{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:VCK3LNMLEGODLIHU5RDOLARAJX","short_pith_number":"pith:VCK3LNML","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"},"canonical_sha256":"a895b5b58b219c35a0f4ec46e582204de533aa61cb01afe689a97826ad6c99b7","source":{"kind":"arxiv","id":"0909.0807","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0807","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0807v3","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0807","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"pith_short_12","alias_value":"VCK3LNMLEGOD","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VCK3LNMLEGODLIHU","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VCK3LNML","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:VCK3LNMLEGODLIHU5RDOLARAJX","target":"record","payload":{"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"},"canonical_sha256":"a895b5b58b219c35a0f4ec46e582204de533aa61cb01afe689a97826ad6c99b7","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"},"source_kind":"arxiv","source_id":"0909.0807","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3r5oTQZEb7xa1m4OkLMh9kA9BqRU6SjxPiZFYvOay4qJK0/U0JniEL6nHhpLmQ96usyzamPwmi4xg/FbDpvVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:24:15.682900Z"},"content_sha256":"ee05a4b710f4f2dc6ff16863b840acb89f04ce78566a582dcb64d535d7e66a17","schema_version":"1.0","event_id":"sha256:ee05a4b710f4f2dc6ff16863b840acb89f04ce78566a582dcb64d535d7e66a17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:VCK3LNMLEGODLIHU5RDOLARAJX","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nIXO+MwwAPDAGfRWtJuaAZzzRCP/jFDbb6qZmHpSjuTdYA62sdkIU+QbcLSHAZJOwQbHAkDWA8I8gBJdWT4kDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:24:15.683267Z"},"content_sha256":"9b30a0bae54d436b763beef1ec459372a415b571f4a942cb5ac047bb1336f712","schema_version":"1.0","event_id":"sha256:9b30a0bae54d436b763beef1ec459372a415b571f4a942cb5ac047bb1336f712"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX/bundle.json","state_url":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCK3LNMLEGODLIHU5RDOLARAJX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T01:24:15Z","links":{"resolver":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX","bundle":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX/bundle.json","state":"https://pith.science/pith/VCK3LNMLEGODLIHU5RDOLARAJX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCK3LNMLEGODLIHU5RDOLARAJX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VCK3LNMLEGODLIHU5RDOLARAJX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"277c27932b77be989b6affff01df426f6ed29758b353ca5de37842eeda31add5","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-04T04:26:14Z","title_canon_sha256":"1b3ae16537862c33d9cb78c09637104e45c1bb0d472250ead8bd2b4141dd8dc0"},"schema_version":"1.0","source":{"id":"0909.0807","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0807","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0807v3","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0807","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"pith_short_12","alias_value":"VCK3LNMLEGOD","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VCK3LNMLEGODLIHU","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VCK3LNML","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:9b30a0bae54d436b763beef1ec459372a415b571f4a942cb5ac047bb1336f712","target":"graph","created_at":"2026-05-18T03:29:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Clara L. Aldana, Fr\\'ed\\'eric Rochon, Pierre Albin","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-04T04:26:14Z","title":"Ricci flow and the determinant of the Laplacian on non-compact surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0807","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ee05a4b710f4f2dc6ff16863b840acb89f04ce78566a582dcb64d535d7e66a17","target":"record","created_at":"2026-05-18T03:29:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"277c27932b77be989b6affff01df426f6ed29758b353ca5de37842eeda31add5","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-04T04:26:14Z","title_canon_sha256":"1b3ae16537862c33d9cb78c09637104e45c1bb0d472250ead8bd2b4141dd8dc0"},"schema_version":"1.0","source":{"id":"0909.0807","kind":"arxiv","version":3}},"canonical_sha256":"a895b5b58b219c35a0f4ec46e582204de533aa61cb01afe689a97826ad6c99b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a895b5b58b219c35a0f4ec46e582204de533aa61cb01afe689a97826ad6c99b7","first_computed_at":"2026-05-18T03:29:28.146706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:28.146706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HBsukvTiRPY5EZ1WIL+syOAcssPdQyJL8Vl0U66UKLTidZKx9R73wgxCJNFrgAM/qMJPfbRxkbHdbRPFZ0FODg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:28.147407Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.0807","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee05a4b710f4f2dc6ff16863b840acb89f04ce78566a582dcb64d535d7e66a17","sha256:9b30a0bae54d436b763beef1ec459372a415b571f4a942cb5ac047bb1336f712"],"state_sha256":"0b7efc79dab3e86e9ba1fa2350af6c511ede78259363f84f555b31b6f74b566e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HO59VjpG1XToJfuVss5MuPLc/OHFeMnK8IN7N6P4YEGbknfWY9fg4heTDdffUl8+RscfG5UbyEUOQ2AgENpfAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T01:24:15.685518Z","bundle_sha256":"69f9acd6bef2ae878cd1555292802bf87173f4aeb1b5c4396c5378f5f8f3ea4f"}}