{"as_of":"2026-08-12T20:19:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fd096ed9a3d6d55d4477887d32577a355c601b602d8c3be0950454c8c2371ff9","coverage":[{"denominator":42,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":42,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T16:33:56.475979Z","state":"measured"},{"denominator":42,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":42,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.18010/citation-record","integrity":"/paper/2607.18010/integrity","json":"/paper/2607.18010/citation-record.json","paper":"/paper/2607.18010"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2401.01120","last_updated":"2024-01-02T09:36:31Z","snapshot_observed_at":"2026-07-06T17:10:48.157731Z","submitted_at":"2024-01-02T09:36:31Z","title":"Van der Corput and metric theorems for geometric progressions for self-similar measures","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.01120","snapshot_observed_at":"2026-08-01T16:33:54.594395Z","title":"Algom, Y","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:54.594395Z"},"links":{"cited_paper":"/paper/2401.01120","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:31cb3d01d522e0f0fb319d728e6d7966aa4ebeb5a52cbad76c0bd276fa07ff63","observation_id":"91eb794e-643d-4d79-a737-0bcccff21122","resolution":{"observed_at":"2026-08-01T16:33:54.594395Z","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":"2026-08-01T16:33:54.638822Z","title":"Algom, F","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:54.638822Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:0fe198d499c727f02a6e096921f2bf9a92bc5c7b05de6071b1504c2777f0d18a","observation_id":"c89aa7a8-d3e1-4ba7-907c-07af8b99a82c","resolution":{"observed_at":"2026-08-01T16:33:54.638822Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.01275","last_updated":"2024-07-01T05:22:23Z","snapshot_observed_at":"2026-08-11T22:52:18.671249Z","submitted_at":"2023-06-02T05:32:54Z","title":"Polynomial Fourier decay and a cocycle version of Dolgopyat's method for self conformal measures","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.01275","snapshot_observed_at":"2026-08-01T16:33:54.684811Z","title":"Algom, F","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:54.684811Z"},"links":{"cited_paper":"/paper/2306.01275","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:f4786d987532547812cabfd490523a0ed6684cc54f6644318a755bd0f869a549","observation_id":"5836b014-7c97-4f2f-99a9-d6a1601d5ba8","resolution":{"observed_at":"2026-08-01T16:33:54.684811Z","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":"2026-08-01T16:33:54.737184Z","title":"Algom, F","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:54.737184Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:a1a9a0bd9f523ae4d216683d2f06fd02a1f3e51df4f17463b678c1289cef2967","observation_id":"48686088-cb33-439d-a413-57539fea0aef","resolution":{"observed_at":"2026-08-01T16:33:54.737184Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.11688","last_updated":"2025-04-11T13:42:36Z","snapshot_observed_at":"2026-07-06T18:47:08.782799Z","submitted_at":"2024-07-16T13:04:17Z","title":"Spectral gaps and Fourier decay for self-conformal measures in the plane","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.11688","snapshot_observed_at":"2026-08-01T16:33:54.775524Z","title":"Algom, F","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:54.775524Z"},"links":{"cited_paper":"/paper/2407.11688","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:422582039409bfaec496d015bed612c800fbfcd1e56ec3a1beb8a213b4701150","observation_id":"fc6619b5-f3c8-4bcf-8b66-1b5645ce3768","resolution":{"observed_at":"2026-08-01T16:33:54.775524Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.01241","last_updated":"2025-01-17T15:00:27Z","snapshot_observed_at":"2026-08-10T09:48:32.010488Z","submitted_at":"2024-01-02T15:18:07Z","title":"Polynomial Fourier decay for fractal measures and their