{"as_of":"2026-08-14T09:02:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7c39db3c3f220e6d3227897ee3607a8abfac3fc5b680e56011c3c1030ca43739","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-13T03:37:26.796410Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.09358/citation-record","integrity":"/paper/2607.09358/integrity","json":"/paper/2607.09358/citation-record.json","paper":"/paper/2607.09358"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s030500412300049x.url:https:","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.679366Z","title":"Multiple recurrence and popular differences for poly- nomial patterns in rings of integers","venue":null,"work_id":"6bb70663-27f3-4b7a-87bd-9cdff57588ed","year":2024},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:cf9766ad6cc507b3f3fb4acfd8e7007f3836682aab50ba5173d918d243d4ecbc","observation_id":"c3e77202-eaca-4ff6-bcfb-4b8d30f4475d","resolution":{"observed_at":"2026-07-13T03:39:17.680897Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:56.467094+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:56.467094+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.19086/da.url:https://doi.org/10.19086/da","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.694550Z","title":"Multiple recurrence and large intersec- tions for abelian group actions","venue":null,"work_id":"72306efe-132b-446f-b352-0250e2634470","year":2021},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:116c613c5f1b57f5f2bffe8114bee6a867e6b9e6a6eecbff6f1c876d9ad9a93e","observation_id":"f270e666-a9aa-4fa7-9e35-f92b2df124bb","resolution":{"observed_at":"2026-07-13T03:39:17.696039Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:56.715361+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:56.715361+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/fms.2022.97.url:https://doi.org/10.1017/fms.2022.97","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.684583Z","title":"Khintchine-type recurrence for 3-point configurations","venue":null,"work_id":"f217f556-80c0-4162-afe9-d1195f3bc7fe","year":2022},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:73aa866816122a2b5d230f1e6d489457d7bfc679b6f6444aba7d6c196a8fd74d","observation_id":"c2051bfd-aa08-4218-8f96-8c72763e5c24","resolution":{"observed_at":"2026-07-13T03:39:17.686189Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:56.960777+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:56.960777+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/bproc/229.url:https://doi.org/10.1090/bproc/229","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.674752Z","title":"On the maximal spectral type of nil- systems","venue":null,"work_id":"b9eb4db3-2539-4ee2-a713-ea7c6b2747e8","year":2024},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:bae5d61c2a9d1e2e9557338607a3a1c35a4c7adb56ab4b71417a70a33cc129c3","observation_id":"cd6be720-aa2b-48e6-92c2-2d4ee6fab923","resolution":{"observed_at":"2026-07-13T03:39:17.676214Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:57.205383+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:57.205383+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":"Minimal idempotents and ergodic Ramsey theory","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:1c1583c3a8bf52b14e9121e0bb42d7e6bb7321e6c73b56369db2070bce3f3076","observation_id":"db7dcace-a20d-4c36-8619-2f93f7121ca6","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s0143385700004090.url:https://doi","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.667458Z","title":"Weakly mixing PET","venue":null,"work_id":"2fe8462d-ccaa-4970-be09-90a24d5a4fc3","year":1987},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:d7dd3cdd4364343a6f800ce3e011103ceab9ade81b7053a51a03e4c29adff89d","observation_id":"302664a1-5749-42f3-810e-d6fbc5596c99","resolution":{"observed_at":"2026-07-13T03:39:17.668745Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:57.468225+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:57.468225+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/conm/631/12592.url:https:","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.646336Z","title":"Cubic averages and large intersections","venue":null,"work_id":"d03b762f-026d-417d-a423-8c6fc820f3c3","year":2015},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:0129fcf5bbd7ccc4e2c3f1f211c18ec214242426076af5c2324cb31e8580dc70","observation_id":"4d04813c-f31a-4b06-bdbe-dacb09e080f6","resolution":{"observed_at":"2026-07-13T03:39:17.648110Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:57.716967+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:57.716967+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":"Rigidity