{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RQQNEV2KFRNTZK3SYR7OG3FO5E","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":"5e97eea272c74f6f864bc2b3f55a1750ab978252f819ca639a55c6b9ac8a1695","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-04T15:18:52Z","title_canon_sha256":"d1bdbc4fc71972a1fdf0d8af322bca2128b6a7534b5ee753d50dca820373e5f4"},"schema_version":"1.0","source":{"id":"1603.01495","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01495","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01495v1","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01495","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"pith_short_12","alias_value":"RQQNEV2KFRNT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RQQNEV2KFRNTZK3S","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RQQNEV2K","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:0d7b928e4cdefca6064b55042a6934a49003005316e0ae4b6b4c60b35d8dc493","target":"graph","created_at":"2026-05-18T01:10:18Z","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":"This is the first of two articles in which we define an elliptically degenerating family of hyperbolic Riemann surfaces and study the asymptotic behavior of the associated spectral theory. Our study is motivated by a result from \\cite{He 83}, which Hejhal attributes to Selberg, proving spectral accumulation for the family of Hecke triangle groups. In this article, we prove various results regarding the asymptotic behavior of heat kernels and traces of heat kernels for both real and complex time. In \\cite{GJ 16}, we will use the results from this article and study the asymptotic behavior of num","authors_text":"Daniel Garbin, Jay Jorgenson","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-04T15:18:52Z","title":"Heat kernel asymptotics on sequences of elliptically degenerating Riemann surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01495","kind":"arxiv","version":1},"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":"sha256:4baee5d874ad6a41aadbaeaf452b380f503ff22458a3f608ed3b6f9ca6fed08c","target":"record","created_at":"2026-05-18T01:10:18Z","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":"5e97eea272c74f6f864bc2b3f55a1750ab978252f819ca639a55c6b9ac8a1695","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-04T15:18:52Z","title_canon_sha256":"d1bdbc4fc71972a1fdf0d8af322bca2128b6a7534b5ee753d50dca820373e5f4"},"schema_version":"1.0","source":{"id":"1603.01495","kind":"arxiv","version":1}},"canonical_sha256":"8c20d2574a2c5b3cab72c47ee36caee934529df36147bf46bf6b8dcf602447bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c20d2574a2c5b3cab72c47ee36caee934529df36147bf46bf6b8dcf602447bb","first_computed_at":"2026-05-18T01:10:18.030665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:18.030665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sI2L+lgAG7KGCkjOXlVwXKLODqce769eNNA4AYoRw6ARcryigkUR2ZP3HVPyo/fXKmFpAFtKmpIShF2t3+kiCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:18.031290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01495","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4baee5d874ad6a41aadbaeaf452b380f503ff22458a3f608ed3b6f9ca6fed08c","sha256:0d7b928e4cdefca6064b55042a6934a49003005316e0ae4b6b4c60b35d8dc493"],"state_sha256":"ad9961d28a505332d61e79e3690656410f0a9b200c96b895937e40b3094e7795"}