pushforwards","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.01241","snapshot_observed_at":"2026-08-01T16:33:54.827744Z","title":"Baker, A","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:54.827744Z"},"links":{"cited_paper":"/paper/2401.01241","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:b16cfaeafa48bd1859662fbaeff52a570aefc7550c0dad981f855bccbd3c0a20","observation_id":"adb01099-e337-4c48-bbaa-987f452aa392","resolution":{"observed_at":"2026-08-01T16:33:54.827744Z","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":"2026-08-01T16:33:54.868964Z","title":"Baker, A","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:54.868964Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:675967e68d2bbee42ec09d4d6b38e988406cc858833fe34eff22444211b6479e","observation_id":"b22a6e8d-59f8-486b-8700-347cee7945fd","resolution":{"observed_at":"2026-08-01T16:33:54.868964Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.01389","last_updated":"2023-06-02T09:20:56Z","snapshot_observed_at":"2026-08-10T13:45:44.601468Z","submitted_at":"2023-06-02T09:20:56Z","title":"Spectral gaps and Fourier dimension for self-conformal sets with overlaps","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.01389","snapshot_observed_at":"2026-08-01T16:33:54.922793Z","title":"Baker, T","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:54.922793Z"},"links":{"cited_paper":"/paper/2306.01389","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:a67b02442f2e603fcc847e58bc7ed5b79f6014c9221dcc0c9a62c4f73e433cf1","observation_id":"70972a23-5602-40ce-9667-b3581311fc47","resolution":{"observed_at":"2026-08-01T16:33:54.922793Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.16699","last_updated":"2024-12-20T13:45:13Z","snapshot_observed_at":"2026-08-12T10:25:56.940043Z","submitted_at":"2024-07-01T16:05:27Z","title":"Fourier Decay from $L^2$-Flattening","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.16699","snapshot_observed_at":"2026-08-01T16:33:54.966863Z","title":"Baker, O","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:54.966863Z"},"links":{"cited_paper":"/paper/2407.16699","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:a603eb390d80263449a92fb8e21c067fef9f1272fd2b2c9be77a32c268b634d2","observation_id":"937deb4d-6a50-4705-8e88-a46c74422c2d","resolution":{"observed_at":"2026-08-01T16:33:54.966863Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.07508","last_updated":"2026-06-24T17:33:36Z","snapshot_observed_at":"2026-08-07T17:16:11.766815Z","submitted_at":"2025-03-10T16:29:39Z","title":"Fourier transform of nonlinear images of self-similar measures: quantitative aspects","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.07508","snapshot_observed_at":"2026-08-01T16:33:55.002239Z","title":"Banaji and H","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.002239Z"},"links":{"cited_paper":"/paper/2503.07508","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:960986f389db97a7642dc26bf85e356b277f94bdb99332c5bac57020ebd00f35","observation_id":"7442f649-5b83-43a1-a342-b013ff1d9321","resolution":{"observed_at":"2026-08-01T16:33:55.002239Z","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":"2026-08-01T16:33:55.061801Z","title":"B´ ar´ any, I","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.061801Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:607d86ccc280615898a9628a3ef0fdfc9dc8bdaf597c1eb78e73d3b187a1dbcd","observation_id":"c82596bf-8af5-4295-9de7-aae1493dc0fe","resolution":{"observed_at":"2026-08-01T16:33:55.061801Z","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":"2026-08-01T16:33:55.117585Z","title":"Bourgain The discretized sum-product and projection theorems.J","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.117585Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:fec8bef7cba8492b85116b2b1a98846e3781d6fde026751ed36f22f6f8b3fb9d","observation_id":"9066f8fe-ea69-43cd-ba82-cda4dd7ed0b6","resolution":{"observed_at":"2026-08-01T16:33:55.117585Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1704.02909","last_updated":"2017-05-17T14:33:48Z","snapshot_observed_at":"2026-08-11T12:02:22.020450Z","submitted_at":"2017-04-10T15:35:10Z","title":"Fourier dimension and spectral gaps for hyperbolic