{"as_of":"2026-08-09T19:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2e815ef0c0c5a1422ffce9f169ce7523012df712a38b9e8eb5bd49de4eae4f89","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T05:49:10.308727Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"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":[],"links":{"evidence":"/evidence","html":"/paper/2607.22156/citation-record","integrity":"/paper/2607.22156/integrity","json":"/paper/2607.22156/citation-record.json","paper":"/paper/2607.22156"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"math/0609329","last_updated":"2006-09-12T16:49:06Z","snapshot_observed_at":"2026-07-07T06:00:18.037490Z","submitted_at":"2006-09-12T16:49:06Z","title":"Decompositions of the free product of graphs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0609329","snapshot_observed_at":"2026-08-01T05:49:08.638501Z","title":"Decompositions of the free product of graphs, September 2006","venue":null,"work_id":null,"year":2006},"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":1,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:08.638501Z"},"links":{"cited_paper":"/paper/math/0609329","citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:c81c27d6592058591339cefda383f05424673533151d27752013f77c92850ed2","observation_id":"d4a428ac-4b02-4573-965b-15de327d3e66","resolution":{"observed_at":"2026-08-01T05:49:08.638501Z","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":"2026-08-01T05:49:08.704611Z","title":"Random schrödinger operators and convolution on wreath products,","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":2,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:08.704611Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:869d7a3d10852da1f2a41d4c370e1bbaba6242d8a331c78c161bbb658f50d7f5","observation_id":"b6414594-51b8-4fda-8762-48c0726fd38a","resolution":{"observed_at":"2026-08-01T05:49:08.704611Z","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":"2026-08-01T05:49:08.846936Z","title":"Freeness over the diagonal for large random matrices.The Annals of Probability, 49(1):157–179, 2021","venue":null,"work_id":null,"year":2021},"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":3,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:08.846936Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:67308441c2aa2d269adcff314cdc150d43ca2057084f88a0b1324042e47ff535","observation_id":"2dd8c8f4-69cc-4a5d-963b-acf04aee5881","resolution":{"observed_at":"2026-08-01T05:49:08.846936Z","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":"2026-08-01T05:49:08.902182Z","title":"Central Limit Theo- rems for Linear Statistics of Heavy Tailed Random Matrices.Communications in Mathematical Physics, 329(2):641–686, July 2014","venue":null,"work_id":null,"year":2014},"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":4,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:08.902182Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:77d4aff2dda29bb25df978643f0b09ea4f101c050d79f43eeba30ad249c5bcfd","observation_id":"91c154e5-0e26-45f5-b7c1-00414d58ad6b","resolution":{"observed_at":"2026-08-01T05:49:08.902182Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.14027","last_updated":"2024-09-21T06:06:51Z","snapshot_observed_at":"2026-08-07T17:18:31.988561Z","submitted_at":"2024-09-21T06:06:51Z","title":"Large deviations for macroscopic observables of heavy-tailed matrices","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.14027","snapshot_observed_at":"2026-08-01T05:49:08.996419Z","title":"Large deviations for macro- scopic observables of heavy-tailed matrices, 2024","venue":null,"work_id":null,"year":2024},"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":5,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:08.996419Z"},"links":{"cited_paper":"/paper/2409.14027","citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:e93a263be5bf0ff48f051613b8c2a6b830e15f01f175430b5fcbc261eab883e0","observation_id":"b48bc90c-2878-47e0-9e69-98225a74c064","resolution":{"observed_at":"2026-08-01T05:49:08.996419Z","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":"2026-08-01T05:49:09.057792Z","title":"Brown and Narutaka Ozawa.C∗-Algebras and Finite-Dimensional Ap- proximations, volume 88 ofGraduate Studies in Mathematics","venue":null,"work_id":null,"year":2008},"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":6,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.057792Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:e7e9999223698fdffc875d1f8781a619baba3b1f55e09f87cbd8755c7b1541f3","observation_id":"77b5b44e-9a2f-4891-b468-7ab445328dcf","resolution":{"observed_at":"2026-08-01T05:49:09.057792Z","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":"2026-08-01T05:49:09.100688Z","title":"The spectral measure of certain elements of the complex group ring of a wreath product.Geometriae Dedicata, 93:121–137, 