{"as_of":"2026-08-12T20:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:af92ea099414cc81fc2f4c4410cccbcf784278c8a66625d1ea83b04a42937381","coverage":[{"denominator":300,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T11:16:42.445474Z","state":"measured"},{"denominator":101,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":101,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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":"2026-08-03T07:57:37.839781Z","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":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.10496","snapshot_observed_at":"2026-08-03T07:57:37.839781Z","title":"A colorful extension of VC-dimension and geomet- ric applications.arXiv preprint arXiv:2607.10496, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.29403","last_updated":"2026-07-31T13:22:12Z","snapshot_observed_at":"2026-08-12T09:29:27.858050Z","submitted_at":"2026-07-31T13:22:12Z","title":"Strong invariants and Tverberg numbers in convexity spaces","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T07:57:37.839781Z"},"links":{"cited_paper":"/paper/2607.10496","citing_paper":"/paper/2607.29403"},"observation_digest":"sha256:4853811ad791d3b21ea14b15df6a408ff7a648b4845bf9a270e4da168e4f23a3","observation_id":"72fba714-486f-4d84-8f3e-7525870f59dc","resolution":{"observed_at":"2026-08-03T07:57:37.839781Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2607.10496/citation-record","integrity":"/paper/2607.10496/integrity","json":"/paper/2607.10496/citation-record.json","paper":"/paper/2607.10496"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T11:16:42.445474Z","title":"Aronov and E","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:deff32c714e6e5ace27544daf01a9367cd0d12e197bb6158806ac856d63e7709","observation_id":"31ca2a73-284e-478a-97bd-828eec679010","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Pyrga and S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:2118f39663fc25980a2a2e472bafa9197675df606b0e093500dd72e7fd0309b2","observation_id":"b883f36c-da1a-4b82-9304-f9e1f975c806","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:c49f95e48e9550cacb844fcad6a720c1e26bf8962e55e41e3c2183b103250d5a","observation_id":"ef3c4c89-4fd3-4e7a-ae3d-c98c346ad8c3","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"and Tardos, G","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:352ea940929571753c599d8261d6fa828ba34fe2dc6b259a54c00c80bb4c916f","observation_id":"e86a9a29-57fc-469e-9432-aad8f7308f3c","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Haussler and E","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:5c45418c24bf47d37a1433c9ef7c627a3e6f0fbee1af636d96085f37da5c0e96","observation_id":"9305e9af-d5ef-4072-9e2c-b8f16ef641b2","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Balogh and J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:e55e00ccddd4251818559a5b1170bbceed0d9b0219825a62fc5db731a60007b3","observation_id":"88abd2ca-8a9e-432f-a1f9-1ff9807fd72b","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Alon , title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:1508f072137ced467388dddd49d5379511dbbb89ef6da9dfb0cb6bd63d06e0a5","observation_id":"e1425315-41d3-4fd3-abac-7039e1d91b43","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"A generalization of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:7a6340b52709912d385431f7ad7f4f3f930f67f3046d7d29b2284e7695274308","observation_id":"bf93e35a-f3f5-42a0-b92f-38a2b2de65d8","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Journal of Combinatorial Theory, Series A , volume =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:de986581fd2a3106f9c5fbdaba5ae98f204f57fa50e3d26510f15441aee70567","observation_id":"ba7781ed-467d-4975-ae9b-a36c60a8196c","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Geometric and Functional Analysis , volume =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:506e372c1b41084e41aab733ff867811fbbdcdc25958be29882c660ee7679e01","observation_id":"e0e8552c-1ce5-4338-aa0a-f7d917cd1449","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Bus and