{"as_of":"2026-08-14T20:33:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:db7f06eda17d703c2b00c42befe07088d2e04304a42de42765cc0bb69e99eac9","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:43:10.517106Z","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":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T20:23:38.534228Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-06T20:23:40.155706Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"cited_work":{"arxiv_id":"2501.08069","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.08069","snapshot_observed_at":"2026-08-06T20:23:40.155706Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","venue":"math.DS","work_id":"6b4d15f6-439a-4207-b3cd-b7814bc06df2","year":2025},"citing_paper":{"arxiv_id":"2507.03338","last_updated":"2025-07-04T06:50:53Z","snapshot_observed_at":"2026-08-13T16:06:46.423899Z","submitted_at":"2025-07-04T06:50:53Z","title":"Local entropy theory, combinatorics, and local theory of Banach spaces","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T20:23:38.534228Z"},"links":{"cited_paper":"/paper/2501.08069","citing_paper":"/paper/2507.03338"},"observation_digest":"sha256:0c64be201a8964e88078ffc82b6cd173a692e0f9c84704eddd6c640b217ce905","observation_id":"5783f4d4-a0fd-4ba1-af6f-c5d14eabd65c","resolution":{"observed_at":"2026-08-06T20:23:40.192348Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.08069","snapshot_observed_at":"2026-08-01T08:15:58.117652Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.27400","last_updated":"2026-07-29T19:13:23Z","snapshot_observed_at":"2026-08-08T11:40:15.565113Z","submitted_at":"2026-07-29T19:13:23Z","title":"Conditional Topomorphic Degree and Multivariate Mean Equicontinuity for Minimal Amenable Group Actions","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-01T08:15:58.117652Z"},"links":{"cited_paper":"/paper/2501.08069","citing_paper":"/paper/2607.27400"},"observation_digest":"sha256:b976ac9ae2cfa8c35790ead1fa434b7e2df948319e4d0aebfe55c27fc1df049a","observation_id":"dba2d984-51ca-414a-bfd8-188eded5b2cf","resolution":{"observed_at":"2026-08-01T08:15:58.117652Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2501.08069/citation-record","integrity":"/paper/2501.08069/integrity","json":"/paper/2501.08069/citation-record.json","paper":"/paper/2501.08069"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:43:10.918657Z","title":"Blanchard, Fully positive topological entropy and topological m ixing","venue":null,"work_id":"d13996a4-5a79-4f9a-a210-cfe215ebcaf9","year":1991},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.379518Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:49f408dcf100c5b9d3350e768d41dde29d945560ccb31b037783e46543c51df2","observation_id":"0daf62ad-b519-424e-aaf3-e248a0e2215c","resolution":{"observed_at":"2026-08-10T20:43:10.923444Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.384840Z","title":"Blanchard, B","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.384840Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:16fc64d198cb313059bd5c32ce678660d072585d163c4b9bdf95fe463e6e2913","observation_id":"d650d319-4e96-4a60-9494-78a1ff419d80","resolution":{"observed_at":"2026-08-10T20:43:10.384840Z","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":"2026-08-10T20:43:10.389068Z","title":"Følner, On groups with full Banach mean value, Math","venue":null,"work_id":null,"year":1955},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.389068Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:89e5c64c14a079a2373ab05e04e341ef6500f20aafbe03aca6704406a9417506","observation_id":"bcd1d85e-d7c2-4536-a0c1-e250e5e64732","resolution":{"observed_at":"2026-08-10T20:43:10.389068Z","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":"2026-08-10T20:43:10.888283Z","title":"Garc ´ ıa-Ramos, Weak forms of topological and measure theo retical equicontinuity: rela- tionships with discrete spectrum and sequence entropy, Ergodic T heory Dynam","venue":null,"work_id":"7524547d-8f8d-4a74-9b2d-c42954b07087","year":2017},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.394206Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:9dc0e23e20f52702efb0d6d8265669940b7a4210c53c19794d38a64d564f581f","observation_id":"68a9f107-3812-435f-89de-c97f147b93c0","resolution":{"observed_at":"2026-08-10T20:43:10.893052Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.10012","last_updated":"2024-01-18T14:29:23Z","snapshot_observed_at":"2026-08-14T11:48:19.926274Z","submitted_at":"2024-01-18T14:29:23Z","title":"Local