and non- recurrence along sequences","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:4d756a3cedfd2cc9d4c1394e1cfcbc2f7183e57aafa026c630eb6eaf2b6a35f4","observation_id":"91ddc0c9-d87e-4808-aad8-3b8ace5df08c","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/cbo9780511662812.002","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Ergodic Ramsey theory—an update","venue":"Cambridge University Press eBooks","work_id":"fb7ada29-2cf4-4915-aa78-d9a91c443ecc","year":1993},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:991bdb75e5892eee13e1604502a94f8e7f06cb47cdfb110607463d404ccaa41a","observation_id":"7f10cfc1-16c3-40c8-bf39-1f179f5f5f54","resolution":{"observed_at":"2026-07-13T03:39:17.656717Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:57.986848+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:57.986848+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/conm/530/10439","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Ultrafilters, IP sets, dynamics, and combinatorial number theory","venue":"Contemporary mathematics - American Mathematical Society","work_id":"01fba37e-3711-48ab-a570-50f109a91cf8","year":2010},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:0e3d9642a75b8f461c174507292cd699dd07c32e019bba2ae3b69ddd6c647c7f","observation_id":"a2826273-8134-43f4-8a01-dd845858fad0","resolution":{"observed_at":"2026-07-13T03:39:17.730657Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:58.216587+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:58.216587+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s0143385700010130.url:https://doi.org/10.1017/s0143385700010130","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.632239Z","title":"IP-sets and polynomial recur- rence","venue":null,"work_id":"a1856aaf-e632-4811-81e2-6e9e84e0b8c7","year":1996},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:7c63cec97fc8aa6f948068fda99a5bdde14bb2a60b69e28e849aaae6ad0a3793","observation_id":"c6dc3d7e-6c9a-4f8e-a2f2-d8e0d843ea29","resolution":{"observed_at":"2026-07-13T03:39:17.633774Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:58.456603+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:58.456603+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s0143385706000010.url:https://doi.org/","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.699107Z","title":"IP-systems, generalized polynomials and recurrence","venue":null,"work_id":"5499c0a6-5bca-49f1-ac3c-cb839a2f315d","year":2006},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:519fcad304fadd2cee0be305c87f5c420cd48c7688f40ce196f94016876cca21","observation_id":"b986adeb-1905-4f87-94c6-ab088104c549","resolution":{"observed_at":"2026-07-13T03:39:17.700769Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00222-004-0428-6.url:https://doi.org/10.1007/s00222-004-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.716919Z","title":"Multiple recurrence and nilsequences","venue":null,"work_id":"8e347513-3a20-420c-9668-677eaad44d88","year":2005},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:a79562b4c1d5d277b92a39cb13b16d6ba5bbdfb52452cc339a9a43fe861bffdb","observation_id":"1d4a6f54-bd81-421a-8d08-479ca4f71301","resolution":{"observed_at":"2026-07-13T03:39:17.718805Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4064/cm-84/85-2-549-576.url:https://doi.org/10.4064/cm-84/85-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.705235Z","title":"Aspects of unifor- mity in recurrence","venue":null,"work_id":"159ba18e-ca35-4682-872f-37d8fbf84063","year":2000},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:fd905df42d538f7497a9324c10a02e6c03a3ae2684b736781b5b2df7095cfb9d","observation_id":"caf7a122-9b52-493e-97e8-7610d61d1c7c","resolution":{"observed_at":"2026-07-13T03:39:17.706756Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/memo/0695","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"An ergodic IP polynomial Szemer ´edi theorem","venue":"Memoirs of the American Mathematical Society","work_id":"d4ecee1b-aee7-4121-a17e-fb7638ed7677","year":2000},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:ceb5a9fde6612d5b2c6ff275e930aef31edffb418b49af52e22f74a4826ec645","observation_id":"3fab1d99-0046-42a8-8685-08f701e8d1d3","resolution":{"observed_at":"2026-07-13T03:39:17.711124Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:58.690959+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:58.690959+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":"Multiple ergodic averages along func- tions from a Hardy field: convergence, recurrence and combinatorial