{"as_of":"2026-08-14T03:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e8f8b0cb29209880457cf81baf89e5ec06651d242f135ce9cd330589eebd700f","coverage":[{"denominator":31,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":31,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T15:57:23.373129Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:14:46.873479Z","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":"2026-05-16T20:31:14.733690Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.13923","snapshot_observed_at":"2026-08-07T15:14:46.873479Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.16405","last_updated":"2025-06-16T03:30:49Z","snapshot_observed_at":"2026-08-07T14:59:24.851616Z","submitted_at":"2025-05-22T08:57:48Z","title":"Microcanonical cascades and random homeomorphisms","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-07T15:14:46.873479Z"},"links":{"cited_paper":"/paper/2411.13923","citing_paper":"/paper/2505.16405"},"observation_digest":"sha256:e92f2db2aaeee852bebcaadb3cad2a9bc832bba5f9175b9b6cdb16ed0c669c69","observation_id":"2ca15100-852d-4f41-8c2a-de6e13ba5257","resolution":{"observed_at":"2026-08-07T15:14:46.873479Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.13923","snapshot_observed_at":"2026-08-06T10:49:09.501454Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban--Vargas conjecture for 1D GMC","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.23494","last_updated":"2025-07-31T12:28:43Z","snapshot_observed_at":"2026-08-06T10:48:47.699719Z","submitted_at":"2025-07-31T12:28:43Z","title":"Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T10:49:09.501454Z"},"links":{"cited_paper":"/paper/2411.13923","citing_paper":"/paper/2507.23494"},"observation_digest":"sha256:7fddbd692b183d494a82aa9378f2541d1aacbfc4aa05b4d46ff1b4c09f635c19","observation_id":"3e4fe713-4831-40cd-bd4a-c89282ddc79f","resolution":{"observed_at":"2026-08-06T10:49:09.501454Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"cited_work":{"arxiv_id":"2411.13923","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.13923","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"[LRV15] Hubert Lacoin, Rémi Rhodes, and Vincent Vargas","venue":null,"work_id":"16ed191b-87ed-4e7e-983b-df8169ea7277","year":null},"citing_paper":{"arxiv_id":"2512.19441","last_updated":"2026-05-12T15:40:34Z","snapshot_observed_at":"2026-08-02T12:30:33.684243Z","submitted_at":"2025-12-22T14:40:44Z","title":"Fourier dimension of imaginary Gaussian multiplicative chaos","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-16T20:29:34.650405Z"},"links":{"cited_paper":"/paper/2411.13923","citing_paper":"/paper/2512.19441"},"observation_digest":"sha256:8231539a56b20ccd33993a3b53a4e8f8465f3050a174b6c1098d6d265f4316bc","observation_id":"a72b54f0-4c4b-475c-b91b-3aab06e67426","resolution":{"observed_at":"2026-05-16T20:31:14.736149Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2411.13923/citation-record","integrity":"/paper/2411.13923/integrity","json":"/paper/2411.13923/citation-record.json","paper":"/paper/2411.13923"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.744731Z","title":"Random conformal weldings","venue":null,"work_id":"5ecafb85-8f5f-4311-8f62-9b1610b37f8e","year":2011},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.273730Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:6f851c006af47e13fff8f658ab57277d4881ead256ae7ee36b6a7837d75970e4","observation_id":"b92e29a7-424e-4ca2-82a7-5a5d9c314316","resolution":{"observed_at":"2026-08-12T15:57:23.747588Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.736205Z","title":"Log-infinitely divisible multifractal processes","venue":null,"work_id":"f1e76d58-4fc5-47c5-beb1-29c582052b1f","year":2003},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.277533Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:8aa18fef26252b6dbfb34cbed7389d7a50a17a3390f53fd06672c54f759cde55","observation_id":"91e66534-f097-48d0-8d70-89aa81a40917","resolution":{"observed_at":"2026-08-12T15:57:23.739231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.727657Z","title":"Self-similar and self-affine sets and measures","venue":null,"work_id":"701c8128-d4cf-42f8-830a-fad74c1d85e4","year":2023},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.280647Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:f87b6cfb5071d4aa78233bab5a4f8f650e57241f891be516dc30a811b21cb5d9","observation_id":"a5eb5ad0-cdd4-4e37-b019-2c48bdbb5beb","resolution":{"observed_at":"2026-08-12T15:57:23.730814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.719286Z","title":"Basic properties of critical lognormal multiplicative chaos","venue":null,"work_id":"de41c349-b760-4c1a-a845-af56521dbcdf","year":2015},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.283930Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:b03ba7b2e986b703f1110b4dc7c1ecfc2d32c5119362985b15a2aea664e1aa55","observation_id":"88bb067d-15fb-4cf0-b469-fe2483df1003","resolution":{"observed_at":"2026-08-12T15:57:23.722415Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.710744Z","title":"The Virasoro