{"as_of":"2026-08-12T20:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0f83b9acdd7d6c5fd872725e1a1b36884b285c9b102d961dc3623a9e9bf33d02","coverage":[{"denominator":40,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":40,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T18:59:47.392211Z","state":"measured"},{"denominator":44,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":44,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T16:05:20.356819Z","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":"2026-07-03T03:47:35.838399Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.07321","snapshot_observed_at":"2026-08-05T16:05:20.356819Z","title":"L2-Flattening of Self-similar Measures on Non-degenerate Curves","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2508.19047","last_updated":"2025-08-26T14:00:58Z","snapshot_observed_at":"2026-08-12T09:10:21.737023Z","submitted_at":"2025-08-26T14:00:58Z","title":"Furstenberg set theorem for transversal families of functions","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T16:05:20.356819Z"},"links":{"cited_paper":"/paper/2507.07321","citing_paper":"/paper/2508.19047"},"observation_digest":"sha256:2a7f540dc15959cbb4978efcc8c42cfd835d8bf49a1c57c384a97221198e8828","observation_id":"d6614cac-8a04-46f4-b27e-7992e84b2380","resolution":{"observed_at":"2026-08-05T16:05:20.356819Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"cited_work":{"arxiv_id":"2507.07321","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07321","snapshot_observed_at":"2026-07-03T03:47:35.838399Z","title":"Algom and O","venue":null,"work_id":"2340fa9a-e887-492e-bcc1-b713878e0091","year":2025},"citing_paper":{"arxiv_id":"2606.09743","last_updated":"2026-06-08T17:05:29Z","snapshot_observed_at":"2026-08-06T22:25:52.426782Z","submitted_at":"2026-06-08T17:05:29Z","title":"Fourier transform of nonlinear images of self-similar measures: qualitative aspects","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-27T14:36:54.793726Z"},"links":{"cited_paper":"/paper/2507.07321","citing_paper":"/paper/2606.09743"},"observation_digest":"sha256:b67f0edaeb28c24f31b1a00bb0e02253581ce3c69953fa34b4e5dbb651cf1460","observation_id":"23f3c984-a34f-4ee1-bb11-a2a3f27685f4","resolution":{"observed_at":"2026-07-03T03:47:35.839802Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"cited_work":{"arxiv_id":"2507.07321","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07321","snapshot_observed_at":"2026-07-03T03:47:35.838399Z","title":"Algom and O","venue":null,"work_id":"2340fa9a-e887-492e-bcc1-b713878e0091","year":2025},"citing_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},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-06-27T05:17:14.220738Z"},"links":{"cited_paper":"/paper/2507.07321","citing_paper":"/paper/2606.13170"},"observation_digest":"sha256:5d7462871a3bc125f4c49f6bbdff57a02dd04671e8e865728160e628e204dd84","observation_id":"27db98a9-8943-4446-b82b-7a99251d29a8","resolution":{"observed_at":"2026-06-27T05:20:35.783439Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.07321","snapshot_observed_at":"2026-08-01T06:16:31.591729Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.22001","last_updated":"2026-07-24T06:01:12Z","snapshot_observed_at":"2026-08-09T07:50:43.765989Z","submitted_at":"2026-07-24T06:01:12Z","title":"Fourier decay and non-decay for pseudo-affine self-conformal measures","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-01T06:16:31.591729Z"},"links":{"cited_paper":"/paper/2507.07321","citing_paper":"/paper/2607.22001"},"observation_digest":"sha256:8fcd73a257cb9258bf0ee0558f59b78aecf94910a445d7b9310f6dc85c3fc9a8","observation_id":"f75c57cc-cfa9-4d59-8784-884327a15938","resolution":{"observed_at":"2026-08-01T06:16:31.591729Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.07321/citation-record","integrity":"/paper/2507.07321/integrity","json":"/paper/2507.07321/citation-record.json","paper":"/paper/2507.07321"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:48.157082Z","title":null,"venue":null,"work_id":"6d3c7599-63ef-4536-a864-b5eb