entropy theory and applications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.10012","snapshot_observed_at":"2026-08-10T20:43:10.398384Z","title":"Garc ´ ıa-Ramos and H","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.398384Z"},"links":{"cited_paper":"/paper/2401.10012","citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:808ed147ace87cc110aaf359b64402948d19c070e7f1c3d008ec0c230a893288","observation_id":"a99c1b3b-a7e1-4539-b967-d567c15e861e","resolution":{"observed_at":"2026-08-10T20:43:10.398384Z","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":"2026-08-10T20:43:10.876774Z","title":"Garc ´ ıa-Ramos and V","venue":null,"work_id":"f9ed199d-6947-417a-9c50-edb7fffaff0e","year":2024},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.402665Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:246915677b0919f526489357d43262d45480ff6c671cd9cc64ee32295973bc33","observation_id":"551017e8-8d59-4175-8f0a-7926325d2d78","resolution":{"observed_at":"2026-08-10T20:43:10.880312Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.864211Z","title":"Glasner, Ergodic theory via joinings, Mathematical Surveys a nd Monographs, Vol","venue":null,"work_id":"acaad62e-a9cf-442d-be40-5b8a3f28adb4","year":2003},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.406501Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:c04655f48f9ee8154c55f339a64fa7664bde76344934e15c15d320553396ebe9","observation_id":"83f7bb3c-56b5-40c2-8e73-f07d4d428083","resolution":{"observed_at":"2026-08-10T20:43:10.868673Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.849065Z","title":"Glasner, On tame dynamical systems, Colloq","venue":null,"work_id":"53a06dea-b7cb-4a69-96ea-1b78a7fa8922","year":2006},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.411925Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:e78a0e939c32c3c77070ff9f73566807997d3c5e72c5037438de16e34444b677","observation_id":"36777a99-9848-471e-a59a-cce4883e6132","resolution":{"observed_at":"2026-08-10T20:43:10.854090Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.837157Z","title":"Glasner and B","venue":null,"work_id":"1e198711-1470-4a4a-b358-476eafea98c7","year":1993},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.415879Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:81e53efdb99156fb37350eb7691819126e5a5245aa0c4caf97c603fa34ed531b","observation_id":"ae68470a-c8f5-4b01-ab28-d29849e27e80","resolution":{"observed_at":"2026-08-10T20:43:10.841342Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.824826Z","title":"Glasner and X","venue":null,"work_id":"92e658fb-fb86-4cc6-9171-56a49f5de800","year":2009},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.420544Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:82818a484fc12185d140bbfceb3085fab07395d61e1b868880c15630c239994b","observation_id":"9f06161e-3642-4b8a-85f2-a98e7e65d876","resolution":{"observed_at":"2026-08-10T20:43:10.829054Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.813178Z","title":null,"venue":null,"work_id":"73f1077f-bac2-4e73-85b3-2c3e2881cd13","year":1942},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.424755Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:bd3da2f04ad75058acccaac4d4bddedba534ef01a85cb15bc75ace5a6cbd5531","observation_id":"9b6244b7-db96-4b45-868e-953d756e73b3","resolution":{"observed_at":"2026-08-10T20:43:10.817078Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.801322Z","title":"Huang and X","venue":null,"work_id":"4ae5448c-66f2-4464-ba01-a535b8ea258e","year":2009},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.429577Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:bc71822e984332503f9cd2673cb6d285065662b610aecb97fd4390838f4c3266","observation_id":"06149def-ddad-4bec-a1ea-d9585955fe6a","resolution":{"observed_at":"2026-08-10T20:43:10.805282Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.434161Z","title":"Huang, Tame systems and scrambled pairs under an Abelian gr oup action, Ergodic Theory