{"as_of":"2026-08-09T12:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a2ebe16ad4c27f1199b3efcef00d6322fa25625374e2cdf371635508daa24132","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":"2026-08-09T06:31:02.800959+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":"2026-08-03T04:16:01.656387Z","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":"2026-05-11T11:36:01.091805Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2407.01341","last_updated":"2025-03-18T15:57:04Z","snapshot_observed_at":"2026-07-06T18:39:38.415138Z","submitted_at":"2024-07-01T14:49:59Z","title":"The geometric size of the fundamental gap","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.01341","snapshot_observed_at":"2026-08-03T04:16:01.656387Z","title":"Amato, D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2602.05968","last_updated":"2026-07-15T17:22:20Z","snapshot_observed_at":"2026-08-03T04:16:00.832978Z","submitted_at":"2026-02-05T18:22:02Z","title":"Stability of the $L^{p}$-Poincar\\'e inequality for the Lebesgue measure and Gaussian probability measure with explicit geometric dependence and applications to spectral gaps","version":4},"reference_index":1989,"source":"pdf_text","source_observed_at":"2026-08-03T04:16:01.656387Z"},"links":{"cited_paper":"/paper/2407.01341","citing_paper":"/paper/2602.05968"},"observation_digest":"sha256:fb97ac2ed88abc9a0743e48dd508c7a08ab8db7e900ceee4d45566216999a858","observation_id":"e626e0f6-987d-4985-a762-d460af58db54","resolution":{"observed_at":"2026-08-03T04:16:01.656387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.01341","last_updated":"2025-03-18T15:57:04Z","snapshot_observed_at":"2026-07-06T18:39:38.415138Z","submitted_at":"2024-07-01T14:49:59Z","title":"The geometric size of the fundamental gap","version":2},"cited_work":{"arxiv_id":"2407.01341","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2407.01341","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Amato, D","venue":null,"work_id":"5a77bc9b-40e3-45dc-bafc-4b29a9b194b3","year":2024},"citing_paper":{"arxiv_id":"2604.13246","last_updated":"2026-04-14T19:21:55Z","snapshot_observed_at":"2026-07-06T23:01:19.191464Z","submitted_at":"2026-04-14T19:21:55Z","title":"Quantitative Kr\\\"{o}ger inequalities for Neumann eigenvalues of convex domains","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-10T14:25:45.778759Z"},"links":{"cited_paper":"/paper/2407.01341","citing_paper":"/paper/2604.13246"},"observation_digest":"sha256:66574797a6dc1ca9a441f7ab5d6454d870fd15163ebc1a6395a90c493c4d8fa4","observation_id":"383caac3-cead-4c96-9ed7-6fb67ebe2391","resolution":{"observed_at":"2026-05-11T11:36:01.095304Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.01341","last_updated":"2025-03-18T15:57:04Z","snapshot_observed_at":"2026-07-06T18:39:38.415138Z","submitted_at":"2024-07-01T14:49:59Z","title":"The geometric size of the fundamental gap","version":2},"cited_work":{"arxiv_id":"2407.01341","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2407.01341","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Amato, D","venue":null,"work_id":"5a77bc9b-40e3-45dc-bafc-4b29a9b194b3","year":2024},"citing_paper":{"arxiv_id":"2604.14000","last_updated":"2026-04-15T15:45:43Z","snapshot_observed_at":"2026-07-06T23:01:50.745555Z","submitted_at":"2026-04-15T15:45:43Z","title":"The Makai inequality in higher dimensions: qualitative and quantitative aspects","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-10T12:20:41.394916Z"},"links":{"cited_paper":"/paper/2407.01341","citing_paper":"/paper/2604.14000"},"observation_digest":"sha256:23fd48662b3da977dc1286350b017086b3a9668cddd325167f82f25ecb46d0e2","observation_id":"0168160b-f2e0-4883-8d4a-a02e489cfc56","resolution":{"observed_at":"2026-05-10T12:25:22.779604Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2407.01341/citation-record","integrity":"/paper/2407.01341/integrity","json":"/paper/2407.01341/citation-record.json","paper":"/paper/2407.01341"},"outbound":[],"paper":{"arxiv_id":"2407.01341","last_updated":"2025-03-18T15:57:04Z","latest_version":2,"primary_category":"math.SP","snapshot_observed_at":"2026-07-06T18:39:38.415138Z","submitted_at":"2024-07-01T14:49:59Z","title":"The geometric size of the fundamental gap"},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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:2407.01341."}