applications","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:3f8c68d4bcf4172ed0f3401fa17ffafbb74614ea4acf36a9df8003cdf33df3d6","observation_id":"99247b38-bebd-4e30-a295-41a50720adf9","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:8d7a6812dd96fbb33d5c567f44b7c3309ac56d6de3443f8aad10444742ea7be2","observation_id":"1c23913b-15e2-4fc0-a88c-da1b56d28add","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11856-017-1606-8.url:https://doi.org/10.1007/s11856-017-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.636778Z","title":"Under-recurrence in the Khint- chine recurrence theorem","venue":null,"work_id":"a9a32ab3-4159-4809-bcfd-71894d47f7b8","year":2017},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:7c41b567c380823e36f434d6689238ab835947e31c673ab553b009c0eb101c78","observation_id":"d05536c2-71e7-4e18-8e87-8b7cdc7e8b5c","resolution":{"observed_at":"2026-07-13T03:39:17.638237Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.20459","last_updated":"2025-07-30T08:36:17Z","snapshot_observed_at":"2026-08-11T13:23:39.199721Z","submitted_at":"2025-06-25T14:08:33Z","title":"Resolving the joint ergodicity problem for Hardy sequences","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.20459","snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"cited_paper":"/paper/2506.20459","citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:1d4bd18a5e33cf1ca72dfb449a5f96414babcff3f28961a0bc6aa17a65339216","observation_id":"b68d57f3-6cf1-412c-b364-0e55530cfd9c","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/etds.2019.72.url:https://doi.org/10.1017/etds","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.721762Z","title":"Optimal lower bounds for multiple recurrence","venue":null,"work_id":"91848f95-3c16-49d8-b350-10164bf3f77d","year":2021},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:aa792a1c3f2a27278a0f930e5bd8061da1702f240bccd6a113da9af326ef80f5","observation_id":"b42becb2-26d5-4c18-afbd-f428be544b0c","resolution":{"observed_at":"2026-07-13T03:39:17.723506Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:58.943945+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:58.943945+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1112/s0024610706023374.url:https://doi.org/10.1112/s0024610706023374","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.663299Z","title":"Ergodic averages for independent polynomials and appli- cations","venue":null,"work_id":"79247b02-a649-4678-8aaa-d46494f64433","year":2006},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:f23da72c180e4d7211c3985906743dfdd9e6b8e62f6c2834e61c566cce7d6cd6","observation_id":"f2b49466-cf08-4286-bd33-f245d2a29021","resolution":{"observed_at":"2026-07-13T03:39:17.664735Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:59.187838+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:59.187838+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02775439.url:","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.659286Z","title":"Polynomial averages converge to the product of integrals","venue":null,"work_id":"92330559-f0b7-4d75-992b-ce07c05f5052","year":2005},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:636dcc4d782242af784a8ab0d5548180e0b8c20683eccd8457d907878df5703e","observation_id":"970814bb-6682-49c3-a76b-cf57e6241004","resolution":{"observed_at":"2026-07-13T03:39:17.660617Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:59.439098+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:59.439098+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00222-024-01313-w.url:https://doi.org/10.1007/","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.651121Z","title":"Joint ergodicity for commuting transformations and ap- plications to polynomial sequences","venue":null,"work_id":"7a4a0bac-d855-4e6a-8e7d-02d00326dd47","year":2025},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:aa502417aa1de4631eb870ff04c5c5edff8c75eb94404befb9b0e612bbd7741d","observation_id":"a40839d9-a022-4ba2-af1b-f4a67284dc71","resolution":{"observed_at":"2026-07-13T03:39:17.652647Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02792547.url:https://doi.org/10.1007/bf02792547","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:39:17.641371Z","title":"An ergodic Szemer ´edi theorem for IP-systems and combi- natorial theory","venue":null,"work_id":"abecbbf5-3337-4836-88e4-a7f8802e6a43","year":1985},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:505199039c81035f12b782d105383072e142f9b80216cf21779e0ce0a7e6a864","observation_id":"ba20fe4f-3cbe-4bb9-9302-aa03e38c9412","resolution":{"observed_at":"2026-07-13T03:39:17.642870Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:59.677103+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:59.677103+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":"A