{"as_of":"2026-08-08T09:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:77a284f5ba3ce090b21fe5264d4b1fa4d6f631c2d826654d80c2fe601b086e31","coverage":[{"denominator":36,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":36,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T13:23:12.811135Z","state":"measured"},{"denominator":37,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":37,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T05:49:08.764840Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.22485","snapshot_observed_at":"2026-08-01T05:49:08.764840Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.22156","last_updated":"2026-07-24T10:00:48Z","snapshot_observed_at":"2026-08-06T05:07:41.922138Z","submitted_at":"2026-07-24T10:00:48Z","title":"A random matrix approach to lamplighter groups","version":1},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:08.764840Z"},"links":{"cited_paper":"/paper/2505.22485","citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:bc796e9acb67591a3b031257adc04f125358fae02f6df9845e755610f78badfa","observation_id":"de3ed2c5-e0d2-4855-985d-ba1743158791","resolution":{"observed_at":"2026-08-01T05:49:08.764840Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2505.22485/citation-record","integrity":"/paper/2505.22485/integrity","json":"/paper/2505.22485/citation-record.json","paper":"/paper/2505.22485"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:23:20.975871Z","title":"Localization at large dis order and at extreme energies: An elementary derivations","venue":null,"work_id":"bdbe24b4-ad5f-4c7a-a0da-030ba9bdf92f","year":1993},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:03.458893Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:0f575b11ebeb0d9a46dfc2ba2435f4838556358875527845dbdd210e3772f04d","observation_id":"5e8695b9-4d88-4c9d-9dbc-eff7da90b3ec","resolution":{"observed_at":"2026-08-07T13:23:21.047991Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:20.796374Z","title":"Stability of the absolutely continuous spectrum of random schr¨ odinger operators on tree graphs","venue":null,"work_id":"988494e7-4b5e-4c23-b159-29a99a71399e","year":2006},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:03.630857Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:1d87a28a0ada3dd3db18b449e57ca34b3721861a2aaf60060218403638c4677b","observation_id":"10bd5489-fa97-40ca-a8d8-496a2571148d","resolution":{"observed_at":"2026-08-07T13:23:20.867410Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:20.648743Z","title":"Random operators, volume 168","venue":null,"work_id":"232b3d27-1d72-4c5e-b641-8a58876c595d","year":2015},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:03.828784Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:7b89c5e3d139db68ab048b3968a0ef31b4051b29e7011536d6c261ac999e3d96","observation_id":"79867ad4-a047-4705-af8b-af5e4988a2fd","resolution":{"observed_at":"2026-08-07T13:23:20.728172Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:20.510998Z","title":"Absence of diffusion in certain random lattices","venue":null,"work_id":"bd45dcfb-6888-4f9a-aa64-8a3b995cf706","year":1958},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:03.995549Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:2467597eb8bb6d7a05e74a30aa2574488d41cd25163b1bf29c2ffc54cdc0ccce","observation_id":"9db1aa0c-f54a-48df-bbbd-51d9048a8056","resolution":{"observed_at":"2026-08-07T13:23:20.577244Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:20.372522Z","title":"Existence of absolutely con tinuous spectrum for galton–watson random trees","venue":null,"work_id":"f779ee6c-c8ff-438f-8cb0-17d345b32293","year":2023},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:04.118263Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:e4bc1206f9af30364813960367c33d055c21e439a8462746374db95edc039258","observation_id":"627a2d29-0bd5-4ac8-a740-b784e638bb0d","resolution":{"observed_at":"2026-08-07T13:23:20.423533Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:20.242261Z","title":"Spectrum of random graphs","venue":null,"work_id":"dc7f4223-7e1f-47e5-8600-9fe14887c6e6","year":2016},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:04.253461Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:fb1f44638f1206e8e45b0a5ccfe960595eaf5d137aa256cfad289744fa6f21c6","observation_id":"2e3c35e7-58db-4423-8ea8-ed7c8b46a1eb","resolution":{"observed_at":"2026-08-07T13:23:20.295239Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:20.122370Z","title":"Random