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Firstly, we will compute the explicit expression of the Rawnsley's $\\varepsilon$-function $\\varepsilon_{(\\alpha,g(\\mu;\\nu))}$ of $\\big(\\big(\\prod_{j=1}^k\\Omega_j\\big)^{{\\mathbb{B}}^{d_0}}(\\mu),g(\\mu;\\nu)\\big)$, where $g(\\mu;\\nu)$ is a K\\\"ahler metric associated with the K\\\"ahler potential $-\\sum_{j=1}^k\\nu_j\\ln N_{\\Omega_j}(z_j,\\overline{z_j})^{\\mu_j}-\\ln(\\prod_{j=1}^kN_{\\Omega_j}(z_j,\\overline{z_j})^{\\mu_j}-\\|w\\|^2)$ on the generalized Cartan-Hartogs domain $\\big(\\prod_{j=1}^k\\Omega_j\\big)^{{\\mathbb{B}}^{d_0}}(\\mu)$ and 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":"1811.04703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-12T13:04:45Z","cross_cats_sorted":[],"title_canon_sha256":"6ea8997d5bbd083adffd30f288a5d2e6c1c21b1baecbe788185b15939acfc732","abstract_canon_sha256":"904fbce5a4d4e41ef35afe936bb22e5c37992f008a754f91a2ba33d1bce1734e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:13.759930Z","signature_b64":"XkExHW++eDGe1ZBSvxfp5ggp0xL41vtOVhYKQY+99EkjIs5IXrG2xyUQzYTx9EWMrFaMqxZcr+gYI45Ak+mzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cd0be30c705e4864f0316cbf911216309a8e6dee4d9d39fa8464689edfc64c3","last_reissued_at":"2026-05-17T23:59:13.759384Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:13.759384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rawnsley's $\\varepsilon$-function on some Hartogs type domains over bounded symmetric domains and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Enchao Bi, Guicong Su, Zhenhan Tu, Zhiming Feng","submitted_at":"2018-11-12T13:04:45Z","abstract_excerpt":"The purpose of this paper is twofold. Firstly, we will compute the explicit expression of the Rawnsley's $\\varepsilon$-function $\\varepsilon_{(\\alpha,g(\\mu;\\nu))}$ of $\\big(\\big(\\prod_{j=1}^k\\Omega_j\\big)^{{\\mathbb{B}}^{d_0}}(\\mu),g(\\mu;\\nu)\\big)$, where $g(\\mu;\\nu)$ is a K\\\"ahler metric associated with the K\\\"ahler potential $-\\sum_{j=1}^k\\nu_j\\ln N_{\\Omega_j}(z_j,\\overline{z_j})^{\\mu_j}-\\ln(\\prod_{j=1}^kN_{\\Omega_j}(z_j,\\overline{z_j})^{\\mu_j}-\\|w\\|^2)$ on the generalized Cartan-Hartogs domain $\\big(\\prod_{j=1}^k\\Omega_j\\big)^{{\\mathbb{B}}^{d_0}}(\\mu)$ and obtain necessary and sufficient con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04703","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":"1811.04703","created_at":"2026-05-17T23:59:13.759447+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.04703v1","created_at":"2026-05-17T23:59:13.759447+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04703","created_at":"2026-05-17T23:59:13.759447+00:00"},{"alias_kind":"pith_short_12","alias_value":"TTIL4MGHAXSI","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"TTIL4MGHAXSIMTYD","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"TTIL4MGH","created_at":"2026-05-18T12:32:56.356000+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/TTIL4MGHAXSIMTYDC3F7SEJBMM","json":"https://pith.science/pith/TTIL4MGHAXSIMTYDC3F7SEJBMM.json","graph_json":"https://pith.science/api/pith-number/TTIL4MGHAXSIMTYDC3F7SEJBMM/graph.json","events_json":"https://pith.science/api/pith-number/TTIL4MGHAXSIMTYDC3F7SEJBMM/events.json","paper":"https://pith.science/paper/TTIL4MGH"},"agent_actions":{"view_html":"https://pith.science/pith/TTIL4MGHAXSIMTYDC3F7SEJBMM","download_json":"https://pith.science/pith/TTIL4MGHAXSIMTYDC3F7SEJBMM.json","view_paper":"https://pith.science/paper/TTIL4MGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.04703&json=true","fetch_graph":"https://pith.science/api/pith-number/TTIL4MGHAXSIMTYDC3F7SEJBMM/graph.json","fetch_events":"https://pith.science/api/pith-number/TTIL4MGHAXSIMTYDC3F7SEJBMM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TTIL4MGHAXSIMTYDC3F7SEJBMM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TTIL4MGHAXSIMTYDC3F7SEJBMM/action/storage_attestation","attest_author":"https://pith.science/pith/TTIL4MGHAXSIMTYDC3F7SEJBMM/action/author_attestation","sign_citation":"https://pith.science/pith/TTIL4MGHAXSIMTYDC3F7SEJBMM/action/citation_signature","submit_replication":"https://pith.science/pith/TTIL4MGHAXSIMTYDC3F7SEJBMM/action/replication_record"}},"created_at":"2026-05-17T23:59:13.759447+00:00","updated_at":"2026-05-17T23:59:13.759447+00:00"}