structure and the scattering matrix for Liouville conformal field theory","venue":null,"work_id":"b5896b58-bbab-4cdf-8449-9f7bfa8cde67","year":2024},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.288240Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:c1ab88755e9176494851c89053fc96875a6b51de73458560f555c307145e076a","observation_id":"efa2bc48-b772-42b3-a127-4661efc38b72","resolution":{"observed_at":"2026-08-12T15:57:23.713895Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.702412Z","title":"Random Hermitian matrices and Gaussian multiplicative chaos","venue":null,"work_id":"26e5b169-5bed-4652-87ce-18b9f07642ee","year":2018},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.291401Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:15a7647b3ef15bb1d0862434b921974267897d3b1c7bef5ff175d53edb6a047b","observation_id":"c47eb5aa-771d-494d-bb63-8aa7b83969dd","resolution":{"observed_at":"2026-08-12T15:57:23.705474Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.694017Z","title":"Multifractal analysis of Gaussian multiplicative chaos and applications","venue":null,"work_id":"95c51677-6c52-4f2b-9e2f-8d81a8987a74","year":2023},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.295007Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:1a033fcc821e08f3a274da4b62cc3df553bd8a50cf483b6b0819bbd735be5741","observation_id":"f6aa993a-94ec-46dd-850d-666a0441cc48","resolution":{"observed_at":"2026-08-12T15:57:23.697008Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.13455","last_updated":"2025-05-20T15:19:15Z","snapshot_observed_at":"2026-08-14T01:09:49.741701Z","submitted_at":"2024-09-20T12:37:31Z","title":"Fourier dimension of Mandelbrot multiplicative cascades","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.13455","snapshot_observed_at":"2026-08-12T15:57:23.298526Z","title":"Fourier dimension of Mandelbrot multiplicative cascades","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.298526Z"},"links":{"cited_paper":"/paper/2409.13455","citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:a6417dc548fda057719c285abaef17c6c51cf5fc88dccda346a54c85c958c540","observation_id":"ffc64088-5da3-45ef-bf8f-4beea65ec725","resolution":{"observed_at":"2026-08-12T15:57:23.298526Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.13164","last_updated":"2025-06-11T01:42:10Z","snapshot_observed_at":"2026-08-13T11:08:11.069058Z","submitted_at":"2024-09-20T02:36:23Z","title":"Harmonic analysis of Mandelbrot cascades -- in the context of vector-valued martingales","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.13164","snapshot_observed_at":"2026-08-12T15:57:23.301856Z","title":"Harmonic analysis of mandelbrot cascades -- in the context of vector-valued martingales","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.301856Z"},"links":{"cited_paper":"/paper/2409.13164","citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:82824b02aae823b14c129b38a841def05b4533b6c3dca8cf4c8c09d7871a2cdb","observation_id":"c86398ea-5508-458c-919f-2606a2a78b3a","resolution":{"observed_at":"2026-08-12T15:57:23.301856Z","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":"1904.00578","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.496893Z","title":"On the circle, Gaussian Multiplicative Chaos and Beta Ensembles match exactly","venue":null,"work_id":"3e3a6ff8-590f-4e5f-a455-2d68dee77da6","year":1904},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.305404Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:b285e4d4cfdd17d012209265b081a592baebd2457745c90faf7155c1ab94ae8f","observation_id":"238a2056-387a-49a3-bfb6-8ef2e229c9df","resolution":{"observed_at":"2026-08-12T15:57:23.501987Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.685695Z","title":"Liouville quantum gravity on the Riemann sphere","venue":null,"work_id":"3282214d-0ece-4411-9cb9-944908a2d4eb","year":2016},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.308493Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:73046ed84ed171cfb2cced633f17f6adbc98b8d52d1534e8d278eeaa2e4d2196","observation_id":"6d7ee90c-3a91-449c-9f8c-aa3df59ee35d","resolution":{"observed_at":"2026-08-12T15:57:23.688874Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.676894Z","title":"Liouville quantum gravity and KPZ","venue":null,"work_id":"b4b07dc7-50e7-490c-9661-f37e9177b703","year":2011},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.312155Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:31517eb9c997e714a345846276bf6e029454887a819b8bd228c54786238662b0","observation_id":"50cb341a-343c-480d-b8f1-66bc2f296761","resolution":{"observed_at":"2026-08-12T15:57:23.679937Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.668276Z","title":"Exact dimensionality and projection properties of Gaussian multiplicative chaos measures","venue":null,"work_id":"c15d4f59-2154-4cc3-bdf3-c05db6bc6b52","year":2019},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.315578Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:01a4b28d7e8f997069dc778aca9bc25c1b0dbbea20c3b5199ff71dc7b5396fea","observation_id":"38dcc2db-166d-4974-a6c8-498d7d334e0c","resolution":{"observed_at":"2026-08-12T15:57:23.671442Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.659457Z","title":"Relationships