mean ergodic theorem for (1/N)PN n=1 f(T nx)g(T n2 x)","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:dde2aff7ab7c2460589940dad4f9ed445ca2ce07a265ccf7cc5c19c7acacd630","observation_id":"6e478307-27fd-4090-b7ae-ec0553878070","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":"Ergodic behaviour of diagonal measures and a theorem of Szemer ´edi on arith- metic progressions","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:13d4c508f38739e5bc5f9a1b31d9d0e248353112a5d41cb96afe8dd4b6482213","observation_id":"91c80a49-ba12-440c-a467-e67bbd5a3c80","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":"Nonconventional ergodic averages and nilmanifolds","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:37c2dc5e21814c2d86c5380760928f06bf85f3608b1a96f269968684167e854b","observation_id":"2302ce19-c9c3-4723-98ac-1689a2f9b990","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:2d1fb82a0633b85b91f8714cdd691b88e96041c4f7be976a29736e46611fc616","observation_id":"184e7409-24d7-4dad-b339-353755214dc7","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.17771","last_updated":"2025-06-21T17:48:25Z","snapshot_observed_at":"2026-08-14T03:02:02.074044Z","submitted_at":"2025-06-21T17:48:25Z","title":"Ergodic averages and the large intersection property along IP sets","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.17771","snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":"REFERENCES 23","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"cited_paper":"/paper/2506.17771","citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:7fc40f03d164f35d9f974361b2063f1236d48041804819a65261c0a7f80a6835","observation_id":"2ad4eb00-c3bd-4743-b163-f7a78dd95f98","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02773538","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Convergence of multiple ergodic averages along polynomials of several vari- ables","venue":"Israel Journal of Mathematics","work_id":"44012571-dc94-4b5a-a0cf-f547e9100456","year":2005},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:90d7b87885bbd534662b4b9bfe873e1c5089de50915cc962948f0f7ff62f8432","observation_id":"624cf5a9-cde4-4193-8dd8-e798a62fd7b5","resolution":{"observed_at":"2026-07-13T03:39:17.691748Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-07-20T22:51:59.906255+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T22:51:59.906255+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":"Pointwise convergence of ergodic averages for polynomial sequences of transla- tions on a nilmanifold","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:e1ae1747433df4187ee44558ca00689d2e09b827da51c93df29aaf9797a94968","observation_id":"39061f80-d24b-430b-9e30-fa9a46da034b","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":"Multiple ergodic averages in abelian groups and Khintchine type recurrence","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:afa7c96889decfab8fbcabdfd3a47a5ba187c32a60504158c5ae1ff8abe92237","observation_id":"e3302e3f-10c6-4cc8-b231-504852614895","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2604.05768","last_updated":"2026-04-07T12:10:38Z","snapshot_observed_at":"2026-08-13T13:25:19.222246Z","submitted_at":"2026-04-07T12:10:38Z","title":"On the Furstenberg-Katznelson constant for the IP Szemeredi theorem over finite fields","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.05768","snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"cited_paper":"/paper/2604.05768","citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:594435b3caa5f69b8f0309d4595280e0443196114ce6509bfbfb764e3d5024a3","observation_id":"d0a646a0-f9c6-4cfd-b1a0-d3f4518f1e76","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T03:37:26.796410Z","title":"Universal characteristic factors and Furstenberg averages","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-07-13T03:37:26.796410Z"},"links":{"citing_paper":"/paper/2607.09358"},"observation_digest":"sha256:d6fe5540670de864b78fdb6523c5c6170a945ae452047f82cefb4d2ef2a66e2c","observation_id":"fad660da-fb1a-4d20-bbed-d0c0c133a765","resolution":{"observed_at":"2026-07-13T03:37:26.796410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.09358","last_updated":"2026-07-10T12:36:18Z","latest_version":1,"primary_category":"math.DS","snapshot_observed_at":"2026-08-07T19:27:32.556883Z","submitted_at":"2026-07-10T12:36:18Z","title":"$\\mathrm{IP}_{\\mathrm{rat}}$-polynomial recurrence and large intersections"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":7,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":15,"verified_fuzzy":0},"total_outbound_references":34},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2607.09358."}