2002","venue":null,"work_id":null,"year":2002},"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":7,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.100688Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:42c83620c1d59118e17b9b71a5683778f44894c91b33fecc92d7ad4292b38813","observation_id":"576e58ec-dc3c-47a6-90da-96cbfeb2fee9","resolution":{"observed_at":"2026-08-01T05:49:09.100688Z","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":"2026-08-01T05:49:09.168106Z","title":null,"venue":null,"work_id":null,"year":2007},"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":8,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.168106Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:1a2fa7a6cf3ca69686e2c751c70e6b3f73b906c10b1ee269d88cd74939360593","observation_id":"4aaeedc2-e7d4-4995-ade9-9363bcf78977","resolution":{"observed_at":"2026-08-01T05:49:09.168106Z","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":"2026-08-01T05:49:09.239933Z","title":"Spectra of cayley graphs of the lamplighter group and random schrödinger operators.Transactions of the American Mathematical Society, 374:1, 03 2020","venue":null,"work_id":null,"year":2020},"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":9,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.239933Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:3b358c650f765e36d715c1fcaebc33812dd8643d1e1a065b57c0edc8345a3627","observation_id":"d76fd012-05d6-4f71-ab5c-614df08eff3c","resolution":{"observed_at":"2026-08-01T05:49:09.239933Z","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":"2026-08-01T05:49:09.345840Z","title":"Grigorchuk and Andrzej .Zuk","venue":null,"work_id":null,"year":2001},"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":10,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.345840Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:dffd214de3e4622e698be502aa3ad9c08f7cf112b1ecc81fa9197a62d9798337","observation_id":"74d1e629-b84f-4a29-803f-23c2cd25f04a","resolution":{"observed_at":"2026-08-01T05:49:09.345840Z","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":"2026-08-01T05:49:09.407757Z","title":"Silva, and Benjamin Steinberg","venue":null,"work_id":null,"year":2006},"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":11,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.407757Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:06bcb82721c2ec66d7d2bed57c43d86d3a1a121952537a3906234c684b2accfe","observation_id":"b3e28249-062d-48cb-a7ff-1ceae76b80cd","resolution":{"observed_at":"2026-08-01T05:49:09.407757Z","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":"2026-08-01T05:49:09.481240Z","title":"A product of invariant random permu- tations has the same small cycle structure as uniform.Electron","venue":null,"work_id":null,"year":2020},"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":12,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.481240Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:580411342a7b21d15e266d4bb0b3391c5fc51936c13e3b8f559032048dad2e3e","observation_id":"9c0b5f91-76a6-4c88-8419-0e7cf9bce88d","resolution":{"observed_at":"2026-08-01T05:49:09.481240Z","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":"2026-08-01T05:49:09.551463Z","title":"Symmetric random walks on groups.Transactions of the American Mathematical Society, 92(2):336–354, 1959","venue":null,"work_id":null,"year":1959},"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":13,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.551463Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:6ed1555a53b3ca99d97359d581dac5804590ee58ddcba65e4c51c4df8f5e5e65","observation_id":"9c1f8205-797f-46d0-861a-1d8eddb43084","resolution":{"observed_at":"2026-08-01T05:49:09.551463Z","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":"2026-08-01T05:49:09.622577Z","title":"The limiting distributions of large heavy Wigner and arbitrary random matrices.Journal of Functional Analysis, 272(1):1–46, 2017","venue":null,"work_id":null,"year":2017},"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":14,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.622577Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:3827f0f43c41a2ee874137bf9c82faf94a54fa67b474bc5f519422e6dba0c2e3","observation_id":"fa563521-df41-4f9d-9721-b0fbcc515fe8","resolution":{"observed_at":"2026-08-01T05:49:09.622577Z","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":"2026-08-01T05:49:09.695396Z","title":null,"venue":null,"work_id":null,"year":2020},"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":15,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.695396Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:0597414534156ce41fe4edd6591a93639c6b6a39e8b5d937ce2cdb2954c15948","observation_id":"7b8aeb2a-1533-4b14-b506-ba46ddabd82c","resolution":{"observed_at":"2026-08-01T05:49:09.695396Z","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":"2026-08-01T05:49:09.749208Z","title":"Mingo and Roland Speicher.Free probability and random matrices, vol- ume 35 ofFields Inst","venue":null,"work_id":null,"year":2017},"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":16,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.749208Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:95534aaf924d52b01855cc6a4a7fbe00184e7fc862d6b3b271d892478789d98e","observation_id":"58cea435-f74f-4d14-88cd-2b9db82fbb40","resolution":{"observed_at":"2026-08-01T05:49:09.749208Z","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":"2026-08-01T05:49:09.846363Z","title":"A