{"as_of":"2026-08-11T06:18:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ecb069363a0b7950aeeecda4522a2a385b519b5de3d488708f501b04700aaad8","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:52:35.666492Z","state":"measured"},{"denominator":40,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":40,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T17:01:18.704135Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-11T14:06:04.775023Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.04691","snapshot_observed_at":"2026-08-06T17:01:18.704135Z","title":"Drimbe, S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.12271","last_updated":"2025-07-16T14:21:06Z","snapshot_observed_at":"2026-08-08T21:47:05.581911Z","submitted_at":"2025-07-16T14:21:06Z","title":"Universal C$^{\\ast}$-Algebras from Graph Products: Structure and Applications","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T17:01:18.704135Z"},"links":{"cited_paper":"/paper/2507.04691","citing_paper":"/paper/2507.12271"},"observation_digest":"sha256:855ad3e5a1298f8bd6c46e92529d6367a09dec7c652c8fb389df486f71bbe686","observation_id":"9ede0054-a0ea-45ec-b254-ce80862406d8","resolution":{"observed_at":"2026-08-06T17:01:18.704135Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.04691","snapshot_observed_at":"2026-08-03T18:50:51.476499Z","title":"W ∗-correlations of II 1 factors and rigidity of tensor products and graph products, preprint arxiv:2507.04691","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2512.04531","last_updated":"2026-07-10T22:20:41Z","snapshot_observed_at":"2026-08-09T14:31:35.914168Z","submitted_at":"2025-12-04T07:27:34Z","title":"A continuum of non-measure equivalent groups","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T18:50:51.476499Z"},"links":{"cited_paper":"/paper/2507.04691","citing_paper":"/paper/2512.04531"},"observation_digest":"sha256:e1128095c7ca4b1dc887cf2b9b8b42049e6cee2709c17f513280fa862cc27e3d","observation_id":"05f11f22-857e-4567-86b8-3b8b6457f13e","resolution":{"observed_at":"2026-08-03T18:50:51.476499Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"cited_work":{"arxiv_id":"2507.04691","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.04691","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"arXiv preprint arXiv:2507.04691 , year=","venue":null,"work_id":"fb4efa8b-d25e-4cc7-9827-0b1feb72f064","year":null},"citing_paper":{"arxiv_id":"2604.20184","last_updated":"2026-04-22T04:55:54Z","snapshot_observed_at":"2026-07-31T17:45:45.960732Z","submitted_at":"2026-04-22T04:55:54Z","title":"On free components of Artin and Coxeter groups","version":1},"reference_index":151,"source":"arxiv_source","source_observed_at":"2026-05-09T23:30:27.175748Z"},"links":{"cited_paper":"/paper/2507.04691","citing_paper":"/paper/2604.20184"},"observation_digest":"sha256:8f33fad48016a6e02fb24a624179b85d45437a78bc14002909752fc950534ffa","observation_id":"15dc3919-4ee6-49f5-8ccc-b7cbf292def0","resolution":{"observed_at":"2026-05-11T14:06:04.779789Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.04691/citation-record","integrity":"/paper/2507.04691/integrity","json":"/paper/2507.04691/citation-record.json","paper":"/paper/2507.04691"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1110.4918","last_updated":"2012-12-10T13:02:38Z","snapshot_observed_at":"2026-07-06T02:36:13.799208Z","submitted_at":"2011-10-21T22:28:33Z","title":"Strong Solidity of the q-Gaussian Algebras for all -1 < q < 1","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1110.4918","snapshot_observed_at":"2026-08-06T19:52:35.558257Z","title":"Avsec, Strong solidity of the q -Gaussian Algebras for all -1 < q < 1","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.558257Z"},"links":{"cited_paper":"/paper/1110.4918","citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:c097d8d4d15dd5ad7d22ccb9f51c80aacd888b67fbc418ed7be8a9b8010f303e","observation_id":"fc1c46dd-9653-4d50-93f3-4080341fda93","resolution":{"observed_at":"2026-08-06T19:52:35.558257Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:52:35.992410Z","title":"Berbec and S","venue":null,"work_id":"e3b8c339-dbc6-40e8-83b3-945e42cfd681","year":2014},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.566812Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:abfa69ea2f388032455e7e29e22da534daaf005353175e840c9581504bd2887c","observation_id":"f5c68037-11fb-47f2-ae0f-3f8b1a4f577d","resolution":{"observed_at":"2026-08-06T19:52:35.995092Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.984259Z","title":"Berendschot