Dynam","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.434161Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:5576b854d26f8766214b349f8d0bb098c199949087152bd71934c74f8d2d225a","observation_id":"1d5a67cf-c468-46c6-bb66-7ac65d431a73","resolution":{"observed_at":"2026-08-10T20:43:10.434161Z","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":"2026-08-10T20:43:10.438560Z","title":"Huang, S","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.438560Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:5293386e0b2619950de672a0395c0202688b5fd298dabfd5d3c108a07d6e99d3","observation_id":"b9623ca4-aa8d-445a-b940-3078ceb42676","resolution":{"observed_at":"2026-08-10T20:43:10.438560Z","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":"2026-08-10T20:43:10.443057Z","title":"Huang, P","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.443057Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:ce5dfa73038b1e991d3a7614851569bdaf883482e2ef6fa83df05f390e331dd0","observation_id":"ca73cbc2-ef0d-406b-91d3-7d0c493a5f63","resolution":{"observed_at":"2026-08-10T20:43:10.443057Z","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":"2026-08-10T20:43:10.761307Z","title":"Huang, A","venue":null,"work_id":"9463b49d-b100-4b0f-be27-f084ad9513eb","year":2004},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.447921Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:f6eed7455ea3e5142107ce35a6adc70c6550156e270623f8b5065a76b68e4489","observation_id":"e4c8bc57-4039-4a9a-945b-de1560ded489","resolution":{"observed_at":"2026-08-10T20:43:10.766914Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.746157Z","title":"Huang and X","venue":null,"work_id":"14df635a-a1de-41ec-b712-2ee4f8a44edd","year":2009},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.451991Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:6fbad02d6ddcd1b559a6483d2f9a231f2e41dbb191d2b820347b8a6ef13e5d07","observation_id":"91a13fe7-3ee6-4c1b-9b00-5a06a6be556c","resolution":{"observed_at":"2026-08-10T20:43:10.750616Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.733779Z","title":null,"venue":null,"work_id":"b1a5dff8-8efb-48ee-8318-b89f59f40616","year":1967},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.457804Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:8a039bd2297af9808b2cf96837c1564b5ad1062da99b6f9386c5c680300dec13","observation_id":"d9b7b269-3d3b-431d-956b-84f4d8b7e046","resolution":{"observed_at":"2026-08-10T20:43:10.737967Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.462349Z","title":"Kerr and H","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.462349Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:37a6996d43c92ec5bd79d29c05edc0e3477fc4a91283ed66ff85dd8f5ffb51dc","observation_id":"f9f7bf38-9f30-46b7-b87c-f01a4dc87eab","resolution":{"observed_at":"2026-08-10T20:43:10.462349Z","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":"2026-08-10T20:43:10.711125Z","title":"Kerr and H","venue":null,"work_id":"f5fba7e1-f26b-401a-97f2-4c41aa5ed643","year":2009},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.467204Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:1404a3019345702cbd05541ec6ff977e113b7956d37cf18805bde8447b1a5989","observation_id":"caf670fa-049c-4c4b-848d-14dd09025e35","resolution":{"observed_at":"2026-08-10T20:43:10.715296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.695637Z","title":"K¨ ohler, Enveloping semigroups for flows, Proc","venue":null,"work_id":"9e4f123e-fa31-4e7a-a370-ec9af1ade55d","year":1995},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.471467Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:c9057da7b2c4ab72f0e76aa3f423c7ee9cf94ec06d2a57aef20b6cb0b14e7ba4","observation_id":"e4299927-719c-4e45-b2f4-db5277a6ef3d","resolution":{"observed_at":"2026-08-10T20:43:10.701215Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.682379Z","title":"Li, Measure-theoretic sensitivity via finite partitions, Nonline arity 29 (2016), 2133–2144","venue":null,"work_id":"7a6b868b-9b32-4848-89ac-d6ec3b0e186a","year":2016},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.475005Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:486adc558a96bb0d22e8148186a6472c0078d9ec3f8a367a6202913b57829faf","observation_id":"d0055f3b-cef7-497f-8444-236fd9bcade0","resolution":{"observed_at":"2026-08-10T20:43:10.686963Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.478407Z","title":"Li and