S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:f08e7629037b1aeadc276240a68ad62d72199400e294d77c2d38db0f1956d626","observation_id":"ce25d32e-2148-4a2e-b482-2f690ea851ef","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:4b689f7c75bf25a1265579b72eed25e55dfc2c2a52fc8a206aa5103a4e37108a","observation_id":"24990f23-a363-45b4-9804-c2b1fc1e6103","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","resolver_source":null,"status":"parse_uncertain"},"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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:95383a48c5c726323b2eaf21e1af1d1369ba80d34c45bc6c0c9b01504ea64131","observation_id":"0d24f407-1cde-48c5-89ce-3d0542929c06","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:d31142deb9d46ad97392ddec0c3793d0bdfd86fde7cbf0244ac63986c872eb73","observation_id":"700c10fb-df0b-4f23-9758-7146a73fe42c","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Kupavskii and N","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:11ad4273c62092ecaa71c416a026c9dbc905e78e574f3047d41ab4b2bc5e5c64","observation_id":"2ffa2f04-cf0b-443e-a908-ab9c42c7bff2","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:50df8a1a87b91ea661697e45010d7f6d288067e3610893913e3d6797f5b932e4","observation_id":"43c45f2e-5198-451e-bf2b-fd962327aa2b","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:a85a9741dc7535f5890483ce34d8aa702688ca0f6506973bf7ba49a0dedb22f1","observation_id":"4f522d31-671a-43a1-8412-b543d115ebaf","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Kupavskii and N","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:a97a2d11dd9ba600fcb15106091409728ff565c5ab7ba740baf00c4b6c4d7b6f","observation_id":"95ee021e-cf0d-41b3-8ba5-b0abf98eb402","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:c77e694de8f2b9180b749cb10497f7edbee9b12d4aaa5a29c04b6de724da4383","observation_id":"11568407-51d2-4710-9f2b-af9a109f0200","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:d60c34551b8669b522e77964a6e6dbde1b72b52632bdade3ac7a3f27f390efdd","observation_id":"4891b3e1-3c83-4691-bd02-b46a1cffbb9c","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:b1514d1ec988c1178201d225e9d43a87694ed2d32df4ed62b4d91bba1b5e17fa","observation_id":"ed459e3e-5e1f-4aba-9c20-ba7e0a484fc8","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Keller and S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:0844baa892e666857a43728598aa17cdf2c9e83bc5baa2060e8e12ed8b1b8b22","observation_id":"6aef12ed-979e-44e4-b839-6ac6368e96bb","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Chalermsook and L","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:4391629fb0f8974f0340e2364a268ad78b9fcb4d80a3c71fdcf35cf469d4928b","observation_id":"283033bd-5251-4337-86e2-2fde88e8e081","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Hunter and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:db7dd574be7e6c51224b3b28134a7a529747530ed1dfa7ecd908c2b3a8e5bb25","observation_id":"58448566-ef92-4c82-ae7d-d55841251309","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Ackerman and B.Keszegh","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:333f055872f2b73116ac31daf631d475c11ce5943b21a47c6a5ba2d2d1a8a585","observation_id":"cd95a0c5-38d1-46ea-9e61-3971bc77d13d","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Basit and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:cdc45997d4cedb3dcb1563e7838738fe27ca71b5099ce3265cd633f926afa476","observation_id":"87245606-8ade-4b74-8ae9-99653f51db2d","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:5b6ce3e32c59848e12da81ae6ec16de63afc9e87afc6844ddc3250ccd16e85ba","observation_id":"14fa275b-c435-45f5-a268-2d1ac24bdeb9","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Fox and J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:407169d7f1fbcd3b6e7abca3ee9835ac9955761298f84845699967889d60fa86","observation_id":"32b248bc-7138-423c-8237-f0feb62a4783","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Janzer and C","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:51fc8e62853a2573e9d9379af714fd2f2dbd5db3fe900715720a3f89a02d0e2a","observation_id":"9d922885-5aef-4819-8a6e-8cb0325b792f","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:5e2fb217d8bef44e21f4176ad4945e47a140685d2b1343c96a59a93a70885d81","observation_id":"c22d663f-4610-4dab-b330-5cd2848c4f94","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Tidor and H","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:f3381bffaf97f48087f38fa8042057e6bfd90db6938c5f39c9bfe99d4cddabc7","observation_id":"47c21f50-2cd1-49dd-969d-c65cceb531ff","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:47a981f951d85fd2bc94ac8ccf783bd8d8e393acf2cab790a974b154253855ab","observation_id":"c2e85a63-a234-49c2-bcbe-970190e67559","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Rubin , title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:b7b65ae4c080fcd6eef68c0021e1a9d154286498091029245e6a1e577875e7be","observation_id":"e99e2901-d5bb-4f95-87b4-9099598d1b04","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Alon