{"as_of":"2026-08-13T10:46:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1711ab6470bf5f8f9a00a3a9df4d88b9bba30972574a1140af84847316a2bc3a","coverage":[{"denominator":10,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":10,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-08T23:20:51.537960Z","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":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T23:40:03.042207Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2607.05823","last_updated":"2026-07-07T04:40:06Z","snapshot_observed_at":"2026-08-13T03:21:09.633426Z","submitted_at":"2026-07-07T04:40:06Z","title":"Large Sets of Integers with No Harmonic Triples","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.05823","snapshot_observed_at":"2026-08-01T23:40:03.042207Z","title":"Large sets of integers with no harmonic triples, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.15419","last_updated":"2026-07-16T19:44:56Z","snapshot_observed_at":"2026-08-06T13:51:27.488145Z","submitted_at":"2026-07-16T19:44:56Z","title":"Sets of unit fractions without two members whose average is a unit fraction","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T23:40:03.042207Z"},"links":{"cited_paper":"/paper/2607.05823","citing_paper":"/paper/2607.15419"},"observation_digest":"sha256:425180c33d64d084f0ec02b843e189e2185ab2740835c72f5c3db8de4101acdc","observation_id":"1c907fcb-8fa1-4d91-b2c4-5e5f799183cb","resolution":{"observed_at":"2026-08-01T23:40:03.042207Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2607.05823/citation-record","integrity":"/paper/2607.05823/integrity","json":"/paper/2607.05823/citation-record.json","paper":"/paper/2607.05823"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1073/pnas.32.12.331","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Proceedings of the National Academy of Sciences","work_id":"160ff5af-ec0e-4ed2-9f5c-abcf2addda40","year":1946},"citing_paper":{"arxiv_id":"2607.05823","last_updated":"2026-07-07T04:40:06Z","snapshot_observed_at":"2026-08-13T03:21:09.633426Z","submitted_at":"2026-07-07T04:40:06Z","title":"Large Sets of Integers with No Harmonic Triples","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-08T23:20:51.537960Z"},"links":{"citing_paper":"/paper/2607.05823"},"observation_digest":"sha256:6d1f08959109da760111a8de5aa07c14cdd855f6a52a06b0bf9a460942640756","observation_id":"941b50cf-9615-4c80-996a-0ab5833ff3cd","resolution":{"observed_at":"2026-07-08T23:25:42.009843Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-07-11T08:19:35.16453+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-11T08:19:35.16453+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2007.03528","last_updated":"2021-09-01T12:10:07Z","snapshot_observed_at":"2026-08-09T03:37:58.169787Z","submitted_at":"2020-07-07T14:58:06Z","title":"Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions","version":2},"cited_work":{"arxiv_id":"2007.03528","doi":null,"metadata_source":"pith","pith_arxiv_id":"2007.03528","snapshot_observed_at":"2026-07-08T23:25:42.063457Z","title":"arXiv preprint arXiv:2007.03528 , year=","venue":"math.NT","work_id":"8a7c6f75-a229-4e43-aef0-4ae65ecd27c8","year":2020},"citing_paper":{"arxiv_id":"2607.05823","last_updated":"2026-07-07T04:40:06Z","snapshot_observed_at":"2026-08-13T03:21:09.633426Z","submitted_at":"2026-07-07T04:40:06Z","title":"Large Sets of Integers with No Harmonic Triples","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-08T23:20:51.537960Z"},"links":{"cited_paper":"/paper/2007.03528","citing_paper":"/paper/2607.05823"},"observation_digest":"sha256:6bb6c0588d47652ae7a35213a4371ead21afadfdc5b1ca0494a2483073db3077","observation_id":"8271704c-2551-4319-8409-69106987f174","resolution":{"observed_at":"2026-07-08T23:25:42.064838Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.02353","last_updated":"2023-09-05T16:08:49Z","snapshot_observed_at":"2026-08-13T10:19:56.801496Z","submitted_at":"2023-09-05T16:08:49Z","title":"An improvement to the Kelley-Meka bounds on three-term arithmetic