3M2CAG4H75LU7FXR/graph.json","events_json":"https://pith.science/api/pith-number/FTCRX64XLT3M2CAG4H75LU7FXR/events.json","paper":"https://pith.science/paper/FTCRX64X"},"agent_actions":{"view_html":"https://pith.science/pith/FTCRX64XLT3M2CAG4H75LU7FXR","download_json":"https://pith.science/pith/FTCRX64XLT3M2CAG4H75LU7FXR.json","view_paper":"https://pith.science/paper/FTCRX64X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.07016&json=true","fetch_graph":"https://pith.science/api/pith-number/FTCRX64XLT3M2CAG4H75LU7FXR/graph.json","fetch_events":"https://pith.science/api/pith-number/FTCRX64XLT3M2CAG4H75LU7FXR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FTCRX64XLT3M2CAG4H75LU7FXR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FTCRX64XLT3M2CAG4H75LU7FXR/action/storage_attestation","attest_author":"https://pith.science/pith/FTCRX64XLT3M2CAG4H75LU7FXR/action/author_attestation","sign_citation":"https://pith.science/pith/FTCRX64XLT3M2CAG4H75LU7FXR/action/citation_signature","submit_replication":"https://pith.science/pith/FTCRX64XLT3M2CAG4H75LU7FXR/action/replication_record"}},"created_at":"2026-05-18T00:20:57.091154+00:00","updated_at":"2026-05-18T00:20:57.091154+00:00"}