lattice schr¨ odinger operators with decayin g potential: some higher dimensional phenomena","venue":null,"work_id":"cf2409cf-3bac-463a-8b38-3049d3c0809b","year":2001},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:04.359218Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:ba65928a71cde7b78fa45491b1a9a656fc2aebe214106c100be803e1cd182efd","observation_id":"d83454e5-04cd-4557-8ab0-245523e11f9c","resolution":{"observed_at":"2026-08-07T13:23:20.167476Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:19.997151Z","title":"On random schr¨ odinger operators on Z2","venue":null,"work_id":"777681fe-f496-4eff-8efa-98d2d8729d30","year":2001},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:04.488080Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:f55774f6114d3e9587191a17937a3c777935c1fa66e53de7e492e1ae5ea850bc","observation_id":"b18df71d-68b6-4e93-9a57-2c66d2fa0f33","resolution":{"observed_at":"2026-08-07T13:23:20.063486Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.06279","last_updated":"2024-02-09T09:44:39Z","snapshot_observed_at":"2026-07-06T17:27:54.211733Z","submitted_at":"2024-02-09T09:44:39Z","title":"Spectra of infinite Cayley graphs, examples with pure band spectra","version":1},"cited_work":{"arxiv_id":"2402.06279","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.06279","snapshot_observed_at":"2026-08-07T13:23:13.523874Z","title":"Spectra of infinite Cayley graphs, examples with pure band spectra","venue":"math.CO","work_id":"a94a9eab-f978-4a4a-85de-19e9a47e38be","year":2024},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:04.670154Z"},"links":{"cited_paper":"/paper/2402.06279","citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:da893cc5c8cb5ee52890620cae58d8986896ccffac08806272fb83637b939c70","observation_id":"9b7b2ecb-4b16-4325-a243-b7a69dbfbcc7","resolution":{"observed_at":"2026-08-07T13:23:13.671955Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:19.728331Z","title":"Les c [*]-alg´ ebres et leurs repr´ esentations","venue":null,"work_id":"ae7bc9c7-a296-4087-bddc-3687e1830c8a","year":1969},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:04.805527Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:7de0fb4cabd035b136ce246a6de06ce72d24f62099f5e8300f0654f358b90de3","observation_id":"c54a00f1-2606-4dc7-a118-209f8768b5c5","resolution":{"observed_at":"2026-08-07T13:23:19.840538Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:19.520937Z","title":"On the analytic zero divisor conjecture of linnell","venue":null,"work_id":"c40c0055-2185-41c6-97a5-38e0a3fb3092","year":2003},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:05.344951Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:81e3faaf9e25e4ccf8b4fd6c9f5a2ca0b706cd9ba7c8abbb24ed7abb1b1b1f67","observation_id":"5dbb03a9-822f-45e0-b67d-d2c2ac431dcd","resolution":{"observed_at":"2026-08-07T13:23:19.603685Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0709.1261","last_updated":"2007-09-09T12:22:58Z","snapshot_observed_at":"2026-07-06T01:29:40.464784Z","submitted_at":"2007-09-09T12:22:58Z","title":"L^2-spectral invariants and convergent sequences of finite graphs","version":1},"cited_work":{"arxiv_id":"0709.1261","doi":null,"metadata_source":"pith","pith_arxiv_id":"0709.1261","snapshot_observed_at":"2026-08-07T13:23:13.246780Z","title":"L^2-spectral invariants and convergent sequences of finite graphs","venue":"math.SP","work_id":"bf3172ce-5073-4f96-80a4-a9851c6dff5d","year":2007},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:07.322512Z"},"links":{"cited_paper":"/paper/0709.1261","citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:931ac65101dc140771bad229e2bb9f54201b2034857169803935fcceb97cc942","observation_id":"9074a663-d5c6-4391-a7f5-bebd2cf289f0","resolution":{"observed_at":"2026-08-07T13:23:13.363302Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:19.312313Z","title":"Isoperimetry for wreath products of markov chains and multiplicity of selfintersections of random