{"as_of":"2026-08-09T03:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7ce837153ec3db3a4001eee841839a2bacac450a554682a2078af1e760e5169e","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":3,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":3,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T19:02:22.424723Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-01T12:25:43.368111Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2106.15043","last_updated":"2021-06-29T00:52:44Z","snapshot_observed_at":"2026-07-06T11:24:00.099154Z","submitted_at":"2021-06-29T00:52:44Z","title":"Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.15043","snapshot_observed_at":"2026-08-07T19:02:22.424723Z","title":"Stability of isoperimetric inequalities for laplace eigenvalues on surfaces","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2502.10225","last_updated":"2025-02-14T15:19:29Z","snapshot_observed_at":"2026-08-07T18:50:23.245867Z","submitted_at":"2025-02-14T15:19:29Z","title":"Large topology asymptotics for spectrally extremal minimal surfaces in $\\mathbb{B}^3$ and $\\mathbb{S}^3$","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T19:02:22.424723Z"},"links":{"cited_paper":"/paper/2106.15043","citing_paper":"/paper/2502.10225"},"observation_digest":"sha256:1eba9217e8f70e14929d46cb3c497ed0975e25a3bc945c1cd5fe2e1d591a2a64","observation_id":"1f2a7aa9-6158-423a-af07-9c40a8081a6b","resolution":{"observed_at":"2026-08-07T19:02:22.424723Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2106.15043","last_updated":"2021-06-29T00:52:44Z","snapshot_observed_at":"2026-07-06T11:24:00.099154Z","submitted_at":"2021-06-29T00:52:44Z","title":"Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.15043","snapshot_observed_at":"2026-08-07T05:01:08.385069Z","title":"Variational aspects of Laplace eigenvalues on Rieman- nian surfaces","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2506.09328","last_updated":"2026-07-30T04:20:30Z","snapshot_observed_at":"2026-08-07T04:48:46.231415Z","submitted_at":"2025-06-11T02:07:08Z","title":"Maximizing higher eigenvalues in dimensions three and above","version":3},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-07T05:01:08.385069Z"},"links":{"cited_paper":"/paper/2106.15043","citing_paper":"/paper/2506.09328"},"observation_digest":"sha256:bfdde299c20257069c21a40396737303a1d3dcf8c7d3cac406619b1b28a456fb","observation_id":"6af9739c-8387-47c7-9952-a6850d818084","resolution":{"observed_at":"2026-08-07T05:01:08.385069Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2106.15043","last_updated":"2021-06-29T00:52:44Z","snapshot_observed_at":"2026-07-06T11:24:00.099154Z","submitted_at":"2021-06-29T00:52:44Z","title":"Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces","version":1},"cited_work":{"arxiv_id":"2106.15043","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2106.15043","snapshot_observed_at":"2026-07-01T12:25:43.368111Z","title":"2021 , bdsk-url-1 =","venue":null,"work_id":"0ebad4e4-9988-4f61-aca0-f052bbd37fb1","year":2021},"citing_paper":{"arxiv_id":"2606.31869","last_updated":"2026-07-30T04:50:34Z","snapshot_observed_at":"2026-08-02T23:18:19.105923Z","submitted_at":"2026-06-30T15:55:54Z","title":"Eigenvalue optimization via a first-variation formula","version":1},"reference_index":121,"source":"arxiv_source","source_observed_at":"2026-07-01T02:09:33.752296Z"},"links":{"cited_paper":"/paper/2106.15043","citing_paper":"/paper/2606.31869"},"observation_digest":"sha256:c9a3ca3693c2e60ab48f231c5b47642a6a464bd19f3ada96f3dddee4d38dac96","observation_id":"1a563817-ea97-43f5-9ec1-96a6d0355228","resolution":{"observed_at":"2026-07-01T12:25:43.369450Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2106.15043/citation-record","integrity":"/paper/2106.15043/integrity","json":"/paper/2106.15043/citation-record.json","paper":"/paper/2106.15043"},"outbound":[],"paper":{"arxiv_id":"2106.15043","last_updated":"2021-06-29T00:52:44Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-07-06T11:24:00.099154Z","submitted_at":"2021-06-29T00:52:44Z","title":"Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:2106.15043."}