{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:F2KQ6AQQFQBAZSMOQAYIIGVPB7","short_pith_number":"pith:F2KQ6AQQ","schema_version":"1.0","canonical_sha256":"2e950f02102c020cc98e8030841aaf0fea3a6ae7e574e97012e4f9de86a87ce3","source":{"kind":"arxiv","id":"math/0701727","version":2},"attestation_state":"computed","paper":{"title":"The determinant of the Dirichlet-to-Neumann map for surfaces with boundary","license":"","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Colin Guillarmou (JAD), Laurent Guillop\\'e (LMJL)","submitted_at":"2007-01-25T05:45:56Z","abstract_excerpt":"For any orientable compact surface with boundary, we compute the regularized determinant of the Dirichlet-to-Neumann (DN) map in terms of particular values of dynamical zeta functions by using natural uniformizations, one due to Mazzeo-Taylor, the other to Osgood-Phillips-Sarnak. We also relate in any dimension the DN map for the Yamabe operator to the scattering operator for a conformally compact related problem by using uniformization."},"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":"math/0701727","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.SP","submitted_at":"2007-01-25T05:45:56Z","cross_cats_sorted":[],"title_canon_sha256":"357502d13755bfe9fa5910656ad13849685457ffd2f207ee292f18f1757d21c7","abstract_canon_sha256":"a15efb2b097a663f72c81a8309d5c366165b2beea9df34719c99cc0d8d2b1557"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:03:25.499988Z","signature_b64":"t3ACIsb0Kqsj/jzhLVxoXyFVstTA368QYR00ObctYbff+Yttk/JnKLwPrHu/L+cyfDnY5+UdZpicUlxRxCBBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e950f02102c020cc98e8030841aaf0fea3a6ae7e574e97012e4f9de86a87ce3","last_reissued_at":"2026-07-04T15:03:25.499637Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:03:25.499637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The determinant of the Dirichlet-to-Neumann map for surfaces with boundary","license":"","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Colin Guillarmou (JAD), Laurent Guillop\\'e (LMJL)","submitted_at":"2007-01-25T05:45:56Z","abstract_excerpt":"For any orientable compact surface with boundary, we compute the regularized determinant of the Dirichlet-to-Neumann (DN) map in terms of particular values of dynamical zeta functions by using natural uniformizations, one due to Mazzeo-Taylor, the other to Osgood-Phillips-Sarnak. We also relate in any dimension the DN map for the Yamabe operator to the scattering operator for a conformally compact related problem by using uniformization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701727","kind":"arxiv","version":2},"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/math/0701727/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":"math/0701727","created_at":"2026-07-04T15:03:25.499696+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0701727v2","created_at":"2026-07-04T15:03:25.499696+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701727","created_at":"2026-07-04T15:03:25.499696+00:00"},{"alias_kind":"pith_short_12","alias_value":"F2KQ6AQQFQBA","created_at":"2026-07-04T15:03:25.499696+00:00"},{"alias_kind":"pith_short_16","alias_value":"F2KQ6AQQFQBAZSMO","created_at":"2026-07-04T15:03:25.499696+00:00"},{"alias_kind":"pith_short_8","alias_value":"F2KQ6AQQ","created_at":"2026-07-04T15:03:25.499696+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.05159","citing_title":"Neumann scalar determinants on constant curvature disks","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F2KQ6AQQFQBAZSMOQAYIIGVPB7","json":"https://pith.science/pith/F2KQ6AQQFQBAZSMOQAYIIGVPB7.json","graph_json":"https://pith.science/api/pith-number/F2KQ6AQQFQBAZSMOQAYIIGVPB7/graph.json","events_json":"https://pith.science/api/pith-number/F2KQ6AQQFQBAZSMOQAYIIGVPB7/events.json","paper":"https://pith.science/paper/F2KQ6AQQ"},"agent_actions":{"view_html":"https://pith.science/pith/F2KQ6AQQFQBAZSMOQAYIIGVPB7","download_json":"https://pith.science/pith/F2KQ6AQQFQBAZSMOQAYIIGVPB7.json","view_paper":"https://pith.science/paper/F2KQ6AQQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0701727&json=true","fetch_graph":"https://pith.science/api/pith-number/F2KQ6AQQFQBAZSMOQAYIIGVPB7/graph.json","fetch_events":"https://pith.science/api/pith-number/F2KQ6AQQFQBAZSMOQAYIIGVPB7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F2KQ6AQQFQBAZSMOQAYIIGVPB7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F2KQ6AQQFQBAZSMOQAYIIGVPB7/action/storage_attestation","attest_author":"https://pith.science/pith/F2KQ6AQQFQBAZSMOQAYIIGVPB7/action/author_attestation","sign_citation":"https://pith.science/pith/F2KQ6AQQFQBAZSMOQAYIIGVPB7/action/citation_signature","submit_replication":"https://pith.science/pith/F2KQ6AQQFQBAZSMOQAYIIGVPB7/action/replication_record"}},"created_at":"2026-07-04T15:03:25.499696+00:00","updated_at":"2026-07-04T15:03:25.499696+00:00"}