{"as_of":"2026-08-13T15:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fccee4ad9746122ad506f92270263da91b575ab484634155a007d32d2012612c","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T12:55:44.253758Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-01T16:03:13.341473Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-01T16:05:49.431740Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"cited_work":{"arxiv_id":"2411.16939","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.16939","snapshot_observed_at":"2026-07-01T16:05:49.431740Z","title":"Villamil","venue":null,"work_id":"af5a5ae7-4a71-4d4f-b397-33cb757212b7","year":2024},"citing_paper":{"arxiv_id":"2605.26980","last_updated":"2026-05-26T13:05:21Z","snapshot_observed_at":"2026-08-06T07:56:10.373297Z","submitted_at":"2026-05-26T13:05:21Z","title":"Dynamical spectra for skew products with unit circle fiber","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-01T16:03:13.341473Z"},"links":{"cited_paper":"/paper/2411.16939","citing_paper":"/paper/2605.26980"},"observation_digest":"sha256:91547219785883f5b9ea2fcc032c21ac3f482f56a4673d47f20063d3768719d3","observation_id":"184bfa73-b603-4c2e-9159-7303fe0b9359","resolution":{"observed_at":"2026-07-01T16:05:49.433234Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2411.16939/citation-record","integrity":"/paper/2411.16939/integrity","json":"/paper/2411.16939/citation-record.json","paper":"/paper/2411.16939"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.623233Z","title":"Arnoux, Le codage du flot g´ eod´ esique sur la surface modulaire, Enseign","venue":null,"work_id":"ed3ddb4e-a738-4866-911e-f23b010afb8b","year":1994},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.182405Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:ed617c19f198448b6c826743d46b9f2eab9d53a2e172ef8bba5dbcd667657ca5","observation_id":"12dcf3d9-f71c-4753-be84-8299b82127a7","resolution":{"observed_at":"2026-08-12T12:55:44.626867Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.613556Z","title":"Lima and C","venue":null,"work_id":"dddb1b15-3708-4dbe-8ae1-b1a4ff60bffd","year":null},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.185981Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:44d53c795016e7821936d62833433b89bab1367bb294809948048ea50f4cc9b0","observation_id":"fa9009cc-5d01-4204-abd7-1eab64eae60c","resolution":{"observed_at":"2026-08-12T12:55:44.616767Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.604745Z","title":"Pesin, Dimension Theory in Dynamical Systems: Contemporary Views and Applications, University of Chicago Press, 1998","venue":null,"work_id":"b0e9a6a6-3d01-407d-b6e7-5214845d096f","year":1998},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.189320Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:75ad40c0db6ff14447ab7cd52f39c326f0274cacb3fc3f4d57a9e0a45a6f8b8d","observation_id":"3e56b43a-ec58-4668-9ad3-69f19f879354","resolution":{"observed_at":"2026-08-12T12:55:44.608141Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2106.06572","last_updated":"2022-08-30T15:39:50Z","snapshot_observed_at":"2026-08-06T07:56:14.215150Z","submitted_at":"2021-06-11T18:47:33Z","title":"Hausdorff dimension of Gauss--Cantor sets and two applications to classical Lagrange and Markov spectra","version":2},"cited_work":{"arxiv_id":"2106.06572","doi":null,"metadata_source":"pith","pith_arxiv_id":"2106.06572","snapshot_observed_at":"2026-08-12T12:55:44.431057Z","title":"Hausdorff dimension of Gauss--Cantor sets and two applications to classical Lagrange and Markov spectra","venue":"math.NT","work_id":"aebda25a-25af-49b5-925b-0716f43027a7","year":2021},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.192723Z"},"links":{"cited_paper":"/paper/2106.06572","citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:9b0a38d749e7bfbbb331a9cb8888c6e0a9ecc0a229825640b6672206f35e61b4","observation_id":"ff21f550-ca51-4df2-a2bd-4e0415a8b8aa","resolution":{"observed_at":"2026-08-12T12:55:44.436702Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.595912Z","title":"Cerqueira, C","venue":null,"work_id":"4de4220c-0763-43ce-b5e2-9d975171534c","year":2018},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.196129Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:5837dcee1576e9c2c9aeb42c1446ef60a32845d225acb88b14cc4b3625bee9e9","observation_id":"8a125dd8-dd22-4dba-b455-4b1d7ee46c4b","resolution":{"observed_at":"2026-08-12T12:55:44.599355Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.586769Z","title":null,"venue":null,"work_id":"89e368cf-5931-4ca0-9f52-055b92c058d0","year":2020},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.199145Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:f6d9b64600d73fb7a09d9c2277bbc28e7233298b1eac060e8edf0e87a671e11a","observation_id":"53b8ca38-da89-4d4d-9c8b-981cc66b235f","resolution":{"observed_at":"2026-08-12T12:55:44.590143Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.576825Z","title":"Freiman, Diophantine