and B","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:a38f285c2875836ff1bdba8d5d41b96a7f8276700a2de4959836f56f04a01989","observation_id":"daea0d45-bd23-46b0-a7ea-2833091391ee","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Khan and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:1fa9eb38deadcda403a7dc0333ba4899097f6e937cf9fecb9cad23bc774b4f48","observation_id":"9a2f96eb-66ee-4475-abb9-e974599d4a10","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Bhore and D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:3ffefe8a76729c80cfbcb864cb67659c9363c493ec575e97350edc95bc0b7c96","observation_id":"b235421e-2653-4d76-a82f-289f9410c690","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"De and S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:42c60b042a94fcdeca7a24b653dd50381f1ec43eb7e2ea3c249eae33f11759ff","observation_id":"bafe2e07-393e-44f7-a156-07dbd9edacd1","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Even and S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:389e332b4efd1efc091b41671e75271d9216c2418566eeb593c787363e3db74d","observation_id":"825feec4-98e7-4d98-a78b-42d9f4956ed5","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"De and S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:4cdabf11e3dd7e2058c57d05bf7d2a969a92e03c9f85e796cabafe36120a938e","observation_id":"5e24fdd5-3c21-4e68-b3c2-2e7d9f01b9c6","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"De and R","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:f463fd06c49583848484b04d581cb535de3a76edcae296f5617fd0d1830716e7","observation_id":"54270f72-cd1a-4e4d-b6af-dbbd13990929","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Charikar and C","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:3aa1c00e55e067bf4b151fe3c69a96dc84ed233847c671d2a5d638a98925e204","observation_id":"b526931c-a727-4d3e-848e-6a2bc0b48655","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Dumitrescu and C","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:3253f39315936e30e296f4a12397c1e6f49062221d688191b9fee30749683f18","observation_id":"79ba0362-1ec8-4a0c-8c6e-b229b1457d04","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:6f82fff9bfd9ce5985dbf692b9fb0dcc2ed8b13d31eb9a601a1c0aa65905ab5b","observation_id":"9c535956-8471-4c31-80ef-4657fa1ec9ba","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Ackerman and B","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:3288c565539a22014eed20cb97d23f99fcc7e3b15ba5b018959638759ce5974b","observation_id":"d95b482f-36fd-4c41-a00f-b0c945ebea13","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Kaplan , title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:cc6321e3c5dc8bba68d37166817ce26251d1edcd71cecbabe29520052d3b6ec6","observation_id":"456b5b78-ff2b-4a29-9bea-e2b3dd900ecd","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Edwards and P","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:976fca32d6e83355f79a277ab3e515d7ad5b55cd11587fae8dcccb7a94e7d851","observation_id":"56934234-8ce7-4be2-823f-be15fa68d4a7","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Jung and D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:6a440baf2c28a3e33094a5735d242fa905f75fd4d84facf1da75d4b84d8cad7f","observation_id":"9cc77eee-af4d-4607-ae34-42cd4c38ae0a","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Gangopadhyay and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:aa5310d66259a7723fdaf7212584e90690a540586c9e2a1ef9bf691742981693","observation_id":"80077e82-0d5d-4988-b95e-c910de7dd370","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Keller and M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:f0bf69dc936ca23297ca6c848a42da27b74599b36f63f74b42a21aa3ef808fc2","observation_id":"52b9e6d7-df37-45ad-88cb-ecc65fd2acc4","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Chakraborty and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:c1e7307cf90a77a0867dc8b36ad98391c02ff61779b5c6a18ef9e475ea1b3c66","observation_id":"b2ca7385-d78e-40d2-a566-cf065ceaeac2","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Lawrence and W","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:08bf53709c40930d752a100aa44f4b11bdef20b659222fd54f92e8a1faacdb84","observation_id":"4c6a7c23-0784-49cd-b824-3aa7c0623b7a","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Kleitman , title =","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:18fd81ded24ae9723fd8b7dc90f4533274a5059e2a50e9080fb08b60ab36535d","observation_id":"46b6508f-da2b-4462-a578-5585cfe2adb2","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Matousek , title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:2cbb58ddbd601d615199edccc8056ef224372f07eafb95b5355a6e8bd3c9924a","observation_id":"94ad4385-e271-4541-849f-f7d2cf40d6e1","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Kleitman and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:67d7424db8cc7d8d1262538228a25aa5ee0ea5eacda14060958300b33fecfb47","observation_id":"9591e5e9-aa4f-4b3f-b4be-3137a09a81ec","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Improved bounds on the","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:de2342442dde8e5b2f7a7a675b4380a70285224b40153fc28fe395a4959d83eb","observation_id":"0e63f3d3-bf89-4c74-b40c-fb4be433ab7f","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Israel J","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:bb98f8e77900af4bd431f9679cbc379a61a102340f5d4796aa5b64cda9c10d07","observation_id":"19f6b075-60da-45aa-8a2b-0a0df247bac3","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Keller and S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:8001fe280112ca730e4b0ce989c8f74f641758a9c1b48196aea0ee2dd9909e9f","observation_id":"750c2a17-0a57-4272-9cac-eff55dd21992","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Rolnick and P","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:e1d4e5c94f0eb56b48c42b7096dba37556a454dfec80ebfdc72311f56eddf2a5","observation_id":"6e8482a4-7083-4bed-818f-f5920313c513","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Frankl and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:abadb03d5c4ea649ef79f816047a338543ed79a3cd4799cacf6f7769b5133ce8","observation_id":"e7177867-5812-4c2b-9267-bf7a9a90a9d2","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Garber and C","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:591665e58f8d4b64daad02bf83eb8f82eee6335824673f75c06d2ffac7d55ece","observation_id":"abba541e-8f48-4510-b9c9-b458aac340e3","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Keller and M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:7d1714c72478ce19cf43b3b874204732d662c1ddbc693051e9206a2c50b432fb","observation_id":"a5a3ea1c-74b9-4561-90f0-f303861fea7e","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Discrete Comput","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:927c0e2b9238eecdaab53563857ec835ee461c03d9c5f28a1d2797cd4dd3c2b4","observation_id":"e546c98e-aa7a-422d-933b-5127181f4d41","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"and Debrunner, H","venue":null,"work_id":null,"year":1957},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:d53ca467eb6e5b95b8237b1457a462b2cef89e38b350f47c4fc489158a498f2f","observation_id":"29e52057-922c-478e-90f9-7fe8bc7a66ce","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:1e1018bdcc77d3eeb06a1ab549ff49f51207d46047c41092c3524c45e16695e6","observation_id":"53759207-b258-48b8-8d2e-43e7fdb1b324","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"On point covers of parallel rectangles , JOURNAL =","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:0975ef071ef196252a094a3c9c06907be25ede1da814ea6b81f7bb9014dc25e6","observation_id":"2b557995-70c2-4077-bf79-b4151fc484c6","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"and Jiang, M","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:b34cba5b1e51bbecad5b5e83159f1ae31e5db344f197cddc7eb37f5f37c99d0d","observation_id":"514734f6-2601-471f-a5c4-c7dba0871983","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:01d88484464d9892dff6428cc9db4dacdb1f9aca3e47d0dc89c71c334a1f9e60","observation_id":"91232cf8-82c6-4ef3-8a0e-d5b4915fbda7","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:457f53717691a6c0191a059d18397a2c18f3be5772023285e20ec9ad83b9e86c","observation_id":"95614ee2-81d4-41a6-8775-e8c4e0bd9718","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Keller and M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:10e32bc316ba1c7fa9e6bd0c4e3467a67e184fbbc488d48d888e661e7562fc69","observation_id":"80ed24bf-ef5c-448c-9cb9-f4939470f54e","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Keller and Y","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:1448cd471b97d0d9de579405659e8aa54707dc693fcd2dec5a5d88e69a0fbee3","observation_id":"00bdf904-65fe-4a2f-8031-577e4ee84f82","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Keller and M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:8917a0a4110d0b58678c16829b595b3cefd237fb78a202ee0651b1d324e9b553","observation_id":"44f2716a-b7eb-4163-babb-6b5d68c74834","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Huang