surfaces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1704.02909","snapshot_observed_at":"2026-08-01T16:33:55.170718Z","title":"Bourgain, S","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.170718Z"},"links":{"cited_paper":"/paper/1704.02909","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:a891a4f743fb93f35e52794496bc556e80792e0e75285044230ff6e66e782bcf","observation_id":"7b0e08ef-9d21-43d9-82b9-adc2b1b3ad16","resolution":{"observed_at":"2026-08-01T16:33:55.170718Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1504.06589","last_updated":"2016-05-11T13:58:55Z","snapshot_observed_at":"2026-08-09T21:39:42.411384Z","submitted_at":"2015-04-24T18:23:50Z","title":"Spectral gaps, additive energy, and a fractal uncertainty principle","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1504.06589","snapshot_observed_at":"2026-08-01T16:33:55.213773Z","title":"Dyatlov, J","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.213773Z"},"links":{"cited_paper":"/paper/1504.06589","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:6dfe6989acdc12fad4a560ce7f2492d1dee6bf034a4c57efc0cd6e1856c1c7ad","observation_id":"5c291ee7-82b1-4d11-b61e-c82a8be6cf6c","resolution":{"observed_at":"2026-08-01T16:33:55.213773Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.13170","last_updated":"2026-06-11T10:42:23Z","snapshot_observed_at":"2026-07-06T23:51:59.619032Z","submitted_at":"2026-06-11T10:42:23Z","title":"Quantitative flatness and obstructions in Fourier analysis","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.13170","snapshot_observed_at":"2026-08-01T16:33:55.258794Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.258794Z"},"links":{"cited_paper":"/paper/2606.13170","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:97141f335d34e1d5370566ae6bcff2c09f5da5863e3a29ffab22b217ed40ff81","observation_id":"319b94e3-9964-4dde-9369-8d119a0929a2","resolution":{"observed_at":"2026-08-01T16:33:55.258794Z","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":"2026-08-01T16:33:55.293675Z","title":"Jakobson, F","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.293675Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:9969efe6e4a3595c52531ea027ca296826767ae51cf23bde8b6ef7d0c9968ef4","observation_id":"862d2e00-6791-4cac-a556-f44ccb21d687","resolution":{"observed_at":"2026-08-01T16:33:55.293675Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1312.3619","last_updated":"2015-02-02T10:41:59Z","snapshot_observed_at":"2026-07-06T03:30:45.152007Z","submitted_at":"2013-12-12T20:40:20Z","title":"Fourier transforms of Gibbs measures for the Gauss map","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1312.3619","snapshot_observed_at":"2026-08-01T16:33:55.349650Z","title":"Jordan, T","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.349650Z"},"links":{"cited_paper":"/paper/1312.3619","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:14de8d9af1e92747fe768223132632e27516ef6abd202422be029951f5e63f36","observation_id":"c225f7bc-f24c-403a-8ff3-a29283a60e89","resolution":{"observed_at":"2026-08-01T16:33:55.349650Z","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":"2026-08-01T16:33:55.391231Z","title":null,"venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.391231Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:9b2b1dd6d75bb37ea438b62bf9a40294ba921be62d5936c9292e9cf050ff3d4e","observation_id":"5fb5e600-1bea-43a4-b5fb-3dbbb5b83a2c","resolution":{"observed_at":"2026-08-01T16:33:55.391231Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.00527","last_updated":"2024-12-28T23:12:31Z","snapshot_observed_at":"2026-08-09T20:23:54.769861Z","submitted_at":"2023-04-30T16:53:08Z","title":"Exponential Mixing Via Additive Combinatorics","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.00527","snapshot_observed_at":"2026-08-01T16:33:55.432311Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.432311Z"},"links":{"cited_paper":"/paper/2305.00527","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:e013cf3899fe170a74faf54b8ffb51441aceb6aeb6e8bb3d56d932d8d76497d2","observation_id":"388e30de-048b-4315-b75a-ca73a7ec044a","resolution":{"observed_at":"2026-08-01T16:33:55.432311Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2211.08088","last_updated":"2022-11-15T12:13:34Z","snapshot_observed_at":"2026-08-10T21:13:49.290195Z","submitted_at":"2022-11-15T12:13:34Z","title":"On oscillatory integrals with H\\\"older