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Let $\\overline{X}:=X\\cup\\lbrace i\\infty\\rbrace$ denote the Satake compactification of $X$. Let $\\Omega_{\\overline{X}}$ denote the cotangent bundle on $\\overline{X}$. For $k\\gg1$, we derive an estimate for $\\mu_{\\overline{X}}^{\\mathrm{Ber},k}$, the Bergman metric associated to the line bundle $\\mathcal{L}^{k}:=\\Omega_{\\overline{X}}\\otimes \\mathcal{O}_{\\overline{X}}\\big((k-1)\\infty\\big)$.\n  For a given $d\\geq 1$, the"},"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":"2305.11609","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2023-05-19T11:38:47Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9e8f51ab2969aa47f1eb14952ea1a20d80b7ab5fae909e3fe84d6f653e48c720","abstract_canon_sha256":"6a1f13eb94f68738a0510687656f7271f7b7b9b39d01771d32191141499631b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:22:20.151229Z","signature_b64":"rQE0qZHWscc1rTCI1goLkPU+qTUewGwEEMDFFzGZvZsIJJfW9T+Vx0MnMudvHUeKL4lfn+6suFUdO7yS6gRaBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e1967f3dfbe20550d1107e8770602f0e3677a828de0ac1cfbe01a19205ab22c","last_reissued_at":"2026-07-05T08:22:20.150837Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:22:20.150837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimates of K\\\"ahler metrics on noncompact finite volume hyperbolic Riemann surfaces, and their symmetric products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Anilatmaja Aryasomayajula, Arijit Mukherjee","submitted_at":"2023-05-19T11:38:47Z","abstract_excerpt":"Let $X$ denote a noncompact finite volume hyperbolic Riemann surface of genus $g\\geq 2$, with only one puncture at $i\\infty$ (identifying $X$ with its universal cover $\\mathbb{H}$). Let $\\overline{X}:=X\\cup\\lbrace i\\infty\\rbrace$ denote the Satake compactification of $X$. Let $\\Omega_{\\overline{X}}$ denote the cotangent bundle on $\\overline{X}$. For $k\\gg1$, we derive an estimate for $\\mu_{\\overline{X}}^{\\mathrm{Ber},k}$, the Bergman metric associated to the line bundle $\\mathcal{L}^{k}:=\\Omega_{\\overline{X}}\\otimes \\mathcal{O}_{\\overline{X}}\\big((k-1)\\infty\\big)$.\n  For a given $d\\geq 1$, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.11609","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.11609/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2305.11609","created_at":"2026-07-05T08:22:20.150892+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.11609v3","created_at":"2026-07-05T08:22:20.150892+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.11609","created_at":"2026-07-05T08:22:20.150892+00:00"},{"alias_kind":"pith_short_12","alias_value":"BYMWP467XYQF","created_at":"2026-07-05T08:22:20.150892+00:00"},{"alias_kind":"pith_short_16","alias_value":"BYMWP467XYQFKDIR","created_at":"2026-07-05T08:22:20.150892+00:00"},{"alias_kind":"pith_short_8","alias_value":"BYMWP467","created_at":"2026-07-05T08:22:20.150892+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/BYMWP467XYQFKDIRA7UHOBQC6D","json":"https://pith.science/pith/BYMWP467XYQFKDIRA7UHOBQC6D.json","graph_json":"https://pith.science/api/pith-number/BYMWP467XYQFKDIRA7UHOBQC6D/graph.json","events_json":"https://pith.science/api/pith-number/BYMWP467XYQFKDIRA7UHOBQC6D/events.json","paper":"https://pith.science/paper/BYMWP467"},"agent_actions":{"view_html":"https://pith.science/pith/BYMWP467XYQFKDIRA7UHOBQC6D","download_json":"https://pith.science/pith/BYMWP467XYQFKDIRA7UHOBQC6D.json","view_paper":"https://pith.science/paper/BYMWP467","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.11609&json=true","fetch_graph":"https://pith.science/api/pith-number/BYMWP467XYQFKDIRA7UHOBQC6D/graph.json","fetch_events":"https://pith.science/api/pith-number/BYMWP467XYQFKDIRA7UHOBQC6D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BYMWP467XYQFKDIRA7UHOBQC6D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BYMWP467XYQFKDIRA7UHOBQC6D/action/storage_attestation","attest_author":"https://pith.science/pith/BYMWP467XYQFKDIRA7UHOBQC6D/action/author_attestation","sign_citation":"https://pith.science/pith/BYMWP467XYQFKDIRA7UHOBQC6D/action/citation_signature","submit_replication":"https://pith.science/pith/BYMWP467XYQFKDIRA7UHOBQC6D/action/replication_record"}},"created_at":"2026-07-05T08:22:20.150892+00:00","updated_at":"2026-07-05T08:22:20.150892+00:00"}