progressions","version":1},"cited_work":{"arxiv_id":"2309.02353","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.02353","snapshot_observed_at":"2026-07-08T23:25:42.061087Z","title":"F., Sisask, O., An improvement to the Kelley–Meka bounds on three-term arithmetic progressions, preprint","venue":"math.NT","work_id":"c5b96535-753b-4a6a-832b-579f1d079374","year":2023},"citing_paper":{"arxiv_id":"2607.05823","last_updated":"2026-07-07T04:40:06Z","snapshot_observed_at":"2026-08-13T03:21:09.633426Z","submitted_at":"2026-07-07T04:40:06Z","title":"Large Sets of Integers with No Harmonic Triples","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-08T23:20:51.537960Z"},"links":{"cited_paper":"/paper/2309.02353","citing_paper":"/paper/2607.05823"},"observation_digest":"sha256:f48afb127a308a587f84d4642cea579e5a39e00dcc7e5f7f5b394f3d8b47f3b7","observation_id":"9ab37b18-2921-4fde-a042-21be96db06e1","resolution":{"observed_at":"2026-07-08T23:25:42.062420Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.12290","last_updated":"2024-06-18T05:53:09Z","snapshot_observed_at":"2026-08-12T23:40:25.635353Z","submitted_at":"2024-06-18T05:53:09Z","title":"Improving Behrend's construction: Sets without arithmetic progressions in integers and over finite fields","version":1},"cited_work":{"arxiv_id":"2406.12290","doi":null,"metadata_source":"pith","pith_arxiv_id":"2406.12290","snapshot_observed_at":"2026-07-08T23:25:42.058387Z","title":"Elsholtz, Z","venue":"math.NT","work_id":"afec485f-9ba3-4d14-95bf-2ca635c05189","year":2024},"citing_paper":{"arxiv_id":"2607.05823","last_updated":"2026-07-07T04:40:06Z","snapshot_observed_at":"2026-08-13T03:21:09.633426Z","submitted_at":"2026-07-07T04:40:06Z","title":"Large Sets of Integers with No Harmonic Triples","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-08T23:20:51.537960Z"},"links":{"cited_paper":"/paper/2406.12290","citing_paper":"/paper/2607.05823"},"observation_digest":"sha256:e91554504624fc565d4c114d20fceb172615a71dca59f20aebe446abd6f24468","observation_id":"eb8129b1-9596-4ee6-8d54-ac1b4fa2b370","resolution":{"observed_at":"2026-07-08T23:25:42.059948Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11856-011-0061-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Elkin,An improved construction of progression-free sets, Israel J","venue":"Israel Journal of Mathematics","work_id":"40772b1b-92ca-438c-9996-54fe687eb906","year":2011},"citing_paper":{"arxiv_id":"2607.05823","last_updated":"2026-07-07T04:40:06Z","snapshot_observed_at":"2026-08-13T03:21:09.633426Z","submitted_at":"2026-07-07T04:40:06Z","title":"Large Sets of Integers with No Harmonic Triples","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-08T23:20:51.537960Z"},"links":{"citing_paper":"/paper/2607.05823"},"observation_digest":"sha256:3159f0171ed0ea671ee91fd24763954e5c91ca3f4e1fcc61029d6685b297a216","observation_id":"0981177a-7ddb-47c9-9da8-3237c5b3f727","resolution":{"observed_at":"2026-07-08T23:25:42.001221Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-07-11T08:19:35.422222+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-11T08:19:35.422222+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1112/jlms/s1-11.4.261","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Erdős and P","venue":"Journal of the London Mathematical Society","work_id":"42dd8544-68f4-4c69-b491-aae6a4e432cc","year":1936},"citing_paper":{"arxiv_id":"2607.05823","last_updated":"2026-07-07T04:40:06Z","snapshot_observed_at":"2026-08-13T03:21:09.633426Z","submitted_at":"2026-07-07T04:40:06Z","title":"Large Sets of Integers with No Harmonic Triples","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-08T23:20:51.537960Z"},"links":{"citing_paper":"/paper/2607.05823"},"observation_digest":"sha256:6a1f413988871771178eef2ab8ce91b8d8f38fcc9b0c9ef234a0542a402321b7","observation_id":"42f9ce07-bc78-4cad-80ce-af70af943364","resolution":{"observed_at":"2026-07-08T23:25:41.998406Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-07-11T08:19:35.651951+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-11T08:19:35.651951+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-0-387-68361-4_9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Green