and Y","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:0d74dd7100fb679e16a3ee190b914fa88503fe90c940328113f02a07e9943b8d","observation_id":"04ed5184-6cef-4d17-bd12-da13bd642444","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Keller and S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:5baf99e463b30a3eb4ff881787e0c58e649038c35be9a9b4b575cbc15ab34440","observation_id":"0ff3830e-3ca7-48ad-abae-e7049d688092","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Holmsen and Donggyu Lee , title =","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:b3825a8e967543e6fb2f5eb4b133c055bc5fd4ab2cd582c529e6b001643529a6","observation_id":"64ca35df-b51d-44fb-ab4d-cb9975878d13","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":75,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:89d7be25571549b4866031548e74594c61a1f5536b4086bd0c91514d9538a3ef","observation_id":"a95bb071-b1aa-4d10-9e06-c728edf0000a","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":76,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:5710717cab15223ea1320668a3fe25dadac11e69a4662f5f4a17aa6b9aafcf60","observation_id":"b02e8738-eeca-4cab-93d4-488152d199b3","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Tverberg , title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":77,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:faabb6cb6b5be2669b1e80ce31aece2407ce212c0b374d329841aebd98acf1b2","observation_id":"25d33fb6-c6fd-4d86-8a71-7b16ba24d94d","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Katchalski and A Liu , title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":78,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:94c4ef130a0385ced9effa7dcb598cd7528c5bde654eb3b0a82ab49e6c497454","observation_id":"2130a407-2760-431e-bdb6-2d820a7220fb","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":", pages=","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":79,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:20d65dc4e84c7aefca93947ebd4e4204f1fe7d40ff626df22ba018cde8f483bb","observation_id":"f3d2f4cf-a644-476b-9e6c-a1fa230e7059","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Chernikov and P","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":80,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:85d02826f59b68d1001f93861d855aed653d9b62ba3dac6a17bcef7028324c55","observation_id":"5c4f3160-7e8e-4eef-98ee-a14c872fd211","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"2024 , journal=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":81,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:116c0ea1c00d9cdde8b165931b1c41e0dddad0dc939645153f4100cfbbc6d989","observation_id":"a10db2a9-c318-449e-bf27-d03029c1254d","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Levi , title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":82,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:bd451347939cbb4e97aafc5f891ba7e68f1111a4cee3a76583cc9455e08a5136","observation_id":"e6dfa22c-f491-407e-983e-60b2a733157f","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":83,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:7cc79cad1f3542e1c158cc95badd6543380839f337aaa9ca30977cfe2c06e336","observation_id":"6d51c510-b45f-4ce8-b2a1-6df7a5b32afc","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Conlon , pages=","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":84,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:d3119c73a4eac0af24619f4507a258cab640f1b93adbd6b2a0e68903dd4f0b56","observation_id":"9f25c6d2-4f45-4811-9b85-e02e1c07783d","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"2024 , journal=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":85,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:0064927e1445ab727e5ea8c8bd4c363e05f9e6ed60c1b6cc775dee36c22d17f5","observation_id":"18f063e6-02e5-4016-9da6-181a98ffabef","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":86,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:23b70505cc3d8351031d0ae1572b1910e2027ed42161e12a6f01bcfbcba97194","observation_id":"490373ca-dde4-40fb-8b85-d1f5c8c4596d","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Charikar and C","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":87,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:f3cb27eba15e5106b55f1898bdaf6ed895388b3c2a14bb692a77c98c924e61e7","observation_id":"4aac2bf4-8ca9-4a2b-ad37-ff7e8baf4981","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Hanneke and