phases","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.08088","snapshot_observed_at":"2026-08-01T16:33:55.469996Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.469996Z"},"links":{"cited_paper":"/paper/2211.08088","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:f3801cea37305f00865c3879e8cffb140dc36a08cc0defddd51e66f4db0ff118","observation_id":"6fd9e941-bff6-4e0c-a326-37f03f718707","resolution":{"observed_at":"2026-08-01T16:33:55.469996Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2301.10623","last_updated":"2023-01-25T15:02:11Z","snapshot_observed_at":"2026-08-10T19:13:05.986670Z","submitted_at":"2023-01-25T15:02:11Z","title":"Fourier decay of equilibrium states for bunched attractors","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2301.10623","snapshot_observed_at":"2026-08-01T16:33:55.514699Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.514699Z"},"links":{"cited_paper":"/paper/2301.10623","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:dd37e967ca0099804222d5eb7c95b759c27e064ad248e7254521d3a60a170b9a","observation_id":"c8fa14e1-35e5-423e-88ff-d36480352d3a","resolution":{"observed_at":"2026-08-01T16:33:55.514699Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.10755","last_updated":"2023-07-20T10:37:24Z","snapshot_observed_at":"2026-07-06T15:56:22.198858Z","submitted_at":"2023-07-20T10:37:24Z","title":"Fourier decay of equilibrium states on hyperbolic surfaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.10755","snapshot_observed_at":"2026-08-01T16:33:55.565804Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.565804Z"},"links":{"cited_paper":"/paper/2307.10755","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:65b884f567e95b79991c48b4e995d9bdc466a9a1a717b9ca39a26b045b131596","observation_id":"f4229cc9-9567-4074-939f-6bb0382743ae","resolution":{"observed_at":"2026-08-01T16:33:55.565804Z","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":"2026-08-01T16:33:55.619446Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.619446Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:860f606cd62aa7f5ec694dd18cc702fdc8bd3760c2da4d4890feaea013240896","observation_id":"c013980f-47a7-4eab-be7d-bb86f763942d","resolution":{"observed_at":"2026-08-01T16:33:55.619446Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.23731","last_updated":"2026-07-01T17:16:30Z","snapshot_observed_at":"2026-08-10T08:11:24.221172Z","submitted_at":"2025-07-31T17:05:51Z","title":"Fourier decay of equilibrium states and the Fibonacci Hamiltonian","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.23731","snapshot_observed_at":"2026-08-01T16:33:55.683530Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.683530Z"},"links":{"cited_paper":"/paper/2507.23731","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:79a59b2c18884c4d6b139f04c21ab7dbed4d93d176ae049998fd030e832b6544","observation_id":"d59db09d-2042-40f2-b3c9-6560415da846","resolution":{"observed_at":"2026-08-01T16:33:55.683530Z","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":"2026-08-01T16:33:55.725210Z","title":"Leclerc, S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.725210Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:f0ba2a159aca22f505a9612f8ad16b7badc8874d5f717b1216d98fcf2d422ff3","observation_id":"ccf72219-2345-4461-a6fb-53d2bd28cc46","resolution":{"observed_at":"2026-08-01T16:33:55.725210Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16621","last_updated":"2024-12-21T13:28:19Z","snapshot_observed_at":"2026-08-11T10:22:05.351552Z","submitted_at":"2024-12-21T13:28:19Z","title":"Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.16621","snapshot_observed_at":"2026-08-01T16:33:55.771823Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.771823Z"},"links":{"cited_paper":"/paper/2412.16621","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:70535c370e0acd59d947ae6f5d3a4eaa8b260c04914616772418dac391439428","observation_id":"40f837c8-ba62-4ebf-8017-ca775cd06224","resolution":{"observed_at":"2026-08-01T16:33:55.771823Z","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":"2026-08-01T16:33:55.810538Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.810538Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:5d12020b74fdf8af0fe38e94c334fc39233c0ba4d576fdef61c7dc7bef1b0e11","observation_id":"f1ee891c-99b2-4f92-8671-0a3bad13b543","resolution":{"observed_at":"2026-08-01T16:33:55.810538Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1811.06484","last_updated":"2020-04-27T07:46:12Z","snapshot_observed_at":"2026-08-07T22:20:29.618618Z","submitted_at":"2018-11-15T17:22:24Z","title":"Fourier