{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:DNTWTHQUH2HTNYRE7U6H4BBZOI","short_pith_number":"pith:DNTWTHQU","schema_version":"1.0","canonical_sha256":"1b67699e143e8f36e224fd3c7e0439721986ba1f81402f0c2d445ea7d2f97e97","source":{"kind":"arxiv","id":"1904.12950","version":3},"attestation_state":"computed","paper":{"title":"On the existence of Kobayashi and Bergman metrics for Model domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Nikolay Shcherbina","submitted_at":"2019-04-29T21:25:08Z","abstract_excerpt":"We prove that for a pseudoconvex domain of the form $\\mathfrak{A} = \\{(z, w) \\in \\mathbb C^2 : v > F(z, u)\\}$, where $w = u + iv$ and F is a continuous function on ${\\mathbb C}_z \\times {\\mathbb R}_u$, the following conditions are equivalent:\n  (1) The domain $\\mathfrak{A}$ is Kobayashi hyperbolic.\n  (2) The domain $\\mathfrak{A}$ is Brody hyperbolic.\n  (3) The domain $\\mathfrak{A}$ possesses a Bergman metric.\n  (4) The domain $\\mathfrak{A}$ possesses a bounded smooth strictly plurisubharmonic function, i.e. the core $\\mathfrak{c}(\\mathfrak{A})$ of $\\mathfrak{A}$ is empty.\n  (5) The graph $\\Gam"},"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":"1904.12950","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-04-29T21:25:08Z","cross_cats_sorted":[],"title_canon_sha256":"5de53de1e6c3a89daabfbf991f0bb98d103f5846dc9e4156f11b3e9d0b9edddf","abstract_canon_sha256":"e1328ffadc9e305061235db645dd39a3f98ea19ceca1e4086b85d9b982b2ad6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:01.240242Z","signature_b64":"TRjL7dmfSuqmEj+g/IMUBxKPR7tFlQw4a1TBpXuXiebHzGwJViHpN2VIXoMbOlOloAnWEqQNEQ/MnxOU97HEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b67699e143e8f36e224fd3c7e0439721986ba1f81402f0c2d445ea7d2f97e97","last_reissued_at":"2026-05-17T23:47:01.239750Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:01.239750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the existence of Kobayashi and Bergman metrics for Model domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Nikolay Shcherbina","submitted_at":"2019-04-29T21:25:08Z","abstract_excerpt":"We prove that for a pseudoconvex domain of the form $\\mathfrak{A} = \\{(z, w) \\in \\mathbb C^2 : v > F(z, u)\\}$, where $w = u + iv$ and F is a continuous function on ${\\mathbb C}_z \\times {\\mathbb R}_u$, the following conditions are equivalent:\n  (1) The domain $\\mathfrak{A}$ is Kobayashi hyperbolic.\n  (2) The domain $\\mathfrak{A}$ is Brody hyperbolic.\n  (3) The domain $\\mathfrak{A}$ possesses a Bergman metric.\n  (4) The domain $\\mathfrak{A}$ possesses a bounded smooth strictly plurisubharmonic function, i.e. the core $\\mathfrak{c}(\\mathfrak{A})$ of $\\mathfrak{A}$ is empty.\n  (5) The graph $\\Gam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12950","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":"1904.12950","created_at":"2026-05-17T23:47:01.239829+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.12950v3","created_at":"2026-05-17T23:47:01.239829+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12950","created_at":"2026-05-17T23:47:01.239829+00:00"},{"alias_kind":"pith_short_12","alias_value":"DNTWTHQUH2HT","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"DNTWTHQUH2HTNYRE","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"DNTWTHQU","created_at":"2026-05-18T12:33:15.570797+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/DNTWTHQUH2HTNYRE7U6H4BBZOI","json":"https://pith.science/pith/DNTWTHQUH2HTNYRE7U6H4BBZOI.json","graph_json":"https://pith.science/api/pith-number/DNTWTHQUH2HTNYRE7U6H4BBZOI/graph.json","events_json":"https://pith.science/api/pith-number/DNTWTHQUH2HTNYRE7U6H4BBZOI/events.json","paper":"https://pith.science/paper/DNTWTHQU"},"agent_actions":{"view_html":"https://pith.science/pith/DNTWTHQUH2HTNYRE7U6H4BBZOI","download_json":"https://pith.science/pith/DNTWTHQUH2HTNYRE7U6H4BBZOI.json","view_paper":"https://pith.science/paper/DNTWTHQU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.12950&json=true","fetch_graph":"https://pith.science/api/pith-number/DNTWTHQUH2HTNYRE7U6H4BBZOI/graph.json","fetch_events":"https://pith.science/api/pith-number/DNTWTHQUH2HTNYRE7U6H4BBZOI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DNTWTHQUH2HTNYRE7U6H4BBZOI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DNTWTHQUH2HTNYRE7U6H4BBZOI/action/storage_attestation","attest_author":"https://pith.science/pith/DNTWTHQUH2HTNYRE7U6H4BBZOI/action/author_attestation","sign_citation":"https://pith.science/pith/DNTWTHQUH2HTNYRE7U6H4BBZOI/action/citation_signature","submit_replication":"https://pith.science/pith/DNTWTHQUH2HTNYRE7U6H4BBZOI/action/replication_record"}},"created_at":"2026-05-17T23:47:01.239829+00:00","updated_at":"2026-05-17T23:47:01.239829+00:00"}