{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:VCK3LNMLEGODLIHU5RDOLARAJX","short_pith_number":"pith:VCK3LNML","schema_version":"1.0","canonical_sha256":"a895b5b58b219c35a0f4ec46e582204de533aa61cb01afe689a97826ad6c99b7","source":{"kind":"arxiv","id":"0909.0807","version":3},"attestation_state":"computed","paper":{"title":"Ricci flow and the determinant of the Laplacian on non-compact surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Clara L. Aldana, Fr\\'ed\\'eric Rochon, Pierre Albin","submitted_at":"2009-09-04T04:26:14Z","abstract_excerpt":"On compact surfaces with or without boundary, Osgood, Phillips and Sarnak proved that the maximum of the determinant of the Laplacian within a conformal class of metrics with fixed area occurs at a metric of constant curvature and, for negative Euler characteristic, exhibited a flow from a given metric to a constant curvature metric along which the determinant increases. The aim of this paper is to perform a similar analysis for the determinant of the Laplacian on a non-compact surface whose ends are asymptotic to hyperbolic funnels or cusps. In that context, we show that the Ricci flow conver"},"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":"0909.0807","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-04T04:26:14Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"1b3ae16537862c33d9cb78c09637104e45c1bb0d472250ead8bd2b4141dd8dc0","abstract_canon_sha256":"277c27932b77be989b6affff01df426f6ed29758b353ca5de37842eeda31add5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:28.147407Z","signature_b64":"HBsukvTiRPY5EZ1WIL+syOAcssPdQyJL8Vl0U66UKLTidZKx9R73wgxCJNFrgAM/qMJPfbRxkbHdbRPFZ0FODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a895b5b58b219c35a0f4ec46e582204de533aa61cb01afe689a97826ad6c99b7","last_reissued_at":"2026-05-18T03:29:28.146706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:28.146706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ricci flow and the determinant of the Laplacian on non-compact surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Clara L. Aldana, Fr\\'ed\\'eric Rochon, Pierre Albin","submitted_at":"2009-09-04T04:26:14Z","abstract_excerpt":"On compact surfaces with or without boundary, Osgood, Phillips and Sarnak proved that the maximum of the determinant of the Laplacian within a conformal class of metrics with fixed area occurs at a metric of constant curvature and, for negative Euler characteristic, exhibited a flow from a given metric to a constant curvature metric along which the determinant increases. The aim of this paper is to perform a similar analysis for the determinant of the Laplacian on a non-compact surface whose ends are asymptotic to hyperbolic funnels or cusps. In that context, we show that the Ricci flow conver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0807","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":"0909.0807","created_at":"2026-05-18T03:29:28.146821+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.0807v3","created_at":"2026-05-18T03:29:28.146821+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0807","created_at":"2026-05-18T03:29:28.146821+00:00"},{"alias_kind":"pith_short_12","alias_value":"VCK3LNMLEGOD","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"VCK3LNMLEGODLIHU","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"VCK3LNML","created_at":"2026-05-18T12:26:02.257875+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/VCK3LNMLEGODLIHU5RDOLARAJX","json":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX.json","graph_json":"https://pith.science/api/pith-number/VCK3LNMLEGODLIHU5RDOLARAJX/graph.json","events_json":"https://pith.science/api/pith-number/VCK3LNMLEGODLIHU5RDOLARAJX/events.json","paper":"https://pith.science/paper/VCK3LNML"},"agent_actions":{"view_html":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX","download_json":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX.json","view_paper":"https://pith.science/paper/VCK3LNML","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.0807&json=true","fetch_graph":"https://pith.science/api/pith-number/VCK3LNMLEGODLIHU5RDOLARAJX/graph.json","fetch_events":"https://pith.science/api/pith-number/VCK3LNMLEGODLIHU5RDOLARAJX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX/action/storage_attestation","attest_author":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX/action/author_attestation","sign_citation":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX/action/citation_signature","submit_replication":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX/action/replication_record"}},"created_at":"2026-05-18T03:29:28.146821+00:00","updated_at":"2026-05-18T03:29:28.146821+00:00"}