and S","venue":null,"work_id":"c56f34bf-ea9e-4f36-8bdc-a0719e4733fa","year":2025},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.569972Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:093499557b93ff2fed4c7e4181d2516e6bce5582360cfdbb96a2de043f8daae0","observation_id":"1df55ff6-fbcb-4d83-af61-50ad11b9bf61","resolution":{"observed_at":"2026-08-06T19:52:35.986956Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.06171","last_updated":"2026-05-11T18:01:50Z","snapshot_observed_at":"2026-07-06T18:59:38.952273Z","submitted_at":"2024-08-12T14:17:07Z","title":"Rigid Graph Products","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.06171","snapshot_observed_at":"2026-08-06T19:52:35.573620Z","title":"Borst, M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.573620Z"},"links":{"cited_paper":"/paper/2408.06171","citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:20b41e6252f86192cd4c88566784fc15e9b1aa7475851de8943c4eed56250ba3","observation_id":"f8163cd7-de75-4d04-9bf8-d96379dbd818","resolution":{"observed_at":"2026-08-06T19:52:35.573620Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:52:35.976160Z","title":"Boutonnet, On solid ergodicity for Gaussian actions","venue":null,"work_id":"772d769f-0a80-42cc-8ecc-ee0d881ad4be","year":2012},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.577739Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:f981373602c5273b8db24642bd55f1083af362ece27a35de49339d882ea6e0ff","observation_id":"8018942d-7bde-4ff9-995a-3d46863b1c3e","resolution":{"observed_at":"2026-08-06T19:52:35.978967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.968264Z","title":"Bo\\.zejko and R","venue":null,"work_id":"b7c4acb6-0570-4e70-b77a-c24b5e794ee0","year":1991},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.580457Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:2d18d892f63204017f8010fe84abe84bb989fa51baee04e95f62e8baf067fb1b","observation_id":"8d7cc9c2-b7c4-4e1e-a0b4-d36c37e9518d","resolution":{"observed_at":"2026-08-06T19:52:35.970870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.959927Z","title":"Brown and N","venue":null,"work_id":"18d8268b-795c-4fef-853d-2ff5a715e39e","year":2008},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.583580Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:5f8385d8a81f9590a0b4bb958ed8ee7451bd92a9ddec83fca4647c87378662ee","observation_id":"77611275-93f8-4940-a8a4-39b9577ca26d","resolution":{"observed_at":"2026-08-06T19:52:35.962710Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.951649Z","title":"Caspers and P","venue":null,"work_id":"01e6d134-d1f0-4a17-b252-a8267d06b7be","year":2017},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.586296Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:a38808ffd7e29ae04bfcc02f0383174ed178ddd032cdfa319a72126a9726aebc","observation_id":"cf4c2f05-3522-4e56-99d3-aa9f7baac767","resolution":{"observed_at":"2026-08-06T19:52:35.954325Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.943731Z","title":"Caspers, Y","venue":null,"work_id":"c6c7454e-d5d2-4158-b251-afd35b62927a","year":2021},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.589275Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:f8a04779ca2e1598571d90b82c5a1f834b266fca8ab00c4ba462d2388be8517f","observation_id":"143a8b4b-7bd7-436f-8d63-f5b40d5e6fed","resolution":{"observed_at":"2026-08-06T19:52:35.946334Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.935142Z","title":"Davis, The geometry and topology of Coxeter groups","venue":null,"work_id":"7149bb4e-7595-4f6c-baef-732cb01cfd25","year":2008},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.591882Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:ce6899f329a6940cc79c46da0cc482810907b7029c1a82f25bab0b3da7f9a2e8","observation_id":"c162e08a-f407-407c-a25a-c9326260aea9","resolution":{"observed_at":"2026-08-06T19:52:35.938076Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.926848Z","title":null,"venue":null,"work_id":"afeee131-14c4-4eff-9fe6-1f14ce528acb","year":2023},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.594645Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:ea403e82351aa000a4570d32cb9d7aaaac5fefcd03a2723ccbbf2191ae80e459","observation_id":"e0ac6d10-93b9-43de-9414-68eed16cdbf4","resolution":{"observed_at":"2026-08-06T19:52:35.929469Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.10161","last_updated":"2023-09-18T21:18:00Z","snapshot_observed_at":"2026-07-06T16:20:13.025092Z","submitted_at":"2023-09-18T21:18:00Z","title":"Biexact