{"as_of":"2026-08-10T00:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0b97fdf436bc38c30be65c453958fd9c064e23ccf41fea1adb26c24fe69c48e5","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":5,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":5,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:14:47.024879Z","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":"2026-07-03T12:58:07.559966Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.03298","last_updated":"2025-06-17T12:57:39Z","snapshot_observed_at":"2026-08-07T15:49:39.985298Z","submitted_at":"2025-05-06T08:28:11Z","title":"Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.03298","snapshot_observed_at":"2026-08-07T15:14:47.024879Z","title":"Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions","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":31,"source":"arxiv_source","source_observed_at":"2026-08-07T15:14:47.024879Z"},"links":{"cited_paper":"/paper/2505.03298","citing_paper":"/paper/2505.16405"},"observation_digest":"sha256:e3632505ad3cfe07cb0a01ac8c456e3e0a66f8fdf08e78aa00946e3bb6f87bab","observation_id":"4f9746ec-cbb1-4796-8943-3a999e5ad258","resolution":{"observed_at":"2026-08-07T15:14:47.024879Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.03298","last_updated":"2025-06-17T12:57:39Z","snapshot_observed_at":"2026-08-07T15:49:39.985298Z","submitted_at":"2025-05-06T08:28:11Z","title":"Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.03298","snapshot_observed_at":"2026-08-06T10:49:09.630961Z","title":"Harmonic analysis of multiplicative chaos Part II: Fourier dimensions of classical multiplicative chaos measures","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":13,"source":"arxiv_source","source_observed_at":"2026-08-06T10:49:09.630961Z"},"links":{"cited_paper":"/paper/2505.03298","citing_paper":"/paper/2507.23494"},"observation_digest":"sha256:497f89e03c6903a288fb0e29919986c3c35ad28ac8a283059b5626d960f5ed72","observation_id":"d6befb78-ddfc-4d37-afc5-079edde27abd","resolution":{"observed_at":"2026-08-06T10:49:09.630961Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.03298","last_updated":"2025-06-17T12:57:39Z","snapshot_observed_at":"2026-08-07T15:49:39.985298Z","submitted_at":"2025-05-06T08:28:11Z","title":"Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions","version":4},"cited_work":{"arxiv_id":"2505.03298","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.03298","snapshot_observed_at":"2026-07-03T12:58:07.559966Z","title":null,"venue":null,"work_id":"a0a1d93d-e69d-48b0-ab8b-ef3596fc089f","year":2025},"citing_paper":{"arxiv_id":"2606.08683","last_updated":"2026-06-11T05:15:25Z","snapshot_observed_at":"2026-07-06T23:48:07.065806Z","submitted_at":"2026-06-07T15:35:06Z","title":"Exact Fourier dimensions of dyadic Mandelbrot cascades under minimal integrability","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-27T17:59:01.483518Z"},"links":{"cited_paper":"/paper/2505.03298","citing_paper":"/paper/2606.08683"},"observation_digest":"sha256:74b3302b82dd63398eb156cf7c209239d293e863257b9a6b3396545c03b4bc9b","observation_id":"68ea8d6c-da83-40e7-bf73-541b825ba0ab","resolution":{"observed_at":"2026-07-02T23:47:27.432210Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.03298","last_updated":"2025-06-17T12:57:39Z","snapshot_observed_at":"2026-08-07T15:49:39.985298Z","submitted_at":"2025-05-06T08:28:11Z","title":"Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions","version":4},"cited_work":{"arxiv_id":"2505.03298","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.03298","snapshot_observed_at":"2026-07-03T12:58:07.559966Z","title":null,"venue":null,"work_id":"a0a1d93d-e69d-48b0-ab8b-ef3596fc089f","year":2025},"citing_paper":{"arxiv_id":"2606.08703","last_updated":"2026-06-11T05:40:40Z","snapshot_observed_at":"2026-07-06T23:48:11.819398Z","submitted_at":"2026-06-07T15:59:39Z","title":"Fourier Dimensions of Mandelbrot Cascades under Minimal Integrability","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-27T17:56:54.767272Z"},"links":{"cited_paper":"/paper/2505.03298","citing_paper":"/paper/2606.08703"},"observation_digest":"sha256:3e4b06adba9bc0b1581bb81fe3d1dbf52a389882ba5def4e378e6eb2742f2ac3","observation_id":"1472891e-f142-4e4f-a6a2-7a2ff851a06e","resolution":{"observed_at":"2026-07-02T23:47:27.552773Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.03298","last_updated":"2025-06-17T12:57:39Z","snapshot_observed_at":"2026-08-07T15:49:39.985298Z","submitted_at":"2025-05-06T08:28:11Z","title":"Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions","version":4},"cited_work":{"arxiv_id":"2505.03298","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.03298","snapshot_observed_at":"2026-07-03T12:58:07.559966Z","title":null,"venue":null,"work_id":"a0a1d93d-e69d-48b0-ab8b-ef3596fc089f","year":2025},"citing_paper":{"arxiv_id":"2606.11758","last_updated":"2026-07-17T13:27:50Z","snapshot_observed_at":"2026-08-02T11:56:27.070874Z","submitted_at":"2026-06-10T07:32:27Z","title":"Exact Fourier dimensions of dyadic Mandelbrot cascades on curves of nonvanishing curvature under minimal integrability","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-27T08:41:56.866507Z"},"links":{"cited_paper":"/paper/2505.03298","citing_paper":"/paper/2606.11758"},"observation_digest":"sha256:2afa0518f018be829a79fc8c7d3a56baa02f7236752d6d0fb2f2392215dd9435","observation_id":"c6605bad-4f9d-400d-900f-54ec0a3ae8ff","resolution":{"observed_at":"2026-07-03T12:58:07.561792Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.03298/citation-record","integrity":"/paper/2505.03298/integrity","json":"/paper/2505.03298/citation-record.json","paper":"/paper/2505.03298"},"outbound":[],"paper":{"arxiv_id":"2505.03298","last_updated":"2025-06-17T12:57:39Z","latest_version":4,"primary_category":"math.PR","snapshot_observed_at":"2026-08-07T15:49:39.985298Z","submitted_at":"2025-05-06T08:28:11Z","title":"Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 5 inbound Pith citation observations for arXiv:2505.03298."}