{"as_of":"2026-08-13T13:46:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4ee4826996cd05e2a625f488c82b00108fe26a31ab8826563ab98b5f97941847","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T12:36:10.430030Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2411.17166/citation-record","integrity":"/paper/2411.17166/integrity","json":"/paper/2411.17166/citation-record.json","paper":"/paper/2411.17166"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.787837Z","title":"An introduction toII1 factors","venue":null,"work_id":"40fe06ff-ebbc-42e1-8c22-f705796527d8","year":null},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.338407Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:64551a8b2bf780fd592e52559d6234750f35e644df20f8e1341f76f1e96b1d27","observation_id":"bdb6ecc1-c2e3-4a13-b900-e5e8b5d137f3","resolution":{"observed_at":"2026-08-12T12:36:10.792644Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2209.11823","last_updated":"2024-02-15T04:52:31Z","snapshot_observed_at":"2026-07-06T13:55:45.499742Z","submitted_at":"2022-09-23T19:28:41Z","title":"The Brown measure of a sum of two free random variables, one of which is triangular elliptic","version":3},"cited_work":{"arxiv_id":"2209.11823","doi":null,"metadata_source":"pith","pith_arxiv_id":"2209.11823","snapshot_observed_at":"2026-08-12T12:36:10.527795Z","title":"The Brown measure of a sum of two free random variables, one of which is triangular elliptic","venue":"math.OA","work_id":"dd5dab7b-fae2-474c-b0eb-83aada46887f","year":2022},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.343289Z"},"links":{"cited_paper":"/paper/2209.11823","citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:a261ea30fb0ea3689abb6b1c52b0eb94324b073bdf13c52e3b02c17e318b7ff3","observation_id":"87b52722-91a0-402f-9418-6466084148a0","resolution":{"observed_at":"2026-08-12T12:36:10.532893Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.773776Z","title":"Eigenvalues of non- Hermitian random matrices and Brown measure of non-normal operators: Hermitian reduction and linearization method","venue":null,"work_id":"7ca4baaa-067e-4100-a110-51c095ffb0eb","year":2018},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.348368Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:3bf56d71b4fc44dbf47564192eb7a2f6585f3591575d8d6f450f3880dd46f796","observation_id":"7015c664-a8b8-4375-8b34-d1744180bc40","resolution":{"observed_at":"2026-08-12T12:36:10.778433Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.759322Z","title":"Lidskii’s theorem in the typeII case","venue":null,"work_id":"b1313918-1d68-45fa-a32d-428bb5add4ec","year":1983},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.353162Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:f334cc21051d36d1c63197f27f4cc5f9f4cd1c457c8dfc172087e9cb1bd58718","observation_id":"f0823af9-f845-479e-8f5f-0e78d26a2f0c","resolution":{"observed_at":"2026-08-12T12:36:10.764001Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.744724Z","title":"Quaternionic R transform and non- Hermitian random matrices","venue":null,"work_id":"0808ecee-3030-4ddf-80a1-52499aba8c78","year":2015},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.357541Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:8d41d45eeb0b8a5fc36b933f8521e785568b9b87bcaedc291ac6aa1d6ec6dca8","observation_id":"794e6d69-234b-4042-8551-9ae0a3415359","resolution":{"observed_at":"2026-08-12T12:36:10.749311Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.730507Z","title":"Support of the Brown measure of the product of a free unitary Brownian motion by a free self-adjoint projection","venue":null,"work_id":"ecde7b0b-1404-46bb-bc1e-756ef1a4b441","year":2022},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.361652Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:1dedd16372273aa419aa2ea2adb4c06d1066fcfa7b8400ae33771dd1c406e8ce","observation_id":"fd1c750f-d259-4867-8445-280f5267d39f","resolution":{"observed_at":"2026-08-12T12:36:10.735164Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.715575Z","title":"The Brown measure of the free multiplicative Brownian motion","venue":null,"work_id":"25ce8f40-239a-47bb-af04-72bd6d223b1f","year":2022},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.366356Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:dc92b8fe76746f72e6a6f6e929c286dcd9b8536f77533e893d15a95d05f5a40c","observation_id":"9f93c0b5-73ea-4ae1-acdc-fd9acd8a7147","resolution":{"observed_at":"2026-08-12T12:36:10.720681Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.701173Z","title":"Non-Hermitian random matrix theory: method of Hermitian