046f2ef6","year":2025},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.189397Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:8b2ba643b952e96b0dad30c94f06c3a6ffcecedddcb335a95eaf8a2a51866ff9","observation_id":"f4a6f751-98c0-4c5a-9bc7-f519c3695aa6","resolution":{"observed_at":"2026-08-06T18:59:48.161945Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:48.140108Z","title":null,"venue":null,"work_id":"77a4398b-f3a3-4c60-a8d9-c6d28aa049fa","year":2022},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.195795Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:1a5ea1521b94b82088bf8eda6e08a86f41820c54a9943df3db3c4fdcab62f2bb","observation_id":"1b156d26-c20f-47fb-8952-7b56163c8834","resolution":{"observed_at":"2026-08-06T18:59:48.146680Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"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":"2026-08-06T18:59:47.200448Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.200448Z"},"links":{"cited_paper":"/paper/2306.01275","citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:938dacd6f27ced929914d25287f278f979235bacb0ebea930d98f3229c0e83ba","observation_id":"334bf01b-4816-4426-bae3-8a1f995ae4c4","resolution":{"observed_at":"2026-08-06T18:59:47.200448Z","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":"2026-08-06T18:59:47.207108Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.207108Z"},"links":{"cited_paper":"/paper/2407.11688","citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:ff5e8119688b0ec7531e50bbe4868ab1e2c44f747ddc01111d39d901c5f124f4","observation_id":"e205a0ff-4449-410b-9d2a-1e92741fff71","resolution":{"observed_at":"2026-08-06T18:59:47.207108Z","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":"2026-08-06T18:59:48.124375Z","title":null,"venue":null,"work_id":"370ab411-10e1-4948-9bbf-42947bb82966","year":2025},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.213108Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:7c10497cfbf4d24de7a1c7a77759af44a0075f5f1849aaf724a318fff965a4ba","observation_id":"e50569de-b4b8-4d1e-b3ed-fab6a0bb3843","resolution":{"observed_at":"2026-08-06T18:59:48.129479Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:48.108834Z","title":null,"venue":null,"work_id":"62cee265-7dd1-4151-ba6a-477f4096b5d4","year":2010},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.218194Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:a7581406a94ace7f05ba987a28b84e946d63d410432d9614c7421fc3e40632dc","observation_id":"c5e68897-23d8-44b8-9a7f-ca6eeefb340d","resolution":{"observed_at":"2026-08-06T18:59:48.113496Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"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":"2026-08-06T18:59:47.224387Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.224387Z"},"links":{"cited_paper":"/paper/2407.16699","citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:dc28c876ec920a18b6e483c64f0e317b1d3d8162aaef7d2a715150671403c2b5","observation_id":"6cd80fa2-9c3b-4010-8f4b-172cf6434895","resolution":{"observed_at":"2026-08-06T18:59:47.224387Z","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":"2026-08-06T18:59:48.091935Z","title":"Bishop and Yuval Peres, Fractals in probability and analysis, Cambridge Studies in Advanced Mathematics, vol","venue":null,"work_id":"41db4997-8bbd-453f-a13f-5ed4ba0b701c","year":2017},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.229223Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:1141382769372c3683ea47acd35f46568b8990ab0c311ccb58d7786d090903f9","observation_id":"7eabaf39-6dce-4b6c-9a49-759f67abbf64","resolution":{"observed_at":"2026-08-06T18:59:48.097290Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:48.075929Z","title":null,"venue":null,"work_id":"8be4ebcc-6149-408e-9968-e9441d8a2ee8","year":2021},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.234121Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:d43f4e0d6a16432a8c3b968134d26dafbe12726faaead9bf3897f9fbc12d65ed","observation_id":"1c107a51-40dd-46f7-a176-0ccea1b66231","resolution":{"observed_at":"2026-08-06T18:59:48.080899Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"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":"2026-08-06T18:59:47.238808Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.238808Z"},"links":{"cited_paper":"/paper/2306.01389","citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:78f25ff85eda004039171930c339887a13ef472edc6f4da31980197414621ff5","observation_id":"297a95f0-682e-4a91-b3b2-b10a20582f51","resolution":{"observed_at":"2026-08-06T18:59:47.238808Z","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":"2026-08-06T18:59:47.243809Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.243809Z"},"links":{"cited_paper":"/paper/2503.07508","citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:c560dcd7bc49d378ab282e08aa62240fdf0ce087d3452a36c1065dddedf0c7ce","observation_id":"2b855854-7fee-48a9-ab07-00f5f1e31feb","resolution":{"observed_at":"2026-08-06T18:59:47.243809Z","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":"2026-08-06T18:59:48.060464Z","title":null,"venue":null,"work_id":"9c717e69-06b0-4dac-b8cd-927d9451433b","year":2024},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.249936Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:45562aa5b2dccea319ab3c947e98077fd26a0f63dc2631e4cef5f2ea2c48cb39","observation_id":"97fecfa7-7402-4511-9031-ad6df397e0ae","resolution":{"observed_at":"2026-08-06T18:59:48.065188Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:48.045460Z","title":null,"venue":null,"work_id":"d1b7849c-a937-47eb-9cc7-77a8bbd41738","year":2007},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.255041Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:0fb13a55fc1596c7098a65c40facc7c57b4f68e813280ca7b6630b9a3ed77bb4","observation_id":"24258702-944d-4bd1-bc50-fe93864531a5","resolution":{"observed_at":"2026-08-06T18:59:48.050111Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:48.028233Z","title":null,"venue":null,"work_id":"6928eb5f-cca9-46ac-b696-01c2ced8e49e","year":2025},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.260328Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:2b4b8352e164219d2aa5621b10a4c2cd52ce14d7d317104976a9c0eb5ed87c6f","observation_id":"840b30d9-e748-41eb-b5c4-1b84d1138598","resolution":{"observed_at":"2026-08-06T18:59:48.033780Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:48.010774Z","title":"1, 109--119","venue":null,"work_id":"360fff3b-3382-4818-87b7-f7245c12bf1e","year":2018},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.265599Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:bb3c51f24e5040d9653ad2515e82491f4cc20f1d2bc7b7e21818f63bd4a3db8a","observation_id":"b260f11e-36d5-4b0f-be34-0886897a840a","resolution":{"observed_at":"2026-08-06T18:59:48.016396Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.993361Z","title":null,"venue":null,"work_id":"df652f8e-e84f-4d0a-8892-46faf4d0fef9","year":2009},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.271223Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:4b63823e31d760250aedc83f5fe459f42bf874d74f94103b0a5405eeadcaf14e","observation_id":"4c78157f-98ac-425a-8035-7b3dd7bd8dbb","resolution":{"observed_at":"2026-08-06T18:59:47.999218Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.976064Z","title":"Nguyen, and Tonghui Wang, Convolutions of equicontractive self-similar measures on the line, Illinois J","venue":null,"work_id":"71910350-1f66-4385-ac3b-23d25034d1da","year":2002},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.276552Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:516c65c6cbde7d5ad270d9d51cba90c9295dcbb4976ac9d0bc3d08cb45bbb776","observation_id":"361da0cd-5886-4cf0-8801-92a9973958c3","resolution":{"observed_at":"2026-08-06T18:59:47.982165Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.958212Z","title":"2, 