survey on spectra of infinite graphs.Bulletin of the London Mathematical Society, 21(3):209–234, 1989","venue":null,"work_id":null,"year":1989},"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":17,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.846363Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:eda14a5ad0f909d5f50cd76839161c5a008dcdd40e2dab0320a0bd6fbbd8698b","observation_id":"19b55c7d-80d0-4dcc-80b4-6f404a039bc5","resolution":{"observed_at":"2026-08-01T05:49:09.846363Z","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":"2026-08-01T05:49:09.926921Z","title":null,"venue":null,"work_id":null,"year":2006},"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":18,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.926921Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:4e7c84b857f31cead855faf670ad7130a8a3a44c5924972de45f1453c0194ed4","observation_id":"33c271d1-56db-455c-8654-34ad5ad0e92f","resolution":{"observed_at":"2026-08-01T05:49:09.926921Z","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":"2026-08-01T05:49:09.979060Z","title":"Paulsen.Completely Bounded Maps and Operator Algebras, volume 78 ofCam- bridge Studies in Advanced Mathematics","venue":null,"work_id":null,"year":2002},"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":19,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:09.979060Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:a4221634d6ee08de0ee5e3e708773d189bdc73d17a14173384db8b6c24f30a92","observation_id":"1a725044-824b-4f90-b046-34ca4aa8827b","resolution":{"observed_at":"2026-08-01T05:49:09.979060Z","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":"2026-08-01T05:49:10.034580Z","title":"Heat kernel asymptotics on the lamplighter group.Electronic Com- munications in Probability, 8:142–151, 2003","venue":null,"work_id":null,"year":2003},"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":20,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:10.034580Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:a6f7a74e64e37f456f32d37722072d8203d32b42882d07a81139d18ec6286c67","observation_id":"04bc8662-cb58-4eb1-b5ee-4c63c564cf86","resolution":{"observed_at":"2026-08-01T05:49:10.034580Z","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":"2026-08-01T05:49:10.138966Z","title":"On universal products.Free Probability Theory, 12:257–266, January","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":21,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:10.138966Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:b0577bbcefbdf01324ef4d3e8e7ce37135d6fe9e877166faee83d0598aef82cd","observation_id":"1286cc7a-4629-46c2-8b4d-6e53fd2446c3","resolution":{"observed_at":"2026-08-01T05:49:10.138966Z","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":"2026-08-01T05:49:10.194972Z","title":"Combinatorial theory of the free product with amalgamation and operator-valued free probability theory.Memoirs of the American Mathematical So- ciety, 132(627):0–0, 1998","venue":null,"work_id":null,"year":1998},"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":22,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:10.194972Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:c2a8507a678f5b99231590ebb7e017b2924b716599a3c660ae5d1a7900931a32","observation_id":"a02ff38d-4860-462d-b628-032610adf209","resolution":{"observed_at":"2026-08-01T05:49:10.194972Z","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":"2026-08-01T05:49:10.251657Z","title":"On the projection of norm one inW∗-algebras.Proceedings of the Japan Academy, 33(10):608–612, 1957","venue":null,"work_id":null,"year":1957},"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":23,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:10.251657Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:b19ff352acc4988c48d6490eecdeb54d76f341ef07186bbb1dadd2eaa1cb94e3","observation_id":"f9c1aaa4-2602-436d-8d21-fe084ceaf94a","resolution":{"observed_at":"2026-08-01T05:49:10.251657Z","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":"2026-08-01T05:49:10.308727Z","title":"Symmetries of some reduced free product C*-algebras","venue":null,"work_id":null,"year":1985},"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":24,"source":"pdf_text","source_observed_at":"2026-08-01T05:49:10.308727Z"},"links":{"citing_paper":"/paper/2607.22156"},"observation_digest":"sha256:f8f2fb35e00f0ee94d3697c4bf430fd720be869b9dd6218de9a894cca2808315","observation_id":"c286ffac-f784-4605-90d6-ae61f25c6747","resolution":{"observed_at":"2026-08-01T05:49:10.308727Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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"}}],"paper":{"arxiv_id":"2607.22156","last_updated":"2026-07-24T10:00:48Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-06T05:07:41.922138Z","submitted_at":"2026-07-24T10:00:48Z","title":"A random matrix approach to lamplighter groups"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":25,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":25},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2607.22156."}