reduction","venue":null,"work_id":"b8ce2e9b-a54c-4022-b626-0992390ecdcb","year":1997},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.371566Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:ff4540e8be78918f0abe661c446b2d619523f86f2e38d12062f21581a23a9618","observation_id":"1925266e-a846-42d2-a65b-1c661939a23e","resolution":{"observed_at":"2026-08-12T12:36:10.705865Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.686451Z","title":"Determinant theory in finite factors","venue":null,"work_id":"093cf248-9444-4657-9719-227370af3d61","year":1952},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.375551Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:d8b621b1df8d0bbfce114891e5d5ab201a83533df11472dcdec47c782f72d9a8","observation_id":"0f65bbd5-96f8-44e9-b1dd-1866b44dbb65","resolution":{"observed_at":"2026-08-12T12:36:10.691150Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.671540Z","title":"Brown measures of unbounded operators affiliated with a finite von Neumann algebra","venue":null,"work_id":"08c53cae-4193-441b-b3ca-773b9cce7f35","year":2007},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.379592Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:15815e62b90158f26fd06ec0250d140c18691467d14e7febd2d06441c8fc7d0b","observation_id":"da30ce82-b9f5-4509-8a4b-3a91a761105f","resolution":{"observed_at":"2026-08-12T12:36:10.676131Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.657270Z","title":"The Brown measure of the sum of a self-adjoint element and an elliptic element","venue":null,"work_id":"8d814172-35fd-4cd5-9989-6746d88c0c49","year":2022},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.383514Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:f219187c8d494280d8f41b13a1f58ddd939738cf901cd05329d59948d046a143","observation_id":"54a47f81-6bee-4938-8171-f731f917a8b3","resolution":{"observed_at":"2026-08-12T12:36:10.661862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.642775Z","title":"Brown measures of free circular and multi- plicative Brownian motions with self-adjoint and unitary initial conditions","venue":null,"work_id":"4898d88d-3bfd-464b-a067-ea633138eb89","year":2023},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.388295Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:bb016bd7674620d950270a171e6a4ec8bc5954f1ab93d37bd9a4190743c9740b","observation_id":"2321d7b8-5566-4237-986e-557274d77e17","resolution":{"observed_at":"2026-08-12T12:36:10.647277Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.628508Z","title":"Non-Hermitian random matrix models","venue":null,"work_id":"42753463-54a7-47bc-8647-e3fdd8355e87","year":1997},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.392412Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:34084586e46982b593a2ba2c58aefe08fe12e6e46791a42a67954b5a1240fd04","observation_id":"5052d729-a626-471a-827a-79aa4634263c","resolution":{"observed_at":"2026-08-12T12:36:10.633130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.614521Z","title":"Random Hermitian versus random non-Hermitian operators—unexpected links","venue":null,"work_id":"cde0927f-2bd8-4b48-b9fc-fef5fce1b8da","year":2006},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.396691Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:9058758f8256ba3833d7b9b7c7fed83f95ca56f8e6ef42a40e227dc0dfc1f279","observation_id":"6989c2e3-e369-4103-96e9-0a461ee40e71","resolution":{"observed_at":"2026-08-12T12:36:10.618896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math-ph/0402057","last_updated":"2004-02-19T15:33:59Z","snapshot_observed_at":"2026-07-07T06:14:38.171617Z","submitted_at":"2004-02-19T15:33:59Z","title":"A Novel Approach to Non-Hermitian Random Matrix Models","version":1},"cited_work":{"arxiv_id":"math-ph/0402057","doi":null,"metadata_source":"pith","pith_arxiv_id":"math-ph/0402057","snapshot_observed_at":"2026-08-12T12:36:10.508030Z","title":"A Novel Approach to Non-Hermitian Random Matrix Models","venue":"math-ph","work_id":"34e00685-a032-4b59-8eca-e7bd7136a5b9","year":2004},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.400634Z"},"links":{"cited_paper":"/paper/math-ph/0402057","citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:f7ce4cba12cf038c9d8e32ac436cc2774d26b561d32486b8ddf72b702a0bd515","observation_id":"505d4592-311c-4963-8588-b110981fa49c","resolution":{"observed_at":"2026-08-12T12:36:10.512732Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.599716Z","title":"Mingo and Roland Speicher.Free probability and random