and J","venue":null,"work_id":"c2019ae0-4b47-4b67-a891-f940b99bd677","year":2010},"citing_paper":{"arxiv_id":"2607.05823","last_updated":"2026-07-07T04:40:06Z","snapshot_observed_at":"2026-08-13T03:21:09.633426Z","submitted_at":"2026-07-07T04:40:06Z","title":"Large Sets of Integers with No Harmonic Triples","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-08T23:20:51.537960Z"},"links":{"citing_paper":"/paper/2607.05823"},"observation_digest":"sha256:c4bff2b2a4759174935a89d558f438f1ed4257064f4d785abfc7b77e6ceaeb7e","observation_id":"c9e082ed-a9ce-4b27-92a2-b1a47db9eada","resolution":{"observed_at":"2026-07-08T23:25:41.991064Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-07-11T08:19:35.890536+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-11T08:19:35.890536+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"7990.2023","doi":"10.1109/focs57990.2023.00008","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS) , pages =","venue":null,"work_id":"a54acb03-1df1-4af5-8acf-770716891711","year":2023},"citing_paper":{"arxiv_id":"2607.05823","last_updated":"2026-07-07T04:40:06Z","snapshot_observed_at":"2026-08-13T03:21:09.633426Z","submitted_at":"2026-07-07T04:40:06Z","title":"Large Sets of Integers with No Harmonic Triples","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-08T23:20:51.537960Z"},"links":{"citing_paper":"/paper/2607.05823"},"observation_digest":"sha256:5ea9aca6a07cb8f333b516fa4fbeca6615031710ba708a977c58dee240b66a03","observation_id":"e235a9f0-deb0-4e7b-acf1-25b6e5532c10","resolution":{"observed_at":"2026-07-08T23:25:42.005947Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1112/jlms/s1-28.1.104","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal of the London Mathematical Society","work_id":"2b37013a-3b1f-4ffd-b837-9b843abfa919","year":1953},"citing_paper":{"arxiv_id":"2607.05823","last_updated":"2026-07-07T04:40:06Z","snapshot_observed_at":"2026-08-13T03:21:09.633426Z","submitted_at":"2026-07-07T04:40:06Z","title":"Large Sets of Integers with No Harmonic Triples","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-08T23:20:51.537960Z"},"links":{"citing_paper":"/paper/2607.05823"},"observation_digest":"sha256:2aada21058bbcd1bde4e9fb1b8110a922fb226e9391387804872f93c04ede4f5","observation_id":"79924a72-32f7-4857-92ae-6f17fffc8d86","resolution":{"observed_at":"2026-07-08T23:25:41.996393Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-07-11T08:19:36.363678+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-11T08:19:36.363678+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1073/pnas.28.12.561","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Salem and D","venue":"Cuadernos de pedagogía","work_id":"0e4de2e0-48d1-49c1-b8c1-43f6401a233a","year":1942},"citing_paper":{"arxiv_id":"2607.05823","last_updated":"2026-07-07T04:40:06Z","snapshot_observed_at":"2026-08-13T03:21:09.633426Z","submitted_at":"2026-07-07T04:40:06Z","title":"Large Sets of Integers with No Harmonic Triples","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-08T23:20:51.537960Z"},"links":{"citing_paper":"/paper/2607.05823"},"observation_digest":"sha256:2d38af1c140ee6b0fab343580e4b36035ce70fdfa40e3f478294373056865ad9","observation_id":"8f5d4699-e11b-469d-a94f-326b3007e607","resolution":{"observed_at":"2026-07-08T23:25:41.993830Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-07-11T08:19:36.616529+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-11T08:19:36.616529+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.05823","last_updated":"2026-07-07T04:40:06Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-13T03:21:09.633426Z","submitted_at":"2026-07-07T04:40:06Z","title":"Large Sets of Integers with No Harmonic Triples"},"reference_resolution":{"displayed":10,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":0,"verified_exact":9,"verified_fuzzy":0},"total_outbound_references":10},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 1 inbound Pith citation observation for arXiv:2607.05823."}