walks","venue":null,"work_id":"70a4669b-2fdf-46d4-85e9-fb33a6d73838","year":2006},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:07.457599Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:5f11459562bc54a0399aea094051d9b36fca6197f6bc0d82ab85804cf87faebc","observation_id":"9079d4ba-0cbc-4fc9-9200-5b9293b2791a","resolution":{"observed_at":"2026-08-07T13:23:19.417383Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:19.091585Z","title":"A course in abstract harmonic analysis","venue":null,"work_id":"9912f049-0647-4893-9ddd-d69005f36f41","year":2016},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:07.624905Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:09f69fccae5f522d47f33dc5dc1ab8a4235c17d604c94833122a5e15293e04d8","observation_id":"da2170e4-a583-41c0-9064-9b64de2dd423","resolution":{"observed_at":"2026-08-07T13:23:19.219497Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:18.832366Z","title":"Absolutely continuous spec- trum for the anderson model on a tree: a geometric proof of klein’s theorem","venue":null,"work_id":"618d976a-7db1-40a4-accb-264ebc9513ec","year":2007},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:08.111935Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:c2c0f0f948001ae11c6227fe728b7a44135e8b421b2991c81bb37bdb1cb1ef7e","observation_id":"674fe04f-16a4-4d2f-9fe9-ab0f1fa62724","resolution":{"observed_at":"2026-08-07T13:23:18.971230Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:18.550923Z","title":"Absence of diffusion in the anderson tight binding model for large disorder or low energy","venue":null,"work_id":"06f11224-eaa1-43d3-8f7d-20eee011e7e0","year":1983},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:09.938667Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:1866721c64d2f4e81094705805e88dd725da787c401314218de00206974449b1","observation_id":"af651222-6564-422d-80d8-d79af31d722f","resolution":{"observed_at":"2026-08-07T13:23:18.668074Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:18.296270Z","title":"Anderson localization and the space-time char acteristic of con- tinuum states","venue":null,"work_id":"6d56dbcd-6534-4069-85ed-23fe9a3e89cb","year":1994},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:10.049498Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:9ad88e9ae6e90af5fabc8b95d55cbd0300130cfe9ff584ca9932351a6d1002ba","observation_id":"3229b356-9dba-4df2-bc8c-052376c66255","resolution":{"observed_at":"2026-08-07T13:23:18.398686Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2102.13542","last_updated":"2022-12-28T11:47:31Z","snapshot_observed_at":"2026-07-06T10:44:59.832110Z","submitted_at":"2021-02-26T15:30:59Z","title":"Laplace and Schr\\\"odinger operators without eigenvalues on homogeneous amenable graphs","version":4},"cited_work":{"arxiv_id":"2102.13542","doi":null,"metadata_source":"pith","pith_arxiv_id":"2102.13542","snapshot_observed_at":"2026-08-07T13:23:12.957307Z","title":"Laplace and Schr\\\"odinger operators without eigenvalues on homogeneous amenable graphs","venue":"math.SP","work_id":"52df9181-871e-4675-9509-339762d7d80b","year":2021},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:10.191152Z"},"links":{"cited_paper":"/paper/2102.13542","citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:7a5a2c7666405f19ab310763e436f55b831599c228b8b68c183ce18c3b7c121a","observation_id":"5954703f-74ee-4f65-91f1-a35684df6220","resolution":{"observed_at":"2026-08-07T13:23:13.076805Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:18.056532Z","title":"The lamplighter group as a group generated by a 2-state automaton, and its spectrum","venue":null,"work_id":"0969efe1-9bec-4fc2-9d68-388dc015b7ff","year":2001},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:10.300703Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:889b2825222435d89442abd7e4fee4543cdf109850edb18dffe3981a8ca19a4c","observation_id":"3dbc7491-429e-4517-b888-b0ee7391e3f6","resolution":{"observed_at":"2026-08-07T13:23:18.147259Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:17.757280Z","title":"The ihara zeta functio n of infinite graphs, the kns spectral measure and integrable maps","venue":null,"work_id":"6cf57406-af39-4e56-9be1-da6d55b40581","year":2004},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:10.427530Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:7d9c1741daf64cf66a838c6e5eaa1c08795c281af7624a935ee1b0bf60585794","observation_id":"968f6d44-8050-4a03-b543-397e25e5d042","resolution":{"observed_at":"2026-08-07T13:23:17.887227Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:17.438450Z","title":"Groups