S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":88,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:a2a2aa8c5ec7c3450bf19bda262da8fdf3682b2b853399b7afd31d0b0921ef5f","observation_id":"26454d44-abe0-4fff-a615-0b7711f105a9","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Eckhoff , title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":89,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:fa515d16c463eebe34f7654322dd46ea229c412d705f5039c6443e90cd19f6c6","observation_id":"1a849362-41b0-4a95-88d6-582304b36aa8","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Proceedings of the 2026 Annual","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":90,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:c1b6b0a51a558a20436ac2d84f3aee859983abf9f1cd5f1e03fd6fc550200f11","observation_id":"2850ed8b-0b9b-4798-97e4-ad047ffd0334","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":91,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:5e12ce71117adaabf5df0d7aa2ec45e74ef0cf8c22abdbb6ae312604662debfd","observation_id":"721a79ad-d9ed-4c38-91fd-925bb6b37573","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":92,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:d667632cf7588f402462fa60c61a9aa197ca00292c765b0e9aa752413d7600f3","observation_id":"feda6c05-8186-4b5b-9f4d-879d64f7299f","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Daniely and S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":93,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:b6695f0f77cc02a2baa1983ef2c9e67fee6ddd8dc4622f8b01b371ed15384882","observation_id":"8ed8d216-aaac-44d7-bf49-194e5af90a96","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"1978 , author =","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":94,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:c7d2e3893520c893c897ba28f0db3e467f5775ed3e1b2e5b3d7f8226e73eee5d","observation_id":"a108c28b-8975-48f4-bf3c-8728e06fbc8e","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Brukhim and D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":95,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:8a9a6b00e4a2a743a3d61c5dd856d42de7f5c5e283119e4f9033f4839f937c15","observation_id":"9b1c13b2-4495-41ba-b0d1-b12c0426ab60","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Daniely and M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":96,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:4356d534d883c85c8bd23a04c3cae41abdd9d7767998ab3b3e3a2d0d71fe3ea4","observation_id":"4028b0ae-915d-46e0-929e-5a4673084ce3","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":97,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:b0b4febdaf3290570d9d57a1be143dc297450455fb805832dcdb4a2a01aa317b","observation_id":"f47c3ab7-14ad-405d-9f8c-703c44dc453c","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"The partition conjecture , journal =","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":98,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:f2ecdfe860fde9945f5e2749c707219a0ccdd0ac4d599323578e7ea5956fc55a","observation_id":"215159c5-0ec9-4245-bcb3-702cf4ba48d8","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"Holmsen , title =","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":99,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:6cba7b69949e93e253d36bd9b7e225f08ae0efba69fe2d30bf2ea014bcbb41ce","observation_id":"1ea426bd-b2fe-435d-9b6f-016f5c5ff756","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","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":"2026-07-14T11:16:42.445474Z","title":"2025 , eprint =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications","version":1},"reference_index":100,"source":"arxiv_source","source_observed_at":"2026-07-14T11:16:42.445474Z"},"links":{"citing_paper":"/paper/2607.10496"},"observation_digest":"sha256:35be9baf8f2c4c3c15208916d1255f88cd6860f75dd469fe0841d3d801fa3d00","observation_id":"c64857ae-27a2-45c1-b44a-8fc80fe93be1","resolution":{"observed_at":"2026-07-14T11:16:42.445474Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.10496","last_updated":"2026-07-11T22:10:16Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-11T14:22:45.561955Z","submitted_at":"2026-07-11T22:10:16Z","title":"A Colorful Extension of VC-dimension and Geometric Applications"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":1,"unresolved":99,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":300},"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 100 of 300 outbound references and 1 inbound Pith citation observation for arXiv:2607.10496."}