{"as_of":"2026-08-12T22:06:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3c41bfbdd236ad22d523b8a1d54bbb2b794e0aa40e1d949530f2a55fc7f67b91","coverage":[{"denominator":9,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":9,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T21:36:13.094538Z","state":"measured"},{"denominator":11,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":11,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T16:21:35.588146Z","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":"2026-06-29T00:02:50.029322Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.04887","last_updated":"2025-01-08T23:57:58Z","snapshot_observed_at":"2026-08-10T21:20:42.261217Z","submitted_at":"2025-01-08T23:57:58Z","title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.04887","snapshot_observed_at":"2026-08-06T16:21:35.588146Z","title":"Uniform nonlinear szemer ' \\ e \\ di theorem for corners in finite fields","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.14414","last_updated":"2025-07-18T23:47:57Z","snapshot_observed_at":"2026-08-06T15:54:34.791808Z","submitted_at":"2025-07-18T23:47:57Z","title":"On weighted multilinear polynomial averages in finite fields","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T16:21:35.588146Z"},"links":{"cited_paper":"/paper/2501.04887","citing_paper":"/paper/2507.14414"},"observation_digest":"sha256:ebb20514021f538c06dfd1027b3d63d7baa259779309fa8221a1c4c32045afd8","observation_id":"7662242a-c75a-44cf-b0f3-91b2cd98c3b2","resolution":{"observed_at":"2026-08-06T16:21:35.588146Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.04887","last_updated":"2025-01-08T23:57:58Z","snapshot_observed_at":"2026-08-10T21:20:42.261217Z","submitted_at":"2025-01-08T23:57:58Z","title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields","version":1},"cited_work":{"arxiv_id":"2501.04887","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.04887","snapshot_observed_at":"2026-06-29T00:02:50.029322Z","title":"Uniform nonlinear Szemerédi theorem for corners in finite fields","venue":null,"work_id":"87ba724c-b336-4bf9-a283-67b6b4232c9c","year":2025},"citing_paper":{"arxiv_id":"2605.30033","last_updated":"2026-05-28T14:54:41Z","snapshot_observed_at":"2026-08-07T18:43:00.437696Z","submitted_at":"2026-05-28T14:54:41Z","title":"On hyperbolic corners and unit-area triangles in planar sets of large measure","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-06-28T23:54:01.597389Z"},"links":{"cited_paper":"/paper/2501.04887","citing_paper":"/paper/2605.30033"},"observation_digest":"sha256:247707acda9beeae79d2948d7a45b76dcdb7f8d0252e85be22303ac61b8e21a0","observation_id":"3bef3e63-2f72-41f4-9529-96acfe8fe4e6","resolution":{"observed_at":"2026-06-29T00:02:50.030841Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2501.04887/citation-record","integrity":"/paper/2501.04887/integrity","json":"/paper/2501.04887/citation-record.json","paper":"/paper/2501.04887"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2407.08637","last_updated":"2024-09-02T08:45:10Z","snapshot_observed_at":"2026-08-12T18:25:06.268762Z","submitted_at":"2024-07-11T16:18:28Z","title":"Corners with polynomial side length","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.08637","snapshot_observed_at":"2026-08-10T21:36:13.073342Z","title":"Multidimensional polynomial patter ns over ﬁnite ﬁelds: bounds, counting estimates and Gowers norm control","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.04887","last_updated":"2025-01-08T23:57:58Z","snapshot_observed_at":"2026-08-10T21:20:42.261217Z","submitted_at":"2025-01-08T23:57:58Z","title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T21:36:13.073342Z"},"links":{"cited_paper":"/paper/2407.08637","citing_paper":"/paper/2501.04887"},"observation_digest":"sha256:4b578961fb07d47b9bca65ff016ecbde954998544278563865c8dd7c2315a0d4","observation_id":"6b163f52-f907-447f-876f-5dfa6fc3e829","resolution":{"observed_at":"2026-08-10T21:36:13.073342Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.07925","last_updated":"2024-01-15T19:34:19Z","snapshot_observed_at":"2026-08-04T21:00:15.120778Z","submitted_at":"2024-01-15T19:34:19Z","title":"A