{"as_of":"2026-08-10T00:08:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fe0390582b91467a15c741d68c880efa1c05a282301c39fd6f6be96771681da6","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":6,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":6,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":6,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T23:02:21.574931Z","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":"2026-06-29T15:13:32.283099Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.09470","last_updated":"2025-01-16T11:15:08Z","snapshot_observed_at":"2026-07-06T20:21:55.366596Z","submitted_at":"2025-01-16T11:15:08Z","title":"Control and its applications in additive combinatorics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.09470","snapshot_observed_at":"2026-08-06T23:02:21.574931Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.20813","last_updated":"2025-11-19T13:09:28Z","snapshot_observed_at":"2026-08-09T08:35:02.619266Z","submitted_at":"2025-06-25T20:22:12Z","title":"Entropic additive energy and entropy inequalities for sums and products","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T23:02:21.574931Z"},"links":{"cited_paper":"/paper/2501.09470","citing_paper":"/paper/2506.20813"},"observation_digest":"sha256:65c664b2aa3da10948243e5b538445e3f52554bbec69d1d760025abf90f00a97","observation_id":"967f244e-916a-4fb3-b3ff-9cde62c9fa86","resolution":{"observed_at":"2026-08-06T23:02:21.574931Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.09470","last_updated":"2025-01-16T11:15:08Z","snapshot_observed_at":"2026-07-06T20:21:55.366596Z","submitted_at":"2025-01-16T11:15:08Z","title":"Control and its applications in additive combinatorics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.09470","snapshot_observed_at":"2026-08-05T12:37:08.515785Z","title":"Control and its applications in additive combinatorics","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.01568","last_updated":"2025-09-01T15:52:59Z","snapshot_observed_at":"2026-08-05T12:37:07.896061Z","submitted_at":"2025-09-01T15:52:59Z","title":"Additive structure in convex sets","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T12:37:08.515785Z"},"links":{"cited_paper":"/paper/2501.09470","citing_paper":"/paper/2509.01568"},"observation_digest":"sha256:bff8ce9dc48c8feeb0daf5394308ca84b61a5a4ee3996936c5473f72f61f967b","observation_id":"e07a0469-c1cc-49fc-8447-d07fea9b0eee","resolution":{"observed_at":"2026-08-05T12:37:08.515785Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.09470","last_updated":"2025-01-16T11:15:08Z","snapshot_observed_at":"2026-07-06T20:21:55.366596Z","submitted_at":"2025-01-16T11:15:08Z","title":"Control and its applications in additive combinatorics","version":1},"cited_work":{"arxiv_id":"2501.09470","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.09470","snapshot_observed_at":"2026-06-29T15:13:32.283099Z","title":"Control and its applications in additive combinatorics.arXiv:2501.09470, 2025","venue":null,"work_id":"7115b26d-4468-470e-b040-65219e93caeb","year":2025},"citing_paper":{"arxiv_id":"2511.02864","last_updated":"2025-12-22T12:49:01Z","snapshot_observed_at":"2026-08-07T08:27:55.662438Z","submitted_at":"2025-11-03T16:04:07Z","title":"Mathematical exploration and discovery at scale","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-18T01:18:42.333269Z"},"links":{"cited_paper":"/paper/2501.09470","citing_paper":"/paper/2511.02864"},"observation_digest":"sha256:eff85c94b4e58ed544872d6adda66fb3061843afc4a268dd6198d84c6ac0003a","observation_id":"e00d0fe5-8c61-48ac-b0bf-7aed58395ef2","resolution":{"observed_at":"2026-05-18T01:20:34.569204Z","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":"2501.09470","last_updated":"2025-01-16T11:15:08Z","snapshot_observed_at":"2026-07-06T20:21:55.366596Z","submitted_at":"2025-01-16T11:15:08Z","title":"Control and its applications in additive combinatorics","version":1},"cited_work":{"arxiv_id":"2501.09470","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.09470","snapshot_observed_at":"2026-06-29T15:13:32.283099Z","title":"Control and its applications in additive combinatorics.arXiv:2501.09470, 2025","venue":null,"work_id":"7115b26d-4468-470e-b040-65219e93caeb","year":2025},"citing_paper":{"arxiv_id":"2604.21949","last_updated":"2026-04-22T19:03:25Z","snapshot_observed_at":"2026-07-06T23:08:28.444591Z","submitted_at":"2026-04-22T19:03:25Z","title":"A note on the sum-product problem for fractal sets","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-05-09T22:20:17.744369Z"},"links":{"cited_paper":"/paper/2501.09470","citing_paper":"/paper/2604.21949"},"observation_digest":"sha256:81c094b8a8492fddc0e4ee84da7c4917a96bc6184aeddf55e9d353499d319fda","observation_id":"2f60ee6f-3c47-4931-b4f0-965d8370c2ec","resolution":{"observed_at":"2026-05-09T22:49:15.693072Z","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":"2501.09470","last_updated":"2025-01-16T11:15:08Z","snapshot_observed_at":"2026-07-06T20:21:55.366596Z","submitted_at":"2025-01-16T11:15:08Z","title":"Control and its applications in additive combinatorics","version":1},"cited_work":{"arxiv_id":"2501.09470","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.09470","snapshot_observed_at":"2026-06-29T15:13:32.283099Z","title":"Control and its applications in additive combinatorics.arXiv:2501.09470, 2025","venue":null,"work_id":"7115b26d-4468-470e-b040-65219e93caeb","year":2025},"citing_paper":{"arxiv_id":"2606.24583","last_updated":"2026-06-26T08:29:55Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-06-23T13:45:26Z","title":"More sum-product type counterexamples: products with shifts and $AA+A$","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-29T05:27:12.157038Z"},"links":{"cited_paper":"/paper/2501.09470","citing_paper":"/paper/2606.24583"},"observation_digest":"sha256:b4c8921ca9feedde9cd9fd01c622634736dfc1d041c99dc401041d3f9748f9c8","observation_id":"395bacf3-1ffb-43c5-ae47-17924f519020","resolution":{"observed_at":"2026-06-29T15:13:32.284946Z","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":"2501.09470","last_updated":"2025-01-16T11:15:08Z","snapshot_observed_at":"2026-07-06T20:21:55.366596Z","submitted_at":"2025-01-16T11:15:08Z","title":"Control and its applications in additive combinatorics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.09470","snapshot_observed_at":"2026-08-03T14:55:04.986154Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.29042","last_updated":"2026-07-31T05:43:56Z","snapshot_observed_at":"2026-08-09T00:27:15.435269Z","submitted_at":"2026-07-31T05:43:56Z","title":"The Entropic Sum-Product Phenomenon","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T14:55:04.986154Z"},"links":{"cited_paper":"/paper/2501.09470","citing_paper":"/paper/2607.29042"},"observation_digest":"sha256:2bfc155273ac4a229909400b793f8278458ed310ad7ca509a175c80ce7adc880","observation_id":"556d978f-f46a-4190-b658-62e921ec54ac","resolution":{"observed_at":"2026-08-03T14:55:04.986154Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2501.09470/citation-record","integrity":"/paper/2501.09470/integrity","json":"/paper/2501.09470/citation-record.json","paper":"/paper/2501.09470"},"outbound":[],"paper":{"arxiv_id":"2501.09470","last_updated":"2025-01-16T11:15:08Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-07-06T20:21:55.366596Z","submitted_at":"2025-01-16T11:15:08Z","title":"Control and its applications in additive combinatorics"},"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 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 6 inbound Pith citation observations for arXiv:2501.09470."}