of polynomial growth and expanding ma ps (with an ap- pendix by jacques tits)","venue":null,"work_id":"292c5d2c-812a-4333-835e-d139820cf4b0","year":1981},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:10.578817Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:5dead2b3d297290ecf043567823290e08c827732b1a3c20deeda2747f469b289","observation_id":"c647af17-1870-4cd5-b88a-ebd29ede7c72","resolution":{"observed_at":"2026-08-07T13:23:17.615161Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:17.238725Z","title":"Quantum theory for mathematicians , volume 267","venue":null,"work_id":"e4258256-1e1c-4d7f-a411-d5c96ae982ce","year":2013},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:10.731335Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:78d550537cfb8bfaa5810835716e30f5ff9fdbf7ea54556548c7baacfc19f2a3","observation_id":"417aa0a6-99bf-495b-a4a3-bdbf192b7f01","resolution":{"observed_at":"2026-08-07T13:23:17.317825Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:17.021347Z","title":"The a nderson model on the bethe lattice: Lifshitz tails","venue":null,"work_id":"72ff3886-8a6b-458f-a6aa-9613bc99f698","year":2014},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:10.901428Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:7347711d41a11d82765aee4b72c200272b0faf14d65ab2add7f38c7047fcd8ad","observation_id":"faf071a3-4668-450d-b03b-9394a15d9bfa","resolution":{"observed_at":"2026-08-07T13:23:17.148909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:16.755585Z","title":"Absolutely cont inuous spectrum for random operators on trees of finite cone type","venue":null,"work_id":"85c6be30-0eaa-4da1-b65d-b8f03c7069fa","year":2012},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:11.090854Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:c5a2fcc8bf1e8ad3b8a3df6a695d86164b401493435496d120b73f7d81a632f7","observation_id":"09252285-12f1-4d8f-b186-fe0d8c71766e","resolution":{"observed_at":"2026-08-07T13:23:16.883543Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:16.518640Z","title":"Symmetric random walks on groups","venue":null,"work_id":"b17be5b9-26d2-46cc-ad7a-0fd5eb6fce88","year":1959},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:11.231787Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:b043cc19b2350550b8ee96c2caf2a59eadd08871d074697dd13e0b7fff899d26","observation_id":"69ce65ea-1598-4ed3-8215-1a65cc023a65","resolution":{"observed_at":"2026-08-07T13:23:16.627832Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:16.282890Z","title":"Extended states in the anderson model on the beth e lattice","venue":null,"work_id":"4cf0badf-4e02-44c3-80d2-b886e5313d03","year":1998},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:11.430353Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:bf3c3eed81770920c75103eb2f4856c9ecf3bcbf974b907c4dcbf3e6553a3f36","observation_id":"1d650fdf-ca8a-40bd-8d5d-2d6fe07a77b9","resolution":{"observed_at":"2026-08-07T13:23:16.386648Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:16.050155Z","title":"On th e spectrum of lamp- lighter groups and percolation clusters","venue":null,"work_id":"f52b70b8-108d-4fdd-be4d-ce3b81623eb6","year":2008},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:11.568348Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:c5cb7ca5f6444d996ef5b1918d0300ed4922d37b0533ce464d8b3be4cfe7566b","observation_id":"10cb9e3b-3dde-4387-a232-086d4b7b1def","resolution":{"observed_at":"2026-08-07T13:23:16.146893Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:15.830786Z","title":"Energy spectrum structure and quan tum states of disor- dered condensed systems","venue":null,"work_id":"c937aa4b-712f-466c-97b0-9c0902d26b33","year":1965},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:11.682770Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:1715fb948e13932f22bd3c95bac3cd0c2dede399c33e9de1b89dd6e30ab62243","observation_id":"c6966502-4a5f-429f-9b7e-cd61394cc065","resolution":{"observed_at":"2026-08-07T13:23:15.954454Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:15.593313Z","title":"Analytic versions of the zero divisor