353--381","venue":null,"work_id":"2aaf5b5f-7657-4b07-a9f1-b29e0dd33bf4","year":2014},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.281376Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:718df0ecb35636d6ec09af31f6f7a66194744194ce21609ff2bbe6d6eaacbd78","observation_id":"d40a9b0c-5c71-4a98-9817-f39331f55b89","resolution":{"observed_at":"2026-08-06T18:59:47.964187Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.940856Z","title":null,"venue":null,"work_id":"c8646070-896c-4b11-963c-65c85963f18f","year":2024},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.286450Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:ce8aaef10ef5c5295a70b675e7427c557e8c675cbd0da790cdf70a949f086bc4","observation_id":"fa97b63d-fa02-4771-a244-3e83a6621f83","resolution":{"observed_at":"2026-08-06T18:59:47.946379Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2209.12342","last_updated":"2022-09-25T22:46:36Z","snapshot_observed_at":"2026-08-10T12:38:40.658604Z","submitted_at":"2022-09-25T22:46:36Z","title":"H\\\"older regularity of stationary measures","version":1},"cited_work":{"arxiv_id":"2209.12342","doi":null,"metadata_source":"pith","pith_arxiv_id":"2209.12342","snapshot_observed_at":"2026-08-06T18:59:47.610208Z","title":"H\\\"older regularity of stationary measures","venue":"math.DS","work_id":"de0e2ddb-0336-4a84-af0a-c02fac776362","year":2022},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.291856Z"},"links":{"cited_paper":"/paper/2209.12342","citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:25a5b94287208f4772ed2f857552daccb97648f2dce958daff87281da36cba57","observation_id":"43020337-a2e8-488f-bb7e-2c9a64c14cc3","resolution":{"observed_at":"2026-08-06T18:59:47.615765Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1503.09043","last_updated":"2017-06-05T18:27:51Z","snapshot_observed_at":"2026-07-06T04:13:40.818302Z","submitted_at":"2015-03-31T13:46:44Z","title":"On self-similar sets with overlaps and inverse theorems for entropy in $\\mathbb{R}^d$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1503.09043","snapshot_observed_at":"2026-08-06T18:59:47.296892Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.296892Z"},"links":{"cited_paper":"/paper/1503.09043","citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:56bd188821f0a35ff3351980d438b1d357f92a89933a1d4c2375c30249609c20","observation_id":"068bc53d-5556-4226-aedf-fe0b2b47691b","resolution":{"observed_at":"2026-08-06T18:59:47.296892Z","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":"2026-08-06T18:59:47.923632Z","title":"Hutchinson, Fractals and self-similarity, Indiana Univ","venue":null,"work_id":"3568029c-b03c-42f3-9786-05aff19e73f4","year":1981},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.302003Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:1b5b8e2a1227ad20efc9e84e8ada461f162f30bb1c85f3b183b38f0db1eccb99","observation_id":"06a1ec90-4009-4d1c-a523-3d4ed7d50a29","resolution":{"observed_at":"2026-08-06T18:59:47.929113Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.907156Z","title":"Math., vol","venue":null,"work_id":"5774e2af-5f77-4690-a78c-ecc600b65d92","year":1982},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.307428Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:5a371ab079f4d5aea07be912438e012a6ae55eea12ec45547535a4464af2173f","observation_id":"17e6a06b-7e31-4287-ba94-e385a334c8eb","resolution":{"observed_at":"2026-08-06T18:59:47.912578Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"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":"2026-08-06T18:59:47.312208Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.312208Z"},"links":{"cited_paper":"/paper/2305.00527","citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:e74007b946d0b3f0ed15423f55030c7f907662f1033afeb9f6df1a1ee5b44b05","observation_id":"68888044-394a-424f-b31c-1c43ad192ddc","resolution":{"observed_at":"2026-08-06T18:59:47.312208Z","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":"2026-08-06T18:59:47.889536Z","title":"(N.S.) 10 (2004), no","venue":null,"work_id":"775f379c-e3e5-46f8-ad9c-3474086e5e61","year":2004},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.317433Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:e1d92151921acd33a15417fb16c6c294825ef482e8ae390934a55d776b93ca59","observation_id":"dd03297d-4452-4927-ba90-1ff7858d4c42","resolution":{"observed_at":"2026-08-06T18:59:47.895849Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.872719Z","title":null,"venue":null,"work_id":"d2a8972e-dfad-49c2-8e5e-8e804e133b07","year":2022},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.322191Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:7e9ee9738206c844378d74e46902ad0d0dd72aa5ae489bf6339cfe4a51e50e21","observation_id":"4552b3af-b851-4845-b817-df20b632ceb1","resolution":{"observed_at":"2026-08-06T18:59:47.878277Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.326859Z","title":"150, Cambridge University Press, Cambridge, 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.326859Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:cdd19dcb1b06e1fb39d8831563f910ebdf7f46a6f4bf93c23946ba1a8a5f2f7a","observation_id":"65b89ff3-5ac4-4da2-8c83-41d7fe9b0661","resolution":{"observed_at":"2026-08-06T18:59:47.326859Z","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":"2026-08-06T18:59:47.332061Z","title":"Mosquera and Pablo S","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.332061Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:c4014cbd3206348b5ef66c50678f624a7c2ebf83d6772a6158f0370d348a8061","observation_id":"4efbfa9b-9b5a-4e66-b7b8-e92998fc70bd","resolution":{"observed_at":"2026-08-06T18:59:47.332061Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.17867","last_updated":"2025-07-08T07:49:26Z","snapshot_observed_at":"2026-08-09T23:58:18.824214Z","submitted_at":"2024-01-31T14:26:13Z","title":"On Fourier transforms of fractal measures on the parabola","version":3},"cited_work":{"arxiv_id":"2401.17867","doi":null,"metadata_source":"pith","pith_arxiv_id":"2401.17867","snapshot_observed_at":"2026-08-06T18:59:47.553364Z","title":"On Fourier transforms of fractal measures on the parabola","venue":"math.CA","work_id":"0ed8148c-fb6d-4ba2-a784-413b5fb42ac4","year":2024},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.337156Z"},"links":{"cited_paper":"/paper/2401.17867","citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:22d9ad13b82890857e5743b9065e5ea94010de5fdd3af79536d67050553a4c76","observation_id":"bd1a9eee-9b6f-47a5-acb4-ee746e733149","resolution":{"observed_at":"2026-08-06T18:59:47.559347Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.834965Z","title":null,"venue":null,"work_id":"3b1fb584-eb66-42fb-b769-a00c6e552a54","year":2023},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.343034Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:804c8ab0b52154e3965cfbb5b2df9af5e2dba3e1c12b2f34a3f29f543276375f","observation_id":"e29f2f9b-ad35-4f69-9c26-626ebb13a53e","resolution":{"observed_at":"2026-08-06T18:59:47.840493Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.817596Z","title":null,"venue":null,"work_id":"435ec7f3-a6c6-47d6-a11b-00f3bfa6e376","year":2022},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.347701Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:3db1cc2c876f32c638454e361f27ac97816edad6c3af3935475cabfae1a67172","observation_id":"aec7884e-9741-4ce1-834d-5b534f295cbd","resolution":{"observed_at":"2026-08-06T18:59:47.823416Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.800559Z","title":null,"venue":null,"work_id":"907816e5-303f-43e7-a4b5-75638f94ca9f","year":2014},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.352691Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:7856ddd4492be0b6064cab499b501e6ff162f4762be2e25147eef326e128def1","observation_id":"f24a5d98-de36-42c2-82e6-2b41e551cefb","resolution":{"observed_at":"2026-08-06T18:59:47.805396Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.784042Z","title":null,"venue":null,"work_id":"124138ed-31e0-4f9c-8391-82d9362e38f8","year":2019},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.357712Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:90a9a89654bc68d728a18397a22d37e8db4fe0ee0d2229729d004afb0b68807a","observation_id":"22e79a53-810a-45bb-95ae-9e1eabbec336","resolution":{"observed_at":"2026-08-06T18:59:47.789413Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.767426Z","title":"1, 