{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6ZOIADXVPWBKA4C7HMSREZOGVQ","short_pith_number":"pith:6ZOIADXV","schema_version":"1.0","canonical_sha256":"f65c800ef57d82a0705f3b251265c6ac017ef7ef2bf3d341467474d96beeef72","source":{"kind":"arxiv","id":"1804.04880","version":1},"attestation_state":"computed","paper":{"title":"The first two coefficients of the Bergman function expansions for Cartan-Hartogs domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Zhiming Feng","submitted_at":"2018-04-13T10:49:29Z","abstract_excerpt":"Let $\\phi$ be a globally defined real K\\\"{a}hler potential on a domain $\\Omega\\subset \\mathbb{C}^d$, and $g_{F}$ be a K\\\"{a}hler metric on the Hartogs domain $ M=\\{(z,w)\\in \\Omega\\times\\mathbb{C}^{d_0}: \\|w\\|^2<e^{-\\phi(z)}\\}$ associated with the K\\\"{a}hler potential $\\Phi_{F}(z,w)=\\phi(z)+F(\\phi(z)+\\ln\\|w\\|^2)$. Firstly, we obtain explicit formulas of the coefficients $\\mathbf{a}_j\\;(j=1,2)$ of the Bergman function expansion for the Hartogs domain $( M,g_F)$ in a momentum profile $\\varphi$. Secondly, using explicit expressions of $\\mathbf{a}_j\\;(j=1,2)$, we obtain necessary and sufficient con"},"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":"1804.04880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-04-13T10:49:29Z","cross_cats_sorted":[],"title_canon_sha256":"b7145bffa573d62f2f7c2819c3241fe0aa87eafb58d6cd61f5fb95f031ba9e4c","abstract_canon_sha256":"aaed2c51f82b55e16562b9b548021a94e203471830e9c01d09d44ecce692a20d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:34.711678Z","signature_b64":"MwANQDNjNNEVWLDFhW2oBXGnOTvNikCySbJEW1q25dJXuNcuX6wzCQEe5aXzoKy5y/aq21zMrKAFYQCCTiGkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f65c800ef57d82a0705f3b251265c6ac017ef7ef2bf3d341467474d96beeef72","last_reissued_at":"2026-05-18T00:18:34.711109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:34.711109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The first two coefficients of the Bergman function expansions for Cartan-Hartogs domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Zhiming Feng","submitted_at":"2018-04-13T10:49:29Z","abstract_excerpt":"Let $\\phi$ be a globally defined real K\\\"{a}hler potential on a domain $\\Omega\\subset \\mathbb{C}^d$, and $g_{F}$ be a K\\\"{a}hler metric on the Hartogs domain $ M=\\{(z,w)\\in \\Omega\\times\\mathbb{C}^{d_0}: \\|w\\|^2<e^{-\\phi(z)}\\}$ associated with the K\\\"{a}hler potential $\\Phi_{F}(z,w)=\\phi(z)+F(\\phi(z)+\\ln\\|w\\|^2)$. Firstly, we obtain explicit formulas of the coefficients $\\mathbf{a}_j\\;(j=1,2)$ of the Bergman function expansion for the Hartogs domain $( M,g_F)$ in a momentum profile $\\varphi$. Secondly, using explicit expressions of $\\mathbf{a}_j\\;(j=1,2)$, we obtain necessary and sufficient con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04880","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.04880","created_at":"2026-05-18T00:18:34.711197+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.04880v1","created_at":"2026-05-18T00:18:34.711197+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04880","created_at":"2026-05-18T00:18:34.711197+00:00"},{"alias_kind":"pith_short_12","alias_value":"6ZOIADXVPWBK","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"6ZOIADXVPWBKA4C7","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"6ZOIADXV","created_at":"2026-05-18T12:32:11.075285+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/6ZOIADXVPWBKA4C7HMSREZOGVQ","json":"https://pith.science/pith/6ZOIADXVPWBKA4C7HMSREZOGVQ.json","graph_json":"https://pith.science/api/pith-number/6ZOIADXVPWBKA4C7HMSREZOGVQ/graph.json","events_json":"https://pith.science/api/pith-number/6ZOIADXVPWBKA4C7HMSREZOGVQ/events.json","paper":"https://pith.science/paper/6ZOIADXV"},"agent_actions":{"view_html":"https://pith.science/pith/6ZOIADXVPWBKA4C7HMSREZOGVQ","download_json":"https://pith.science/pith/6ZOIADXVPWBKA4C7HMSREZOGVQ.json","view_paper":"https://pith.science/paper/6ZOIADXV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.04880&json=true","fetch_graph":"https://pith.science/api/pith-number/6ZOIADXVPWBKA4C7HMSREZOGVQ/graph.json","fetch_events":"https://pith.science/api/pith-number/6ZOIADXVPWBKA4C7HMSREZOGVQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6ZOIADXVPWBKA4C7HMSREZOGVQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6ZOIADXVPWBKA4C7HMSREZOGVQ/action/storage_attestation","attest_author":"https://pith.science/pith/6ZOIADXVPWBKA4C7HMSREZOGVQ/action/author_attestation","sign_citation":"https://pith.science/pith/6ZOIADXVPWBKA4C7HMSREZOGVQ/action/citation_signature","submit_replication":"https://pith.science/pith/6ZOIADXVPWBKA4C7HMSREZOGVQ/action/replication_record"}},"created_at":"2026-05-18T00:18:34.711197+00:00","updated_at":"2026-05-18T00:18:34.711197+00:00"}