{"as_of":"2026-08-12T09:33:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5cbf850e80f74a48d8cdb9e4186afc1f2c91c5c4249638d01822d9a6be4524ef","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":7,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":7,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":7,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":7,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T12:38:32.022086Z","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":"2026-06-29T19:23:54.212447Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2308.14859","last_updated":"2023-09-14T15:05:18Z","snapshot_observed_at":"2026-07-06T16:11:27.419669Z","submitted_at":"2023-08-28T19:30:27Z","title":"An improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.14859","snapshot_observed_at":"2026-08-11T12:38:32.022086Z","title":"and Yang, X., An improvement on Gauss’s Circle Problem and Dirichlet’s Divisor Problem, arXiv:2308.14859","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.14059","last_updated":"2024-12-18T17:07:22Z","snapshot_observed_at":"2026-08-11T18:32:57.634036Z","submitted_at":"2024-12-18T17:07:22Z","title":"Bessel functions and Weyl's law for balls and spherical shells","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T12:38:32.022086Z"},"links":{"cited_paper":"/paper/2308.14859","citing_paper":"/paper/2412.14059"},"observation_digest":"sha256:e31a594c70c6b901d89d3b50e3c1abea20a1dd727313df741c4062700da5c92c","observation_id":"08ee2b8e-4ec1-4485-9e4c-7672299ee75f","resolution":{"observed_at":"2026-08-11T12:38:32.022086Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.14859","last_updated":"2023-09-14T15:05:18Z","snapshot_observed_at":"2026-07-06T16:11:27.419669Z","submitted_at":"2023-08-28T19:30:27Z","title":"An improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.14859","snapshot_observed_at":"2026-08-06T22:24:58.304687Z","title":"Li and X","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.22587","last_updated":"2025-06-27T19:08:24Z","snapshot_observed_at":"2026-08-06T22:00:14.562282Z","submitted_at":"2025-06-27T19:08:24Z","title":"The Piltz divisor Problem in Number Fields Using The Resonance Method","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T22:24:58.304687Z"},"links":{"cited_paper":"/paper/2308.14859","citing_paper":"/paper/2506.22587"},"observation_digest":"sha256:0adee9cbf3ab90012b775bcf67d7437bcfda1f1db377b4fee591ca4e35e0637d","observation_id":"a8b35e7a-5278-4068-82d1-bb7b2ccf896e","resolution":{"observed_at":"2026-08-06T22:24:58.304687Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.14859","last_updated":"2023-09-14T15:05:18Z","snapshot_observed_at":"2026-07-06T16:11:27.419669Z","submitted_at":"2023-08-28T19:30:27Z","title":"An improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.14859","snapshot_observed_at":"2026-08-03T12:58:46.713469Z","title":"Li and X","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2601.01905","last_updated":"2026-06-26T05:49:29Z","snapshot_observed_at":"2026-08-03T12:58:44.664523Z","submitted_at":"2026-01-05T08:49:33Z","title":"On a Smoothed Dirichlet Divisor Problem","version":3},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-03T12:58:46.713469Z"},"links":{"cited_paper":"/paper/2308.14859","citing_paper":"/paper/2601.01905"},"observation_digest":"sha256:c0f372dfc34ad8655fb97f0a16832b2266aee814c4927779be01622258571f4b","observation_id":"442c3fe0-f3ca-4f74-bcb9-9b6a65412926","resolution":{"observed_at":"2026-08-03T12:58:46.713469Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.14859","last_updated":"2023-09-14T15:05:18Z","snapshot_observed_at":"2026-07-06T16:11:27.419669Z","submitted_at":"2023-08-28T19:30:27Z","title":"An improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem","version":2},"cited_work":{"arxiv_id":"2308.14859","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2308.14859","snapshot_observed_at":"2026-06-29T19:23:54.212447Z","title":"Li and X","venue":null,"work_id":"3c5090ba-0f64-476f-99b0-db4de28a01b2","year":2023},"citing_paper":{"arxiv_id":"2605.26033","last_updated":"2026-05-26T09:10:23Z","snapshot_observed_at":"2026-08-04T10:10:40.855572Z","submitted_at":"2026-05-25T17:01:32Z","title":"Lattice