{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:T22OUZWHRXCGIOZUPELEXZYSYA","short_pith_number":"pith:T22OUZWH","schema_version":"1.0","canonical_sha256":"9eb4ea66c78dc4643b3479164be712c01e1d57c7174501a6eae631b23fb86fc7","source":{"kind":"arxiv","id":"0801.3492","version":1},"attestation_state":"computed","paper":{"title":"On the appearance of Eisenstein series through degeneration","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dan Garbin, Jay Jorgenson, Michael Munn","submitted_at":"2008-01-23T18:23:08Z","abstract_excerpt":"Let $\\Gamma$ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane $\\mathbb H$, and let $M = \\Gamma \\backslash \\mathbb H$ be the associated finite volume hyperbolic Riemann surface. If $\\gamma$ is parabolic, there is an associated (parabolic) Eisenstein series, which, by now, is a classical part of mathematical literature. If $\\gamma$ is hyperbolic, then, following ideas due to Kudla-Millson, there is a corresponding hyperbolic Eisenstein series. In this article, we study the limiting behavior of parabolic and hyperbolic Eisenstein series on a degenerating family of f"},"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":"0801.3492","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2008-01-23T18:23:08Z","cross_cats_sorted":[],"title_canon_sha256":"e7993287f5a095fc0a6dcc095afd256e44b35f2a7ba891ac898c4b3c3a934db3","abstract_canon_sha256":"0642908dc001ea3fe2cd266eaaf1155aa18fe787e485e41735ead5f8162efcea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:01.629270Z","signature_b64":"ML05q6gxEiIj5dk1flARrQwxl92/LpmtPgMnekXJyNnHOkeXCqlrBqDiIqojQWhdhE09ZcNpZvqNOmWlI65/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9eb4ea66c78dc4643b3479164be712c01e1d57c7174501a6eae631b23fb86fc7","last_reissued_at":"2026-05-18T02:16:01.628769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:01.628769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the appearance of Eisenstein series through degeneration","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dan Garbin, Jay Jorgenson, Michael Munn","submitted_at":"2008-01-23T18:23:08Z","abstract_excerpt":"Let $\\Gamma$ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane $\\mathbb H$, and let $M = \\Gamma \\backslash \\mathbb H$ be the associated finite volume hyperbolic Riemann surface. If $\\gamma$ is parabolic, there is an associated (parabolic) Eisenstein series, which, by now, is a classical part of mathematical literature. If $\\gamma$ is hyperbolic, then, following ideas due to Kudla-Millson, there is a corresponding hyperbolic Eisenstein series. In this article, we study the limiting behavior of parabolic and hyperbolic Eisenstein series on a degenerating family of f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3492","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":"0801.3492","created_at":"2026-05-18T02:16:01.628854+00:00"},{"alias_kind":"arxiv_version","alias_value":"0801.3492v1","created_at":"2026-05-18T02:16:01.628854+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.3492","created_at":"2026-05-18T02:16:01.628854+00:00"},{"alias_kind":"pith_short_12","alias_value":"T22OUZWHRXCG","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"T22OUZWHRXCGIOZU","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"T22OUZWH","created_at":"2026-05-18T12:25:58.018023+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/T22OUZWHRXCGIOZUPELEXZYSYA","json":"https://pith.science/pith/T22OUZWHRXCGIOZUPELEXZYSYA.json","graph_json":"https://pith.science/api/pith-number/T22OUZWHRXCGIOZUPELEXZYSYA/graph.json","events_json":"https://pith.science/api/pith-number/T22OUZWHRXCGIOZUPELEXZYSYA/events.json","paper":"https://pith.science/paper/T22OUZWH"},"agent_actions":{"view_html":"https://pith.science/pith/T22OUZWHRXCGIOZUPELEXZYSYA","download_json":"https://pith.science/pith/T22OUZWHRXCGIOZUPELEXZYSYA.json","view_paper":"https://pith.science/paper/T22OUZWH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0801.3492&json=true","fetch_graph":"https://pith.science/api/pith-number/T22OUZWHRXCGIOZUPELEXZYSYA/graph.json","fetch_events":"https://pith.science/api/pith-number/T22OUZWHRXCGIOZUPELEXZYSYA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T22OUZWHRXCGIOZUPELEXZYSYA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T22OUZWHRXCGIOZUPELEXZYSYA/action/storage_attestation","attest_author":"https://pith.science/pith/T22OUZWHRXCGIOZUPELEXZYSYA/action/author_attestation","sign_citation":"https://pith.science/pith/T22OUZWHRXCGIOZUPELEXZYSYA/action/citation_signature","submit_replication":"https://pith.science/pith/T22OUZWHRXCGIOZUPELEXZYSYA/action/replication_record"}},"created_at":"2026-05-18T02:16:01.628854+00:00","updated_at":"2026-05-18T02:16:01.628854+00:00"}