bilinear estimate in $\\mathbb{F}_p$","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.07925","snapshot_observed_at":"2026-08-10T21:36:13.084767Z","title":"Number of points of varie ties in ﬁnite ﬁelds","venue":null,"work_id":null,"year":1954},"citing_paper":{"arxiv_id":"2501.04887","last_updated":"2025-01-08T23:57:58Z","snapshot_observed_at":"2026-08-10T21:20:42.261217Z","submitted_at":"2025-01-08T23:57:58Z","title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T21:36:13.084767Z"},"links":{"cited_paper":"/paper/2401.07925","citing_paper":"/paper/2501.04887"},"observation_digest":"sha256:a1e8929179972573f2a05f69f9b4db5d9911e210f4d96143030177c401401b8d","observation_id":"f8c95380-e240-4b31-8d22-2601e87d254d","resolution":{"observed_at":"2026-08-10T21:36:13.084767Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.08338","last_updated":"2024-07-11T09:40:55Z","snapshot_observed_at":"2026-08-09T19:25:11.327167Z","submitted_at":"2024-07-11T09:40:55Z","title":"Bounds in a popular multidimensional nonlinear Roth theorem","version":1},"cited_work":{"arxiv_id":"2407.08338","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.08338","snapshot_observed_at":"2026-08-10T21:36:13.130440Z","title":"Bounds in a popular multidimensional nonlinear Roth theorem","venue":"math.NT","work_id":"2de00f75-de62-49ed-870a-967094ab735f","year":2024},"citing_paper":{"arxiv_id":"2501.04887","last_updated":"2025-01-08T23:57:58Z","snapshot_observed_at":"2026-08-10T21:20:42.261217Z","submitted_at":"2025-01-08T23:57:58Z","title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T21:36:13.094538Z"},"links":{"cited_paper":"/paper/2407.08338","citing_paper":"/paper/2501.04887"},"observation_digest":"sha256:06dc90bf1ca7fb6cb5c6e86ae81687593b2a0853ee5b12fb16ba076f0c36b502","observation_id":"7037d9bc-e152-43e4-894b-aa0c0c4dc0c4","resolution":{"observed_at":"2026-08-10T21:36:13.138755Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T21:36:13.255861Z","title":"Springer-Verlag, New York-Heidelberg, 1977, pp","venue":null,"work_id":"5c940230-e0ca-4e74-9d27-b6c851e68d3b","year":1977},"citing_paper":{"arxiv_id":"2501.04887","last_updated":"2025-01-08T23:57:58Z","snapshot_observed_at":"2026-08-10T21:20:42.261217Z","submitted_at":"2025-01-08T23:57:58Z","title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-10T21:36:13.063190Z"},"links":{"citing_paper":"/paper/2501.04887"},"observation_digest":"sha256:5b00b74ffd5f690cfb36a1fe5b01764b3a2e0199a8bd6d2abac2f368923d2135","observation_id":"3f98b921-ca95-4df2-bcfb-da7a2811225f","resolution":{"observed_at":"2026-08-10T21:36:13.260907Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T21:36:13.225041Z","title":"Subsets of Fn p ×Fn p without L-shaped conﬁgurations","venue":null,"work_id":"5ada653c-868b-48c6-b36a-63e8ca6a870d","year":2024},"citing_paper":{"arxiv_id":"2501.04887","last_updated":"2025-01-08T23:57:58Z","snapshot_observed_at":"2026-08-10T21:20:42.261217Z","submitted_at":"2025-01-08T23:57:58Z","title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-10T21:36:13.089578Z"},"links":{"citing_paper":"/paper/2501.04887"},"observation_digest":"sha256:abedfeb00ff0c9937d9b8b24db7bb81c95e8a34819e50fd3f6bc9b46f18c1ab2","observation_id":"8f3e2b52-2de2-4032-916b-9e7d3e535cf3","resolution":{"observed_at":"2026-08-10T21:36:13.229930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T21:36:13.240578Z","title":"Multidimensional polynomial Szemer ´ edi theorem in ﬁnite ﬁelds for polynomials of distinct