von Neumann algebras","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.10161","snapshot_observed_at":"2026-08-06T19:52:35.597383Z","title":"Ding and J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.597383Z"},"links":{"cited_paper":"/paper/2309.10161","citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:bc5486d0e685c4946c1cc7ef3dde856371494c1812bc368ed36839d7412144b9","observation_id":"86ab0282-6622-4a0f-a065-7b94beb91982","resolution":{"observed_at":"2026-08-06T19:52:35.597383Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:52:35.919099Z","title":"Donvil and S","venue":null,"work_id":"939060e5-398d-42aa-b450-be4cf2a7a67b","year":2025},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.600344Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:2ba8488c6123994cd98f9fe8bca2c2de8a57b79e58f7a17af8bcb2da655b12ec","observation_id":"eaf8e4e0-5b9c-4e29-bfba-0a2177e26064","resolution":{"observed_at":"2026-08-06T19:52:35.921525Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.911025Z","title":"Drimbe, Measure equivalence rigidity via s-malleable deformations","venue":null,"work_id":"0ecc8770-0de5-4b55-8f8b-9072e6771b84","year":2023},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.603344Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:cdfed3c761919cbc527e219688b834831e4b6800ab01cbca052e4604a45a9bcc","observation_id":"a4a454c1-9df8-4755-a547-85812f126873","resolution":{"observed_at":"2026-08-06T19:52:35.913682Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.903244Z","title":"Drimbe, D","venue":null,"work_id":"19f8aaa3-b91d-4cea-a1b8-8af166b1622f","year":2019},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.606882Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:ce34482fe05b529e3305c4a12eb2c83c75da9dde71e601b697286558c33da93a","observation_id":"f85daffb-f8c7-4660-bd2e-7fa1120a41da","resolution":{"observed_at":"2026-08-06T19:52:35.905716Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.894902Z","title":"Effros, Property and inner amenability","venue":null,"work_id":"c36d9a77-50bb-4198-80d8-ecf534909dfc","year":1975},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.610049Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:c072a160fe85598b66dcb48883854cb339b1d1da1754828a02a04b9e97ce0c2d","observation_id":"4df52b97-4f16-4306-8898-70e2988ad58e","resolution":{"observed_at":"2026-08-06T19:52:35.897830Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.886496Z","title":"Gromov, Asymptotic invariants of infinite groups","venue":null,"work_id":"4563ad82-d82f-45e4-80f1-1218c46fa0f4","year":1991},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.612590Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:0e4054d8ed0d1221739f1101e7fea2a6375fc49fe584965261e45b86c888c1d8","observation_id":"ba99ef06-e9aa-445b-91f7-f47ab00d4459","resolution":{"observed_at":"2026-08-06T19:52:35.889323Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.878198Z","title":"Houdayer and Y","venue":null,"work_id":"4588853e-fcdf-4523-888e-7a98c5cf5546","year":2017},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.615900Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:05f6a6e6f2bc3b5caf1b02302fbbcc19575726db355d6904b8a05b54f066524d","observation_id":"9383a4ac-a021-4a88-921a-059555008842","resolution":{"observed_at":"2026-08-06T19:52:35.880761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.869367Z","title":"Ioana, Cartan subalgebras of amalgamated free product II _1 factors","venue":null,"work_id":"ae0e522f-8bef-4af2-8f06-88e8683d2e68","year":2015},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.619146Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:337657785ddc982c4e254cc3464bb0bda55ac8aa7b00aa2676845d8c9504afb9","observation_id":"0ddcd160-faed-47e1-8e76-6b4a5d9d17b7","resolution":{"observed_at":"2026-08-06T19:52:35.872067Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.861426Z","title":"Ishan, Von Neumann equivalence and group approximation