65--82","venue":null,"work_id":"a6e6084d-c9ea-4595-bbdc-1a22a3a278d4","year":2025},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.362259Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:9d7df63fe46e7bb0d621db91549c666e0ee65e63094fd99dfd20cbee6d2d6e13","observation_id":"05a6aa98-b781-49e1-bc7d-1321a0336f59","resolution":{"observed_at":"2026-08-06T18:59:47.773154Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.750828Z","title":null,"venue":null,"work_id":"88bad449-1709-412d-8df3-947fbdf6cb3b","year":2021},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.367179Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:c4d28dd97899047ed6fa8f58e042d1e73036211f7a0e362f50bb355c4ca70093","observation_id":"53f85ac4-c245-4a73-87b9-4264b09acc7b","resolution":{"observed_at":"2026-08-06T18:59:47.755819Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.372182Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.372182Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:143a5abb3199325b8b51aca0d577eae640dc2a79b644dbb6860f211ba9207a4e","observation_id":"41406e9e-2d6d-481b-98d5-8963524c9f2a","resolution":{"observed_at":"2026-08-06T18:59:47.372182Z","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":"2026-08-06T18:59:47.733925Z","title":null,"venue":null,"work_id":"509be213-ea2e-4736-8190-c34f4e5c5f1c","year":2015},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.376968Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:bda50c0d6fdeee241b334aa4d9c5297d5a1e42ed5ad78ff31055f9915d8e2463","observation_id":"15210ace-bf74-4a29-9983-a7fd34a0de07","resolution":{"observed_at":"2026-08-06T18:59:47.739709Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:59:47.381949Z","title":"105, Cambridge University Press, Cambridge, 2006","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.381949Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:82e7f5fddf54306b058046763b067fe71b3142bca7552d82cea952981c21a1f5","observation_id":"09cebfa9-13fe-49fc-80f7-b1d4526025da","resolution":{"observed_at":"2026-08-06T18:59:47.381949Z","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":"2026-08-06T18:59:47.707094Z","title":"Varj\\' u and Han Yu, Fourier decay of self-similar measures and self-similar sets of uniqueness, Anal","venue":null,"work_id":"08804da7-5331-433e-925f-28d14f154928","year":2022},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.386679Z"},"links":{"citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:2e6d722cd5988704abd3a13dbc35852123e15bd1330090366be8a60cd4c48f0c","observation_id":"364dd577-21ef-440c-b392-85d85705094d","resolution":{"observed_at":"2026-08-06T18:59:47.712107Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.23080","last_updated":"2024-10-30T14:54:07Z","snapshot_observed_at":"2026-08-04T04:58:32.385427Z","submitted_at":"2024-10-30T14:54:07Z","title":"On bounded energy of convolution of fractal measures","version":1},"cited_work":{"arxiv_id":"2410.23080","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.23080","snapshot_observed_at":"2026-08-06T18:59:47.429142Z","title":"On bounded energy of convolution of fractal measures","venue":"math.CA","work_id":"507e04df-3dd6-4814-8f61-3faf2ecf74c5","year":2024},"citing_paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-06T18:59:47.392211Z"},"links":{"cited_paper":"/paper/2410.23080","citing_paper":"/paper/2507.07321"},"observation_digest":"sha256:6a7f6f253765978a07946e7aaf322937f8123a078b92f2de7dd5cc019c000f57","observation_id":"061ae98b-b9c9-4fa0-9b8a-4b6ff263dc44","resolution":{"observed_at":"2026-08-06T18:59:47.437298Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.07321","last_updated":"2025-07-09T22:45:19Z","latest_version":1,"primary_category":"math.CA","snapshot_observed_at":"2026-08-10T12:39:35.330425Z","submitted_at":"2025-07-09T22:45:19Z","title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves"},"reference_resolution":{"displayed":40,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":28,"verified_exact":3,"verified_fuzzy":9},"total_outbound_references":40},"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 40 of 40 outbound references and 4 inbound Pith citation observations for arXiv:2507.07321."}