approximation and geometry of numbers (The Mar koff spectrum) , Kalininskii Gosudarstvennyi Universitet, Moscow, 1975","venue":null,"work_id":"51844784-0784-4186-9b01-4f727527ba89","year":1975},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.202286Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:169bd12150dae549565a0fc1f10c73510a2cf47c3d878412d89650a7d57bb541","observation_id":"f79d09e0-b75a-482a-8908-3f5dbf8b5173","resolution":{"observed_at":"2026-08-12T12:55:44.580321Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.567179Z","title":"Lima and C","venue":null,"work_id":"13255b79-5f95-4673-b191-5e53abfa3fa4","year":2020},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.205391Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:a8ce6ca9443743a20c021cb36067e36847925d6c8f061c858deb1b3693c71eb4","observation_id":"2bb35ea6-a5fe-45ff-8474-15ecaa3d66ca","resolution":{"observed_at":"2026-08-12T12:55:44.570943Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.558171Z","title":null,"venue":null,"work_id":"cc54c444-a3d2-45c8-adce-e2ec00d8a4d7","year":1997},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.208614Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:1330657dba3d0dccad07ea7fcb15355cdad28a2539a14660998b771444abc9a8","observation_id":"cc504922-06a6-4662-a7e0-73696e1e8015","resolution":{"observed_at":"2026-08-12T12:55:44.561671Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.548407Z","title":"McCluskey and A","venue":null,"work_id":"4da4de52-27ac-46c2-8794-df0f9f8ef149","year":1983},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.211906Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:f532d1735df9159a58c683464ce16a71a3b0bb108a6d015088eba7e2de763782","observation_id":"fbd5d5ed-e0fc-4a10-8fc8-e6e8e4ded317","resolution":{"observed_at":"2026-08-12T12:55:44.551725Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.538705Z","title":null,"venue":null,"work_id":"562564e8-ca97-4855-8cd4-5afa09f3362d","year":1986},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.214810Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:e02ded8b6dbf77bc9ae28a9a5bc707af4c226e730bc63283a38079b520aabd52","observation_id":"304b19c6-83fe-4bad-a372-f7fccfde8816","resolution":{"observed_at":"2026-08-12T12:55:44.541926Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.530059Z","title":null,"venue":null,"work_id":"3f61d09d-6308-4c4b-8302-a594446ecadf","year":null},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.217844Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:132a715ad79921dd69251feb13ff2f75d58af8c7efbad22a5ae0b9344821a558","observation_id":"9fba46fa-9f5e-49b1-a424-b0aba3350c88","resolution":{"observed_at":"2026-08-12T12:55:44.533250Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.220780Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.220780Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:250aae3a4287e8f684d9b14d255adcfc4a24922ae3f7ab3e1d92c9064c5d40f1","observation_id":"5b531115-c79d-4db0-b569-c373adbdeefe","resolution":{"observed_at":"2026-08-12T12:55:44.220780Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.521004Z","title":null,"venue":null,"work_id":"c6311d63-54e5-4ffa-9525-a09385a62ace","year":2023},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.223557Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:69a1962bfe3995ded55f37696f23f48902d5d3a975d205c5be661ab3220b7359","observation_id":"424b492c-b9bc-4a80-9840-e6af21e5c3cf","resolution":{"observed_at":"2026-08-12T12:55:44.524004Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.226325Z","title":"Villamil","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.226325Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:d67dafb071deecbf48d645fcd4555bea8dd641f32d4abfbcd201e895f2e9ae62","observation_id":"00ebdb25-1d99-4137-912b-6292a92c0b4d","resolution":{"observed_at":"2026-08-12T12:55:44.226325Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.511665Z","title":null,"venue":null,"work_id":"17f33082-1e21-4aab-8f50-c3472c7639a6","year":2018},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.229171Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:eda29b7a6aa6b1f248ebc2269f7e7b7f1a1cd94ea3401e6490fd7b66911a74da","observation_id":"e5f4d9fc-76e3-4284-89c9-9734f8b1574d","resolution":{"observed_at":"2026-08-12T12:55:44.514760Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.501421Z","title":"Perron, ¨Uber die Approximation irrationaler Zahlen durch rational e II , S.