decay, Renewal theorem and Spectral gaps for random walks on split semisimple Lie groups","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1811.06484","snapshot_observed_at":"2026-08-01T16:33:55.860208Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.860208Z"},"links":{"cited_paper":"/paper/1811.06484","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:b5648e75a88aac8bd6c11449d4ea7c6b9fa4e212a7de83972fbca0bc319f49a3","observation_id":"04865661-c80a-4a64-8559-a6fcf5a76128","resolution":{"observed_at":"2026-08-01T16:33:55.860208Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.01103","last_updated":"2019-02-04T09:50:24Z","snapshot_observed_at":"2026-08-10T07:35:35.248527Z","submitted_at":"2019-02-04T09:50:24Z","title":"Kleinian Schottky groups, Patterson-Sullivan measures and Fourier decay","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.01103","snapshot_observed_at":"2026-08-01T16:33:55.907120Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.907120Z"},"links":{"cited_paper":"/paper/1902.01103","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:16406ca1eaae5a9aee210088c09279dbdb11053a1c9a8f7ef215d489d57f9044","observation_id":"c6ad15a9-5ba4-4826-a7a6-644b0fb28330","resolution":{"observed_at":"2026-08-01T16:33:55.907120Z","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":"2026-08-01T16:33:55.952964Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.952964Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:fa01bd5e048f91a2e70d783d2919f508ceef0a801bdba7f6ab6b303dcdc2ce9d","observation_id":"13f87092-1e9f-471c-89e9-84496693f573","resolution":{"observed_at":"2026-08-01T16:33:55.952964Z","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":"2026-08-01T16:33:55.998572Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:55.998572Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:9152db1a87ec40a9693da5ea3b9ea84beba6e24569527e13c08ac0210216864d","observation_id":"3a119cfb-a58a-4165-8a0c-3313d2d814ee","resolution":{"observed_at":"2026-08-01T16:33:55.998572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.00426","last_updated":"2021-01-04T18:02:53Z","snapshot_observed_at":"2026-08-10T07:31:42.421557Z","submitted_at":"2019-02-01T16:01:14Z","title":"Trigonometric series and self-similar sets","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.00426","snapshot_observed_at":"2026-08-01T16:33:56.038051Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:56.038051Z"},"links":{"cited_paper":"/paper/1902.00426","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:f0b97468924660cccb229241fb9783ef82156c221912a8bc2ce86b5ec1685306","observation_id":"2c516cb4-c8cf-427e-a15c-7fe4e91b120f","resolution":{"observed_at":"2026-08-01T16:33:56.038051Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1405.4426","last_updated":"2015-08-14T10:24:54Z","snapshot_observed_at":"2026-08-02T07:57:32.818830Z","submitted_at":"2014-05-17T19:03:27Z","title":"Random walks in the group of Euclidean isometries and self-similar measures","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1405.4426","snapshot_observed_at":"2026-08-01T16:33:56.078565Z","title":"Lindenstrauss, P","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:56.078565Z"},"links":{"cited_paper":"/paper/1405.4426","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:d4c72261386a768a414580b27af2a2624037850e6559c7ae07183c18047a0e75","observation_id":"c480f42b-4320-4d37-8e6c-6c0e9beb3b49","resolution":{"observed_at":"2026-08-01T16:33:56.078565Z","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":"2026-08-01T16:33:56.119337Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:56.119337Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:5a47994c15dd9287c2a57189e9de951b2de908b62c84ec7d2df660107fd6b773","observation_id":"fac231e4-bf5b-4b42-8156-a51c146b5e06","resolution":{"observed_at":"2026-08-01T16:33:56.119337Z","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":"2026-08-01T16:33:56.164881Z","title":"Pollington, S","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:56.164881Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:6e42a905aeac1061e130336e8aac7120374346c8d0085c99bd91fe200adf039f","observation_id":"db0403ac-f6ee-4ffd-8c4a-a9677eb945ce","resolution":{"observed_at":"2026-08-01T16:33:56.164881Z","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":"2026-08-01T16:33:56.198688Z","title":"Queff´ elec, O","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:56.198688Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:31217c7304ed687a64954600b4a5f3e9e042008b57d64d38a0333c45773a37b1","observation_id":"4b35a918-0bac-423e-9361-a796c4a4f542","resolution":{"observed_at":"2026-08-01T16:33:56.198688Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16753","last_updated":"2025-01-10T16:15:44Z","snapshot_observed_at":"2026-08-11T15:32:14.804534Z","submitted_at":"2024-12-21T20:06:10Z","title":"Dimension of self-conformal measures associated to an exponentially separated analytic IFS on $\\mathbb{R}$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.16753","snapshot_observed_at":"2026-08-01T16:33:56.248722Z","title":"Rapaport","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:56.248722Z"},"links":{"cited_paper":"/paper/2412.16753","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:315d92934fbdf4bb1a1a64fe9e88f3aeb2fdadcd28a9ce6f83036c5a81127773","observation_id":"6f4f5103-0d3a-44e0-b5b9-aa8fff2b15c1","resolution":{"observed_at":"2026-08-01T16:33:56.248722Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00585","last_updated":"2025-02-27T14:34:21Z","snapshot_observed_at":"2026-08-10T13:45:11.624575Z","submitted_at":"2023-11-01T15:32:08Z","title":"Fourier transforms and iterated function systems","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.00585","snapshot_observed_at":"2026-08-01T16:33:56.301954Z","title":"Sahlsten","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:56.301954Z"},"links":{"cited_paper":"/paper/2311.00585","citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:5856237fcfd98a92ae82b86f4f88c27663ac5d0c9876503dce48f86cde796d8f","observation_id":"c235e613-ac1c-4384-8a47-689af5ff9922","resolution":{"observed_at":"2026-08-01T16:33:56.301954Z","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":"2026-08-01T16:33:56.350319Z","title":"Sahlsten, C","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:56.350319Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:ab87b1a1b9768c0355c461b26532dcb7c3d6cea5c972e7e508f909bbb7b96eda","observation_id":"9f0cf7bb-7aac-4e1f-bced-5b0c4f4fa039","resolution":{"observed_at":"2026-08-01T16:33:56.350319Z","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":"2026-08-01T16:33:56.399151Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:56.399151Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:c04eb39611747d4f116c82390811eeab049e4d0ae5fbf2da48865012284ae194","observation_id":"f887b9da-f897-4608-ad38-65387d0b76a2","resolution":{"observed_at":"2026-08-01T16:33:56.399151Z","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":"2026-08-01T16:33:56.440697Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:56.440697Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:0765c0458ebfb914b9dda1b8ad80062c5b7fb7d0a1da7fcecb644f61fa612226","observation_id":"7d1adde3-4c11-4ed4-8f55-7db589c3511b","resolution":{"observed_at":"2026-08-01T16:33:56.440697Z","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":"2026-08-01T16:33:56.475979Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-01T16:33:56.475979Z"},"links":{"citing_paper":"/paper/2607.18010"},"observation_digest":"sha256:c55c9d94e8f4721476c629ffe7e9cd3962d751547229f78ee718a2d75d11e00f","observation_id":"f64927f2-3330-49b4-91c3-cf802809f412","resolution":{"observed_at":"2026-08-01T16:33:56.475979Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.18010","last_updated":"2026-07-20T14:45:30Z","latest_version":1,"primary_category":"math.DS","snapshot_observed_at":"2026-08-10T15:59:56.845426Z","submitted_at":"2026-07-20T14:45:30Z","title":"Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$"},"reference_resolution":{"displayed":42,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":42,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":42},"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 42 of 42 outbound references and 0 inbound Pith citation observations for arXiv:2607.18010."}