degrees","venue":null,"work_id":"f95b54dc-25c7-49ed-b93f-0f81294670ab","year":2024},"citing_paper":{"arxiv_id":"2501.04887","last_updated":"2025-01-08T23:57:58Z","snapshot_observed_at":"2026-08-10T21:20:42.261217Z","submitted_at":"2025-01-08T23:57:58Z","title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-10T21:36:13.078981Z"},"links":{"citing_paper":"/paper/2501.04887"},"observation_digest":"sha256:948642926d48ef3e24cadbf1c7dd9186f3bf74de44821457b14781456afcf431","observation_id":"db166535-39a0-4e2d-bfc5-9262be228fb5","resolution":{"observed_at":"2026-08-10T21:36:13.245479Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T21:36:13.271756Z","title":"Springer-Verlag, Berlin, 1984, p p","venue":null,"work_id":"9e5bd9ff-1fb3-4b44-b1d9-182399057740","year":1984},"citing_paper":{"arxiv_id":"2501.04887","last_updated":"2025-01-08T23:57:58Z","snapshot_observed_at":"2026-08-10T21:20:42.261217Z","submitted_at":"2025-01-08T23:57:58Z","title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields","version":1},"reference_index":265,"source":"pdf_text","source_observed_at":"2026-08-10T21:36:13.058030Z"},"links":{"citing_paper":"/paper/2501.04887"},"observation_digest":"sha256:33cf189f98fd8a6c4c625dff9f54c2f3d4e84544054652295f1c5b3bf4e38fe7","observation_id":"98b2c534-e815-4fe0-8514-155ebcc0b9fb","resolution":{"observed_at":"2026-08-10T21:36:13.277161Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1305.7269","last_updated":"2014-10-25T21:53:36Z","snapshot_observed_at":"2026-08-12T19:31:29.952498Z","submitted_at":"2013-05-30T23:21:14Z","title":"Partial difference equations over compact Abelian groups, I: modules of solutions","version":5},"cited_work":{"arxiv_id":"1305.7269","doi":null,"metadata_source":"pith","pith_arxiv_id":"1305.7269","snapshot_observed_at":"2026-08-10T21:36:13.209600Z","title":"Partial difference equations over compact Abelian groups, I: modules of solutions","venue":"math.FA","work_id":"7db7cada-f459-44e3-8c2f-44ebdf9eed58","year":2013},"citing_paper":{"arxiv_id":"2501.04887","last_updated":"2025-01-08T23:57:58Z","snapshot_observed_at":"2026-08-10T21:20:42.261217Z","submitted_at":"2025-01-08T23:57:58Z","title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields","version":1},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-10T21:36:13.052454Z"},"links":{"cited_paper":"/paper/1305.7269","citing_paper":"/paper/2501.04887"},"observation_digest":"sha256:7d778237b1571718fefde9e3eeeda785de857856cf5cec35a68eeffe21f13541","observation_id":"f8051649-6946-4d46-baa3-489f6205b18f","resolution":{"observed_at":"2026-08-10T21:36:13.214599Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.01137","last_updated":"2024-01-02T10:28:22Z","snapshot_observed_at":"2026-07-06T17:10:48.157731Z","submitted_at":"2024-01-02T10:28:22Z","title":"Three term rational function progressions in finite fields","version":1},"cited_work":{"arxiv_id":"2401.01137","doi":null,"metadata_source":"pith","pith_arxiv_id":"2401.01137","snapshot_observed_at":"2026-08-10T21:36:13.188192Z","title":"Three term rational function progressions in finite fields","venue":"math.NT","work_id":"ee335162-1677-458e-acfb-2a48531b20f2","year":2024},"citing_paper":{"arxiv_id":"2501.04887","last_updated":"2025-01-08T23:57:58Z","snapshot_observed_at":"2026-08-10T21:20:42.261217Z","submitted_at":"2025-01-08T23:57:58Z","title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-10T21:36:13.068184Z"},"links":{"cited_paper":"/paper/2401.01137","citing_paper":"/paper/2501.04887"},"observation_digest":"sha256:af41f20f3e94f67eaac392cc0a3631869706ff9123845ea94b4a3112e890f055","observation_id":"7667ec2c-09be-432f-becf-c8ed6568f525","resolution":{"observed_at":"2026-08-10T21:36:13.193388Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.04887","last_updated":"2025-01-08T23:57:58Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-10T21:20:42.261217Z","submitted_at":"2025-01-08T23:57:58Z","title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields"},"reference_resolution":{"displayed":9,"state_counts":{"malformed_identifier":0,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":2,"verified_exact":1,"verified_fuzzy":4},"total_outbound_references":9},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 9 of 9 outbound references and 2 inbound Pith citation observations for arXiv:2501.04887."}