between different dimensions of a measure","venue":null,"work_id":"5f90558e-31f4-457a-b3ba-11e3e59818e2","year":2002},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.318556Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:4f1ca83eb2e471c61570566120b225256af007d8dd314e81c9fc1a8ae9201b5d","observation_id":"cb79e1bd-6955-4e30-bb2d-362e62ad6788","resolution":{"observed_at":"2026-08-12T15:57:23.662894Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.04027","last_updated":"2024-02-28T21:15:17Z","snapshot_observed_at":"2026-08-13T05:30:34.425900Z","submitted_at":"2023-11-07T14:26:22Z","title":"Harmonic analysis of Gaussian multiplicative chaos on the circle","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.04027","snapshot_observed_at":"2026-08-12T15:57:23.321547Z","title":"Harmonic analysis of Gaussian multiplicative chaos on the circle","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.321547Z"},"links":{"cited_paper":"/paper/2311.04027","citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:b1ec67d352f39d0d3ea41cbf36779b931f3c3fae46cd362a0181144ad1586a79","observation_id":"a805598e-f465-4caa-a158-111f9e89d334","resolution":{"observed_at":"2026-08-12T15:57:23.321547Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.07732","last_updated":"2023-06-13T12:38:23Z","snapshot_observed_at":"2026-08-13T11:18:14.105836Z","submitted_at":"2023-06-13T12:38:23Z","title":"Random analytic functions via Gaussian multiplicative chaos","version":1},"cited_work":{"arxiv_id":"2306.07732","doi":null,"metadata_source":"pith","pith_arxiv_id":"2306.07732","snapshot_observed_at":"2026-08-12T15:57:23.398706Z","title":"Random analytic functions via Gaussian multiplicative chaos","venue":"math.PR","work_id":"b892299d-b882-4110-ae51-eca22ea29a55","year":2023},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.324959Z"},"links":{"cited_paper":"/paper/2306.07732","citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:d9fa35f3e859d53a512b4763c0935cdc363fa466ec79adbf0f96d4cdb6dec5bf","observation_id":"0cbc8235-8768-4f67-a953-0d558ff34fed","resolution":{"observed_at":"2026-08-12T15:57:23.403784Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.650976Z","title":"Hunt and Vadim Yu","venue":null,"work_id":"eefb5b24-9011-44a4-a033-1ac3d205527e","year":1997},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.328230Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:4b9842889c0489a3ec157f0e2c69444774e61e721bae639cd9f2ba87f0a39039","observation_id":"6776e042-fe28-47e7-8b1e-05499b30d866","resolution":{"observed_at":"2026-08-12T15:57:23.653930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.642498Z","title":"Decompositions of log-correlated fields with applications","venue":null,"work_id":"238e0175-6768-4abe-9e29-5e145f145499","year":2019},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.331325Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:27d2f02ef6eda44ba1046cc6ee69ce7bcc440897236f910351e6b6d3cfd20a1b","observation_id":"0d679d36-2a7e-4f35-8da5-7dcc6a405766","resolution":{"observed_at":"2026-08-12T15:57:23.645605Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.634086Z","title":"Sur le chaos multiplicatif","venue":null,"work_id":"2219df9d-d870-470c-916b-d0b9610160d2","year":1985},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.334284Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:ed4e41ddbe7b65a6f7d26f85d8e100dd3a2a50494a65ab2fba88c7927a4f5783","observation_id":"f78507ce-1487-4d7a-afe0-a08dfcac23a0","resolution":{"observed_at":"2026-08-12T15:57:23.636923Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.625636Z","title":"Some random series of functions","venue":null,"work_id":"5e9628a2-1726-4330-9cb8-5a3d169959bc","year":1985},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.338430Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:5f703b207f88ad2efd39512d8febc935e6ff1af09327ac294523929cfbc55e92","observation_id":"f7567549-587e-4d74-82fa-1d4a54237f3c","resolution":{"observed_at":"2026-08-12T15:57:23.628722Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.616850Z","title":"Positive martingales and random measures","venue":null,"work_id":"ed7e653f-01d6-4eb2-b3b6-c24dcf48e3dd","year":1987},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.341754Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:c44e3b096b29ec5a88e069ccf04fd258df8cc472dfbc5baf476a1cffe7f9a08a","observation_id":"2b6ac041-bcc0-438f-bdaa-982a1439a2c3","resolution":{"observed_at":"2026-08-12T15:57:23.620119Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.607079Z","title":"An introduction to harmonic analysis","venue":null,"work_id":"a9df3225-c1ba-4daa-b94b-96ce2671d486","year":2004},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.344898Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:9fc30277b2414ec10bc35d2db134db98a10decabef8ee29dd247c9e124e44120","observation_id":"7eae2ffc-18df-4e5a-8a78-4cb29e0021d7","resolution":{"observed_at":"2026-08-12T15:57:23.610376Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.597864Z","title":"Integrability