point counting problems on step-two nilpotent Lie groups","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-06-29T19:15:19.129835Z"},"links":{"cited_paper":"/paper/2308.14859","citing_paper":"/paper/2605.26033"},"observation_digest":"sha256:ea713e83313943f0e3c7b9d82c2cb2840ec3752d18b7e31aa9fdd7dbfa138b74","observation_id":"8a0de71a-5a27-45f6-b9a2-8eb683037141","resolution":{"observed_at":"2026-06-29T19:23:54.213783Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2308.14859","last_updated":"2023-09-14T15:05:18Z","snapshot_observed_at":"2026-07-06T16:11:27.419669Z","submitted_at":"2023-08-28T19:30:27Z","title":"An improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.14859","snapshot_observed_at":"2026-07-14T07:57:31.989340Z","title":"Li and X","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.10971","last_updated":"2026-07-13T00:35:24Z","snapshot_observed_at":"2026-08-06T04:21:39.979054Z","submitted_at":"2026-07-13T00:35:24Z","title":"Lattice point counting in Cygan--Kor\\'anyi balls on Heisenberg groups","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-14T07:57:31.989340Z"},"links":{"cited_paper":"/paper/2308.14859","citing_paper":"/paper/2607.10971"},"observation_digest":"sha256:f0ad42af4e4b7704b778ec7fd37559019d15d0260303fbd975cede49a83e8262","observation_id":"5b3e8dde-9abb-43cf-84e4-a7935da784d9","resolution":{"observed_at":"2026-07-14T07:57:31.989340Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.14859","last_updated":"2023-09-14T15:05:18Z","snapshot_observed_at":"2026-07-06T16:11:27.419669Z","submitted_at":"2023-08-28T19:30:27Z","title":"An improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.14859","snapshot_observed_at":"2026-08-01T20:19:12.959929Z","title":"Li and X","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.16695","last_updated":"2026-07-18T08:06:23Z","snapshot_observed_at":"2026-08-09T22:50:03.727947Z","submitted_at":"2026-07-18T08:06:23Z","title":"Counterexamples of Friedlander--Iwaniec dual sums conjecture","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T20:19:12.959929Z"},"links":{"cited_paper":"/paper/2308.14859","citing_paper":"/paper/2607.16695"},"observation_digest":"sha256:3849e112182cd82ab3a39e0233976295cff70ab140506b19af9efafe1a2ff11b","observation_id":"750be5b2-85e6-4d1e-81ca-c3b2a319be0d","resolution":{"observed_at":"2026-08-01T20:19:12.959929Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.14859","last_updated":"2023-09-14T15:05:18Z","snapshot_observed_at":"2026-07-06T16:11:27.419669Z","submitted_at":"2023-08-28T19:30:27Z","title":"An improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.14859","snapshot_observed_at":"2026-08-01T09:01:22.051287Z","title":"Li and X","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.20960","last_updated":"2026-07-23T06:37:50Z","snapshot_observed_at":"2026-08-12T07:17:39.754059Z","submitted_at":"2026-07-23T06:37:50Z","title":"Fibonacci, Dirichlet, and Gauss in a single sum","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T09:01:22.051287Z"},"links":{"cited_paper":"/paper/2308.14859","citing_paper":"/paper/2607.20960"},"observation_digest":"sha256:49366f7cc82573f46b936d4940aa7b70352b94e7f7b70af6a7109d73b355b613","observation_id":"cea5d29b-5a51-467b-83ea-28f13318f856","resolution":{"observed_at":"2026-08-01T09:01:22.051287Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2308.14859/citation-record","integrity":"/paper/2308.14859/integrity","json":"/paper/2308.14859/citation-record.json","paper":"/paper/2308.14859"},"outbound":[],"paper":{"arxiv_id":"2308.14859","last_updated":"2023-09-14T15:05:18Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-07-06T16:11:27.419669Z","submitted_at":"2023-08-28T19:30:27Z","title":"An improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem"},"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":"2026-08-12T06:34:41.77262+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 0 of 0 outbound references and 7 inbound Pith citation observations for arXiv:2308.14859."}