{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TI4B4YDSRNQKFEYAO3Z3RQZKIC","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":"1002701aefe4a56da77433b81388776d10f6bf872595979ae6294dea4ddbecd7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-30T06:18:50Z","title_canon_sha256":"d2eb1e473c9fb8ff1d224d4a3e05de7703e2a1d58a719fbd428d9bec9ac2eada"},"schema_version":"1.0","source":{"id":"1701.08491","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08491","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08491v4","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08491","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"pith_short_12","alias_value":"TI4B4YDSRNQK","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TI4B4YDSRNQKFEYA","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TI4B4YDS","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:98e2682d6aaa58c3399a5d70fb6d41fce67332a2020c9a7e8e585d29922c3df2","target":"graph","created_at":"2026-05-17T23:48:53Z","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":"We consider the first non-zero eigenvalue $\\lambda_1$ of the Laplacian on hyperbolic surfaces for which one disconnecting collar degenerates and prove that $8\\pi \\nabla\\log(\\lambda_1)$ essentially agrees with the dual of the differential of the degenerating Fenchel-Nielsen length coordinate. As a consequence, we can improve previous results of Schoen, Wolpert, Yau and Burger to obtain estimates with optimal error rates and obtain new information on the leading order terms of the polyhomogeneous expansion of $\\lambda_1$ of Albin, Rochon and Sher.","authors_text":"Melanie Rupflin, Nadine Gro{\\ss}e","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-30T06:18:50Z","title":"Sharp eigenvalue estimates on degenerating surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08491","kind":"arxiv","version":4},"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":"sha256:03f918cc65a72fd0c6effe087bce1bcf9935c6af3330a76f40866243526483ef","target":"record","created_at":"2026-05-17T23:48:53Z","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":"1002701aefe4a56da77433b81388776d10f6bf872595979ae6294dea4ddbecd7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-30T06:18:50Z","title_canon_sha256":"d2eb1e473c9fb8ff1d224d4a3e05de7703e2a1d58a719fbd428d9bec9ac2eada"},"schema_version":"1.0","source":{"id":"1701.08491","kind":"arxiv","version":4}},"canonical_sha256":"9a381e60728b60a2930076f3b8c32a408bb812f6f7f70f78a3060440baca981a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a381e60728b60a2930076f3b8c32a408bb812f6f7f70f78a3060440baca981a","first_computed_at":"2026-05-17T23:48:53.217236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:53.217236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0zzwqjmnSW7En0oBTfYRB07kK0IQLYu525U7vQdi14Gx6tWNYfbxcB28YjgICqnmb45S1plDExYIPLbf5c7yAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:53.217770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08491","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03f918cc65a72fd0c6effe087bce1bcf9935c6af3330a76f40866243526483ef","sha256:98e2682d6aaa58c3399a5d70fb6d41fce67332a2020c9a7e8e585d29922c3df2"],"state_sha256":"631dc6d862fafabea34c8109a72387d82a9f1c90a1eae7ef4ac76efcf6205242"}