of Liouville theory: proof of the DOZZ formula","venue":null,"work_id":"0adb0537-0429-45b4-b261-fe51b2769c35","year":2020},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.347847Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:dcfdbc86354b12bd8551dca49be16159953e1ed955f0838993b1eae0b81d0d63","observation_id":"cd8c3f84-6e32-4010-9c40-5a185d429cc5","resolution":{"observed_at":"2026-08-12T15:57:23.601096Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.588233Z","title":"Complex gaussian multiplicative chaos","venue":null,"work_id":"85ee072d-f6e3-4b7a-8c1b-8163eef26cf7","year":2015},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.350937Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:acda7bffcf4d301354384e069e11969c751990983a2e166b5525756600d16caa","observation_id":"836c6218-4ccb-4219-b896-94d8801bcb58","resolution":{"observed_at":"2026-08-12T15:57:23.591755Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.578938Z","title":"Fourier analysis and Hausdorff dimension","venue":null,"work_id":"5e40d412-3dc7-4ead-b3fe-a16599f0b355","year":2015},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.353905Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:d667a082535a92a9aef5a8d8f3ac1aa6feeb159f9389c3139b60c444f75c2a55","observation_id":"a4ba70d6-d78b-42fc-b210-bce681a9bd38","resolution":{"observed_at":"2026-08-12T15:57:23.582187Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.570126Z","title":"Salem sets and restriction properties of F ourier transforms","venue":null,"work_id":"bb9f5d89-9c3e-4b95-ba28-08863af60951","year":2000},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.356908Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:d7316a67bd1874dbb8b36d0fc8b5f6c84beddcec527069ab70d8b945b86e9421","observation_id":"9c936250-a006-455b-84a9-fda757431d8a","resolution":{"observed_at":"2026-08-12T15:57:23.573212Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.359926Z","title":"Martingales in Banach spaces","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.359926Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:7f932b3d37edcfb0e49978d4d0d7590d245d7898b15b70aa6d4d1106eb60f099","observation_id":"546a27dc-7311-46e7-9f43-f13f706364a9","resolution":{"observed_at":"2026-08-12T15:57:23.359926Z","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":"2026-08-12T15:57:23.556169Z","title":"Continuous martingales and Brownian motion","venue":null,"work_id":"16d8360e-30ae-46c9-a06e-b221dcde3d62","year":1999},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.363065Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:85d177b69a21c7c4af1268db7f721dcacc34d08ee5d49ed2b5f3e94bb9bdf89d","observation_id":"ffbd4c0e-5528-44fe-82b8-5212c08ab034","resolution":{"observed_at":"2026-08-12T15:57:23.559340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.546744Z","title":"Gaussian multiplicative chaos and applications: a review","venue":null,"work_id":"71ed84ac-476f-4f08-ac6c-e20250ad1dc2","year":2014},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.366059Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:24fdf6ab20b9528c1de65621064b5604fbae84d83b9c74678b09bdf4c2343585","observation_id":"f12ca41a-9be8-4d99-b223-59bb83a23100","resolution":{"observed_at":"2026-08-12T15:57:23.550454Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.537001Z","title":"Conformal weldings of random surfaces: SLE and the quantum gravity zipper","venue":null,"work_id":"2940236a-3c8c-40f1-ac97-84840bc16cdf","year":2016},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.369147Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:63206a78cb1455d90bc168dface09412f601dcb0a8481a122af5e51841550ee2","observation_id":"0f909bb1-2960-4d8b-950c-25d6727ccd13","resolution":{"observed_at":"2026-08-12T15:57:23.540474Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:57:23.527221Z","title":"The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos--the L^2 -phase","venue":null,"work_id":"c8c4dc71-f9c1-4e6f-92ec-e86de569b644","year":2015},"citing_paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC","version":3},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-12T15:57:23.373129Z"},"links":{"citing_paper":"/paper/2411.13923"},"observation_digest":"sha256:9039ca49dfadf869c93393fd4e714076cfaf88add64bea7f63e192da251e0610","observation_id":"317568ca-993e-4082-89d7-a9c979836369","resolution":{"observed_at":"2026-08-12T15:57:23.530624Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.13923","last_updated":"2025-05-06T08:20:20Z","latest_version":3,"primary_category":"math.PR","snapshot_observed_at":"2026-08-12T15:41:48.424519Z","submitted_at":"2024-11-21T08:18:37Z","title":"Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC"},"reference_resolution":{"displayed":31,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":2,"verified_fuzzy":25},"total_outbound_references":31},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 3 inbound Pith citation observations for arXiv:2411.13923."}