properties","venue":null,"work_id":"a1106fde-c5c2-4c41-8165-2897a6794200","year":2024},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.622490Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:530e03c7e5bea7b4135c2f62563ee2747279ef5af6ef39bb32b92b59f211de60","observation_id":"b4a33c28-cc4d-4f16-9359-6885fa3fd24a","resolution":{"observed_at":"2026-08-06T19:52:35.864058Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.853486Z","title":"Ishan, J","venue":null,"work_id":"dab97028-cb36-4abf-8b72-f1a931ee92d8","year":2024},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.625721Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:fbd39793300ac9b39a27ee2c21418396d3ba41a9f41a8b82217adad24e8857c2","observation_id":"d2e30cbe-beb7-4e0f-a764-8202b7c4dd7e","resolution":{"observed_at":"2026-08-06T19:52:35.856146Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.845239Z","title":"Isono, Examples of factors which have no Cartan subalgebras","venue":null,"work_id":"534135f4-7a38-41df-bed2-d1d5fcc3fba7","year":2015},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.628092Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:75e9191b557b123032eadb1fae1c683a6090f52baf568d02120dc8a8b9be9f19","observation_id":"3de33aee-a274-4056-9d18-fa09e8c3bd72","resolution":{"observed_at":"2026-08-06T19:52:35.847917Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.837182Z","title":"Isono, Unique prime factorization for infinite tensor product factors","venue":null,"work_id":"879462e6-5d77-44f8-b648-3c9d5139fb71","year":2019},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.630522Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:fa98620854b26967cd5504e78a3f6228e69da55ed39a6759350fe847b53e1a6c","observation_id":"e8c7ebc1-45c4-4076-89b5-7f9dba0f4415","resolution":{"observed_at":"2026-08-06T19:52:35.839888Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.829096Z","title":"Isono and A","venue":null,"work_id":"092b3b1b-6a33-4b5d-b6d9-aa5cb35200cf","year":2022},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.632866Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:2f966d44d8995ff645074fccf6228f2772306c7057298d9cb268ebe4037ab648","observation_id":"0ddd56ac-4273-498b-a5e1-6db6dbb0d460","resolution":{"observed_at":"2026-08-06T19:52:35.831792Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.820625Z","title":"Monod and Y","venue":null,"work_id":"afb796bd-de0d-4233-8912-a045779221bb","year":2006},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.635457Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:b1ea2e6e889470777ffb513fbdb9ded6fe7e65c59d3e034b3f89c0068431954d","observation_id":"b35779dd-8e1f-4793-8a95-b2b3a48734dc","resolution":{"observed_at":"2026-08-06T19:52:35.823438Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.812522Z","title":"Nou, Non injectivity of the q -deformed von Neumann algebra","venue":null,"work_id":"0a6cf621-efae-46a0-8b60-c0164e189d39","year":2004},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.638233Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:b2fc8e2714315818b6bb809eb3e6f3f2413665697da55b2c299d90a140726456","observation_id":"58799ecd-d184-4a9d-b93e-3a40954dd066","resolution":{"observed_at":"2026-08-06T19:52:35.815237Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.804135Z","title":"Ozawa, Solid von Neumann algebras","venue":null,"work_id":"9f95d07a-cd8e-4633-bbe1-eb4b1823f1d3","year":2004},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.640906Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:392144999a393d58ecca7123eba03da9637e61bb12d81cfb0e141064fab0fd76","observation_id":"9a9bb333-f84a-439b-9fdb-fcfe048a63a5","resolution":{"observed_at":"2026-08-06T19:52:35.806808Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.795940Z","title":"Ozawa, A Kurosh-type theorem for type II _1 factors","venue":null,"work_id":"bf19bffa-aaf7-4715-9e0e-71665dac10e5","year":2006},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.643579Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:45505196c502f8c92eab05843387facec67d5b188d6b0f2c0fc94051e1111acf","observation_id":"00cfb4f7-3dce-4e6b-b051-d1c0b8ed6412","resolution":{"observed_at":"2026-08-06T19:52:35.798616Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.787667Z","title":"Ozawa and S","venue":null,"work_id":"d13fcded-bfe5-4ffa-b909-e9dec5723db7","year":2004},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.646158Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:8016c6f29fcff3caeac962ee110347077877dcef8fadf91d2674b0cc7e0e537e","observation_id":"416fe6c9-5d13-4473-a32d-8055a7894f04","resolution":{"observed_at":"2026-08-06T19:52:35.790379Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.779211Z","title":"Ozawa and