matrices","venue":null,"work_id":"3b0f5037-659a-4fd8-b5a2-a1451bb47141","year":2017},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.404952Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:1807da096a35ff6c3ee66e84a676228d3356568bb9387849c808303252eb3855","observation_id":"cc8bbae8-bc67-4210-99c5-861858fc9a92","resolution":{"observed_at":"2026-08-12T12:36:10.604142Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.585160Z","title":"An Introduction to the Theory of Resultants","venue":null,"work_id":"3398cb71-3bc8-4fc8-96e0-13450b5a9981","year":1996},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.408800Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:c59bc2f06e55a9b21b2d77428ba5d2c301ad21a4141ae6117bcca2fc48023e72","observation_id":"de1611e2-ae4e-4186-9d6b-dba3e3e44381","resolution":{"observed_at":"2026-08-12T12:36:10.590228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.571010Z","title":"Graduate Studies in Mathe- matics","venue":null,"work_id":"e6af16fd-ecb6-404e-bb7b-695f4e0e15b6","year":2012},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.412817Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:017b6a1592464d6f5df53d091bdafd47f57680efd565eeb7ed483bcc644af22b","observation_id":"885e5176-d12c-45d7-89c9-40e67282bd31","resolution":{"observed_at":"2026-08-12T12:36:10.575591Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.556704Z","title":"Convergence of the Laws of Non-Hermitian Sums of Projections","venue":null,"work_id":"8aad35ef-6efb-4967-9720-a3d235f5e1a7","year":null},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.416905Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:26826a4940d8e9256b8fea1a14e441621290ff1b678fbf4de386f6faf1f887ca","observation_id":"742b0fdb-b754-45f4-9c2e-b5c596660665","resolution":{"observed_at":"2026-08-12T12:36:10.560853Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T12:36:10.542838Z","title":null,"venue":null,"work_id":"159748bc-98cd-4783-b45b-4929e54c722c","year":null},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.426023Z"},"links":{"citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:d8f9c7b4fd06de8cb52869833eb31ed13b3135a7c0cf3cdf60437c7f6452c4e3","observation_id":"ae11dbac-979a-45d6-9701-ab9f0ee5707b","resolution":{"observed_at":"2026-08-12T12:36:10.547100Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.13804","last_updated":"2024-11-26T06:45:33Z","snapshot_observed_at":"2026-08-12T15:49:45.418873Z","submitted_at":"2024-11-21T03:08:30Z","title":"The Brown Measure of Non-Hermitian Sums of Projections","version":2},"cited_work":{"arxiv_id":"2411.13804","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.13804","snapshot_observed_at":"2026-08-12T12:36:10.465778Z","title":"The Brown Measure of Non-Hermitian Sums of Projections","venue":"math.OA","work_id":"d653c614-71f9-48dd-a19d-8dedcadaf0f2","year":2024},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.430030Z"},"links":{"cited_paper":"/paper/2411.13804","citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:973d584377dead873f34ec65cb1d960fe23395b42925302c0ebcd001ffd8c07c","observation_id":"ba78a9e6-d022-4ae2-a757-8de934f10553","resolution":{"observed_at":"2026-08-12T12:36:10.471958Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.17159","last_updated":"2025-01-01T23:56:03Z","snapshot_observed_at":"2026-08-12T12:24:15.574281Z","submitted_at":"2024-11-26T07:01:16Z","title":"Convergence of the Laws of Non-Hermitian Sums of Projections","version":2},"cited_work":{"arxiv_id":"2411.17159","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.17159","snapshot_observed_at":"2026-08-12T12:36:10.487993Z","title":"Convergence of the Laws of Non-Hermitian Sums of Projections","venue":"math.OA","work_id":"50ba4d16-111b-412d-b113-6d89657d0263","year":2024},"citing_paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators","version":2},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-12T12:36:10.421495Z"},"links":{"cited_paper":"/paper/2411.17159","citing_paper":"/paper/2411.17166"},"observation_digest":"sha256:46374469c5aca6f6fb6b823c4294f6b6866d9c63a755e8702819e784c9dd15d0","observation_id":"f1252fd6-769a-465f-a68d-255bfcf0e902","resolution":{"observed_at":"2026-08-12T12:36:10.492755Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.17166","last_updated":"2025-01-04T18:43:33Z","latest_version":2,"primary_category":"math.OA","snapshot_observed_at":"2026-08-12T22:41:22.247713Z","submitted_at":"2024-11-26T07:10:35Z","title":"Quaternionic Green's Function and the Brown Measure of Atomic Operators"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":4,"verified_fuzzy":17},"total_outbound_references":22},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2411.17166."}