-B","venue":null,"work_id":"a0e97b42-a7ef-491f-89b5-0e5f1574ae56","year":1921},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.232188Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:a6f5e923c400d5668185b9814c33c05113b1528214a61ecc350edb7190c9cf2f","observation_id":"864d23ad-2bf3-49ce-8345-8ccd3bdb20e6","resolution":{"observed_at":"2026-08-12T12:55:44.505615Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.491392Z","title":null,"venue":null,"work_id":"89c95550-7051-4c14-a41b-5497160e281d","year":2017},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.235190Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:e9e4cd1097e8bc9815dd773ab3088e0871a3ad74899465ce0bc9a505b8d54299","observation_id":"b34ae249-42d3-42aa-986e-c446378ce5d8","resolution":{"observed_at":"2026-08-12T12:55:44.494727Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.481103Z","title":"Cusick and M","venue":null,"work_id":"1d2efc37-c891-4279-b56e-219e51064a02","year":1989},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.238099Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:40dfc86db9f4216e9e0ff32781e36338f7156b116555dd4b9a6fa3cc8ebaf577","observation_id":"351ef54b-2096-40c5-900e-1402a712e66f","resolution":{"observed_at":"2026-08-12T12:55:44.484438Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.471569Z","title":null,"venue":null,"work_id":"50c86798-b0c8-4556-9de8-f424ccd4a97a","year":2010},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.241364Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:7a47fded57576298df70073b7a2262cfdbaeb0b95a6acfd636214c600e93e3e4","observation_id":"aae650ec-4336-4afe-9233-41492e802007","resolution":{"observed_at":"2026-08-12T12:55:44.475017Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.244509Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.244509Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:9e813d853fbd4e4b4e5ab19048b8837353056e8fa799439ff8bc7fc6a9acc781","observation_id":"39bc8bbb-24b5-4ba6-85d6-e8f075a90cc8","resolution":{"observed_at":"2026-08-12T12:55:44.244509Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.462424Z","title":"Palis and F","venue":null,"work_id":"0dd250d4-94f4-43b2-a695-9c1d53ee4b92","year":1993},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.247525Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:496f7171eff543edfcd4d83f6d12c5f827a443dec5be94cc61ea128d2773ecec","observation_id":"467948bb-b5c8-4456-aa92-59f19b64495c","resolution":{"observed_at":"2026-08-12T12:55:44.465412Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.452946Z","title":"Ito, Number Theoretic expansions, Algorithms and Metrical observations","venue":null,"work_id":"3d5ab3e1-c88e-45eb-9c9f-b8c75e870d23","year":1984},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.250683Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:6d8508c624b335fa97768fe6e60b796197887296da70ce861f848b2b1a4efca7","observation_id":"72c49052-419e-48ce-a146-3a07d9ccb861","resolution":{"observed_at":"2026-08-12T12:55:44.456198Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:55:44.443727Z","title":null,"venue":null,"work_id":"4201a87b-7eb8-4ca7-8eb2-cccca1889ec4","year":2020},"citing_paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T12:55:44.253758Z"},"links":{"citing_paper":"/paper/2411.16939"},"observation_digest":"sha256:e0eba8911707b9b37fbf8857593eb9ec08cd2323c45c881b5bf5ce4af052dc96","observation_id":"285d773d-679a-4a84-8ebd-24ce6d8af15a","resolution":{"observed_at":"2026-08-12T12:55:44.446960Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.16939","last_updated":"2024-11-25T21:20:40Z","latest_version":1,"primary_category":"math.DS","snapshot_observed_at":"2026-08-12T12:41:03.812937Z","submitted_at":"2024-11-25T21:20:40Z","title":"Concentration of dimension in the Lagrange spectrum"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":1,"verified_fuzzy":11},"total_outbound_references":24},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2411.16939."}