T","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.478407Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:a8e89d95055a62617395bcb630801515523c4c687c057736baa1c04b1571d95b","observation_id":"6a34600d-adb3-4074-8109-868bb56e2957","resolution":{"observed_at":"2026-08-10T20:43:10.478407Z","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":"2026-08-10T20:43:10.662543Z","title":null,"venue":null,"work_id":"be151395-9b6b-4551-a5b4-665b660407eb","year":2022},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.482515Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:4c637e368fc7f520948bc4b57952c169e9962f6e5daa42f6a29b88be16914044","observation_id":"787f4ec4-a9f2-4b73-8a6d-61a2c1ec0d81","resolution":{"observed_at":"2026-08-10T20:43:10.666203Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.485944Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.485944Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:765df53272ea526943264586dbcd512478e978fe87586adaa97814145457685f","observation_id":"9a0ee61f-ff5e-427f-836a-3e9cfd47a975","resolution":{"observed_at":"2026-08-10T20:43:10.485944Z","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":"2026-08-10T20:43:10.640101Z","title":"Lindenstrauss, Pointwise theorems for amenable groups","venue":null,"work_id":"c83688f8-04b7-4d5d-af8f-77e046990ae0","year":2001},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.490833Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:4141840d9cb463b954a2c70ca95e14f9771d069a93ea234e6094ba0b1bf3c261","observation_id":"cb8036a6-9d41-4c7e-bb5d-3c87e5ec9051","resolution":{"observed_at":"2026-08-10T20:43:10.644774Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.627320Z","title":"Liu and X","venue":null,"work_id":"d0cc9346-7e4b-46c8-9a31-5605553331d1","year":2025},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.495832Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:7463843d4dc0ff6d9919ae181472f8ba4ec75838fdaf659a904e148a378de56c","observation_id":"2306f7ca-8441-41f0-b845-6f9b4b927a5b","resolution":{"observed_at":"2026-08-10T20:43:10.631597Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.613328Z","title":"Liu and K","venue":null,"work_id":"a111b0bd-8b26-4b1a-b992-a2b82668ab35","year":2023},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.499568Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:889be67f67d2f08896906b4e5168506a42ec8e130af79f0c0a83e0f448bae8e0","observation_id":"4053fe41-21c9-4097-b9d7-32cc0f5a656e","resolution":{"observed_at":"2026-08-10T20:43:10.617732Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.598760Z","title":"Lehrer, Topological mixing and uniquely ergodic systems, Isr ael J","venue":null,"work_id":"761101f5-d751-43b0-9997-7a27d3fd98f5","year":1987},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.503903Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:c13bffda08f40ae892d6cf6903ee1309f494435b736fb7453751fca17b96db0e","observation_id":"016e34e7-0cf2-4180-9ec9-9e3133c0f901","resolution":{"observed_at":"2026-08-10T20:43:10.603327Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.586096Z","title":null,"venue":null,"work_id":"82cd5f90-0a95-4e65-badd-50a5c441c104","year":1964},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.508244Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:c71c167205be0043863dc6a1ee50a20f9c5e33a39fe8f9e24a51e9a5a287bdf9","observation_id":"ab86494b-7132-4bcb-a3a8-f998eb42aa13","resolution":{"observed_at":"2026-08-10T20:43:10.590584Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.573519Z","title":null,"venue":null,"work_id":"66ebe79d-f6f4-497f-a254-c1ebbf34d5be","year":2021},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.513027Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:823c965a89306e33b346e923bb3d3b29459a616db18db3d6c8b329bfeb87b83d","observation_id":"bf467966-4b02-4abb-b7d0-1aeb8c006697","resolution":{"observed_at":"2026-08-10T20:43:10.577182Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:43:10.558914Z","title":null,"venue":null,"work_id":"b0bdc893-a3d7-459c-8c74-4a52060f13d5","year":1976},"citing_paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T20:43:10.517106Z"},"links":{"citing_paper":"/paper/2501.08069"},"observation_digest":"sha256:975427177106dbfb731b56b09c4c26e84bdfcf735ff35d0890eba0563fe3b9f8","observation_id":"63565034-040b-4dfe-bf09-fe1b1c57fbcf","resolution":{"observed_at":"2026-08-10T20:43:10.564191Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.08069","last_updated":"2025-04-02T09:22:08Z","latest_version":2,"primary_category":"math.DS","snapshot_observed_at":"2026-08-14T10:08:22.365439Z","submitted_at":"2025-01-14T12:34:29Z","title":"Independence, sequence entropy and mean sensitivity for invariant measures"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":0,"verified_fuzzy":17},"total_outbound_references":32},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 2 inbound Pith citation observations for arXiv:2501.08069."}