S","venue":null,"work_id":"94c773df-d83c-4ec0-b9db-541a962a699c","year":2010},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.648734Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:ea0b3472cfdd959dda4e9054a518ef755508620cfe8dad7a755fcc9ff9997794","observation_id":"3b218838-769e-4d9a-893a-d1cb06cdb023","resolution":{"observed_at":"2026-08-06T19:52:35.781827Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.770693Z","title":"Popa, Strong rigidity of II _1 factors arising from malleable actions of w -rigid groups, I","venue":null,"work_id":"250911a3-ef65-4076-93d9-10d4a5dc65b0","year":2006},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.651292Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:6c5fa69322b13312cb9efc3d7953bd43d7ae18659530a4f3e43b2ab20fde9e7d","observation_id":"ba5f2339-41ba-4b15-8465-f17ef4f59eb1","resolution":{"observed_at":"2026-08-06T19:52:35.773545Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.761293Z","title":"Popa, Deformation and rigidity for group actions and von Neumann algebras","venue":null,"work_id":"776737e2-c8a9-4d2d-a352-1de2feb230f9","year":2007},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.653854Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:38ab3c507b872a22ccb52d5e7e670d91bafd71ba04551d1a9535efa40191b34f","observation_id":"ac7847c8-7362-4d05-a3de-b618ca1892b1","resolution":{"observed_at":"2026-08-06T19:52:35.764649Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.750683Z","title":"Popa and S","venue":null,"work_id":"d089e14d-cc9d-40d3-a913-e8dc71d26f76","year":2014},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.656274Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:6ae0e4e8192db116db2af0a9cd2dc32464e4da8f906d53ad0932b5d378329a4a","observation_id":"a7ee37bf-370a-43c4-80fb-99b97619c113","resolution":{"observed_at":"2026-08-06T19:52:35.753293Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.742378Z","title":"Popa and S","venue":null,"work_id":"9d244e0a-de0a-4c62-bbda-6c5aae902c77","year":2014},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.659045Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:23abb4981d95ef400c72869ad7f9508514f6d1ff9ac109f0db21394e654d6b81","observation_id":"955371b5-0c95-41a0-8203-f915d95a4620","resolution":{"observed_at":"2026-08-06T19:52:35.744955Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.733394Z","title":"Ricard, Factoriality of q -Gaussian von Neumann algebras","venue":null,"work_id":"a46f810f-5cdd-4a90-849c-3960e755cfc2","year":2005},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.661437Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:8374486cbfdce06ab2ed488afe3ca4e5986be2162ecc2fb0c911de4012f0ecf6","observation_id":"04261f4c-a318-4849-89c7-b953dff47211","resolution":{"observed_at":"2026-08-06T19:52:35.736381Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.724833Z","title":"Vaes, An inner amenable group whose von Neumann algebra does not have property Gamma","venue":null,"work_id":"918c7716-a0a3-4c7b-85b2-e6c3f804001f","year":2012},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.664042Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:13df942d10e9367e1f255b05a0044c892817941ab296963312ccfc46c834833e","observation_id":"f3027b93-2ea8-4167-a034-20f6e3cc94b9","resolution":{"observed_at":"2026-08-06T19:52:35.727589Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T19:52:35.714285Z","title":"Wildschut, Strong solidity of q -Gaussian algebras","venue":null,"work_id":"b9e4f9a2-13cf-4fae-8966-561f23909d65","year":2020},"citing_paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products","version":2},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-06T19:52:35.666492Z"},"links":{"citing_paper":"/paper/2507.04691"},"observation_digest":"sha256:a3c351f4cde2cc64f5d73071ec179b315539c291d8a30b08dd5cb96566e32111","observation_id":"a042463e-53b9-40c3-bcbe-61dcf53cad23","resolution":{"observed_at":"2026-08-06T19:52:35.718474Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.04691","last_updated":"2025-08-12T15:08:53Z","latest_version":2,"primary_category":"math.OA","snapshot_observed_at":"2026-08-08T12:40:12.686316Z","submitted_at":"2025-07-07T06:13:56Z","title":"W*-correlations of II$_1$ factors and rigidity of tensor products and graph products"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":0,"verified_fuzzy":33},"total_outbound_references":37},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 3 inbound Pith citation observations for arXiv:2507.04691."}