{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:J4B77JFBG34WRWNNOK2525P57R","short_pith_number":"pith:J4B77JFB","schema_version":"1.0","canonical_sha256":"4f03ffa4a136f968d9ad72b5dd75fdfc4738909e67019254aa899450ea9aff33","source":{"kind":"arxiv","id":"1310.4336","version":1},"attestation_state":"computed","paper":{"title":"Extension of a key identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anilatmaja Aryasomayajula","submitted_at":"2013-10-16T11:47:10Z","abstract_excerpt":"In this article, we extend a certain key identity proved by J. Jorgenson and J. Kramer for compact hyperbolic Riemann surfaces to noncompact hyperbolic Riemann orbisurfaces of finite volume, which can be realized as the quotient space of the action of a Fuchsian subgroup of the first kind acting on the hyperbolic upper half-plane.\n  The key identity of J. Jorgenson and J. Kramer relates the two natural metrics, namely the hyperbolic metric and the canonical metric defined on a hyperbolic Riemann surface. Via the spectral expansion of the hyperbolic heat kernel, this identity serves as a trace "},"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":"1310.4336","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-16T11:47:10Z","cross_cats_sorted":[],"title_canon_sha256":"4b0e427af563985e288c773308b2036815b2b6094ca18f742d439b49a81d6845","abstract_canon_sha256":"085899f0e0a6a695cea41adb3f6259c3d8657dc83c24b35aaf8a4f6fa9b96148"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:23.143108Z","signature_b64":"8i0x4z4lSnI4Tfm8GcRiExLruKBtmHJEmV+dDUeDl2vjUrSeorkL6VBnJzz9HhTHcm/ajHchnE6k3O37dEHoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f03ffa4a136f968d9ad72b5dd75fdfc4738909e67019254aa899450ea9aff33","last_reissued_at":"2026-05-18T03:10:23.142188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:23.142188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extension of a key identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anilatmaja Aryasomayajula","submitted_at":"2013-10-16T11:47:10Z","abstract_excerpt":"In this article, we extend a certain key identity proved by J. Jorgenson and J. Kramer for compact hyperbolic Riemann surfaces to noncompact hyperbolic Riemann orbisurfaces of finite volume, which can be realized as the quotient space of the action of a Fuchsian subgroup of the first kind acting on the hyperbolic upper half-plane.\n  The key identity of J. Jorgenson and J. Kramer relates the two natural metrics, namely the hyperbolic metric and the canonical metric defined on a hyperbolic Riemann surface. Via the spectral expansion of the hyperbolic heat kernel, this identity serves as a trace "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4336","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":"1310.4336","created_at":"2026-05-18T03:10:23.142331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.4336v1","created_at":"2026-05-18T03:10:23.142331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4336","created_at":"2026-05-18T03:10:23.142331+00:00"},{"alias_kind":"pith_short_12","alias_value":"J4B77JFBG34W","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"J4B77JFBG34WRWNN","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"J4B77JFB","created_at":"2026-05-18T12:27:49.015174+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/J4B77JFBG34WRWNNOK2525P57R","json":"https://pith.science/pith/J4B77JFBG34WRWNNOK2525P57R.json","graph_json":"https://pith.science/api/pith-number/J4B77JFBG34WRWNNOK2525P57R/graph.json","events_json":"https://pith.science/api/pith-number/J4B77JFBG34WRWNNOK2525P57R/events.json","paper":"https://pith.science/paper/J4B77JFB"},"agent_actions":{"view_html":"https://pith.science/pith/J4B77JFBG34WRWNNOK2525P57R","download_json":"https://pith.science/pith/J4B77JFBG34WRWNNOK2525P57R.json","view_paper":"https://pith.science/paper/J4B77JFB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.4336&json=true","fetch_graph":"https://pith.science/api/pith-number/J4B77JFBG34WRWNNOK2525P57R/graph.json","fetch_events":"https://pith.science/api/pith-number/J4B77JFBG34WRWNNOK2525P57R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J4B77JFBG34WRWNNOK2525P57R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J4B77JFBG34WRWNNOK2525P57R/action/storage_attestation","attest_author":"https://pith.science/pith/J4B77JFBG34WRWNNOK2525P57R/action/author_attestation","sign_citation":"https://pith.science/pith/J4B77JFBG34WRWNNOK2525P57R/action/citation_signature","submit_replication":"https://pith.science/pith/J4B77JFBG34WRWNNOK2525P57R/action/replication_record"}},"created_at":"2026-05-18T03:10:23.142331+00:00","updated_at":"2026-05-18T03:10:23.142331+00:00"}