conjecture","venue":null,"work_id":"32b41978-fbe1-4920-aa45-f0969893ed82","year":1998},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:11.844802Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:0a71fc520312ac19e55041b0b7f1be10e662c7518837de261565f126cda510b9","observation_id":"d228369e-c516-4851-8e56-76b3bd6794fa","resolution":{"observed_at":"2026-08-07T13:23:15.677652Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:15.301213Z","title":"Spectral analysis for convo lution operators on locally compact groups","venue":null,"work_id":"bc86c8a1-60fc-45c0-aef5-0d72dce04809","year":2007},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:11.957021Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:9e67aa5713c4e0704c979f0a801d118685d0cb7999b64b373e1e4f0bd38b8e6a","observation_id":"8283d07d-6f48-4646-84f6-b1c89f55f71a","resolution":{"observed_at":"2026-08-07T13:23:15.453785Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:15.118620Z","title":"A survey on spectra of infinit e graphs","venue":null,"work_id":"aeac5cb1-5da2-4981-bd89-1efd6f764c8c","year":1989},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:12.103625Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:7e12eb60685caa6d80a333e02c70d9c3f3a72fb6c828d0f8ec8af225a3526cb9","observation_id":"6d759c60-2215-478e-badc-049fa2b1bb12","resolution":{"observed_at":"2026-08-07T13:23:15.177131Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:14.947468Z","title":"On the stability of the beha vior of random walks on groups","venue":null,"work_id":"741ffd6d-d724-4dcd-be41-ad228dbeb0ea","year":2000},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:12.223199Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:3ed4eed8992883f115e376595bb4d5c83675796c098a680e1db3cc70c98c4de7","observation_id":"fb2e6a23-f8a3-4827-a6bc-533291392e05","resolution":{"observed_at":"2026-08-07T13:23:15.012698Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:14.734163Z","title":"Methods of modern mathematical physics, volume 1","venue":null,"work_id":"5dca9251-1749-42fa-83cd-6963c7aae28d","year":1972},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:12.395967Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:0a389c47d5a5b123d4a80ed8401a62f7d73588526531db6489e6b7117e44c286","observation_id":"929f4198-cee6-4fc0-b7f7-458673a5fbbb","resolution":{"observed_at":"2026-08-07T13:23:14.833457Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:14.497579Z","title":"Lifschitz tails for the anderson model","venue":null,"work_id":"de8e2674-fd1f-426e-b67f-eba8db5cc917","year":1985},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:12.498625Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:515c1eabb5ce0f455e7543723e7855aae4f266065c97c8397596742fa6aa35fb","observation_id":"919a1fdf-41b9-4b90-9921-5cdd28c1e61a","resolution":{"observed_at":"2026-08-07T13:23:14.622880Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:14.206384Z","title":"An introduction to the mathematics of anderso n localization","venue":null,"work_id":"71f59a66-dac4-4103-b308-4eca227027f5","year":2011},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:12.620164Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:5a5ce42b8138e90f866679a5e98c8bfeedbbb1119b4201810c2fa7631445fe34","observation_id":"d9d63c12-3aeb-4544-a2b2-9cb58b870978","resolution":{"observed_at":"2026-08-07T13:23:14.373377Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:23:13.868455Z","title":"Springer, 2008","venue":null,"work_id":"da2884d0-5409-4030-8c8d-621e81067693","year":1917},"citing_paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T13:23:12.811135Z"},"links":{"citing_paper":"/paper/2505.22485"},"observation_digest":"sha256:6dd721d6a3b360bd515b4928ed324543a08c0011eea4963f0d7e6d85432abb30","observation_id":"0d8d7f2b-f027-4fea-8822-d66ebd1464f3","resolution":{"observed_at":"2026-08-07T13:23:14.041635Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.22485","last_updated":"2025-05-28T15:35:45Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-07T19:52:53.541597Z","submitted_at":"2025-05-28T15:35:45Z","title":"Random Schr\\\"odinger operators and convolution on wreath products"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":3,"verified_fuzzy":33},"total_outbound_references":36},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 1 inbound Pith citation observation for arXiv:2505.22485."}