{"as_of":"2026-08-16T15:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6afba19ffc1eff7fa0e0ce109ec994049949ab48b8a9b32c43ce80eaa00e551b","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T17:13:32.543732Z","state":"measured"},{"denominator":39,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":39,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-09T16:01:00.069427Z","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":"2026-05-11T16:36:08.510064Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"cited_work":{"arxiv_id":"2508.18978","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2508.18978","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Amrutam, Y","venue":null,"work_id":"c4c42593-6e66-4380-a739-1c5d7d5dc19e","year":2025},"citing_paper":{"arxiv_id":"2605.01795","last_updated":"2026-05-03T09:20:07Z","snapshot_observed_at":"2026-08-08T13:58:36.471879Z","submitted_at":"2026-05-03T09:20:07Z","title":"Factors with prescribed number of invariant subalgebras not arising from subgroups","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-09T16:01:00.069427Z"},"links":{"cited_paper":"/paper/2508.18978","citing_paper":"/paper/2605.01795"},"observation_digest":"sha256:1e2e240118ff9326f291e1b1972850587dd27dec88bb7e79be4f8eb8cbc8c4bf","observation_id":"6feef0cb-7931-47d4-910d-01dc48a97d91","resolution":{"observed_at":"2026-05-11T16:36:08.512691Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2508.18978/citation-record","integrity":"/paper/2508.18978/integrity","json":"/paper/2508.18978/citation-record.json","paper":"/paper/2508.18978"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:13:34.612173Z","title":"3, 465–488","venue":null,"work_id":"38031c54-3308-4fad-ac03-cdde4942a4f4","year":2014},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.146147Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:febe44571cb5f5cd90b0daea2fb2c3a992fd436db14e05f1f51df34f04a08339","observation_id":"b3a28c9b-a56c-40c6-a93d-6807a4872800","resolution":{"observed_at":"2026-08-15T17:13:34.616778Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:34.566545Z","title":"1, 380–395","venue":null,"work_id":"a21d518d-6225-422a-9a4b-acbcc1a38f69","year":2024},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.228288Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:b4e4e72df241e6bd4cc7467885fd022bc5bdd513c4b084be7be5c4dea66051c8","observation_id":"19dfca1b-d298-4ac3-b2f8-1fc18f012dcb","resolution":{"observed_at":"2026-08-15T17:13:34.601295Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:34.490940Z","title":"2, 110718","venue":null,"work_id":"322525fa-66ac-442f-98b8-3c2daed58b8f","year":2025},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.302294Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:50b1a6d7f95b752f462272e620881a63333c7031457c8efda53be39b585a5fd7","observation_id":"310c353f-7d3c-456e-8af9-2b313cbd9d65","resolution":{"observed_at":"2026-08-15T17:13:34.495293Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:34.423608Z","title":"6, e70205","venue":null,"work_id":"6cc4d4cb-257f-42a8-8b26-92216f748a27","year":2025},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.308022Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:547db781d21cf10f5f233ab76d5bcf614097b4992a315c090784da83fcb17c08","observation_id":"30115269-6748-4e27-8a15-3e8dd6d652c1","resolution":{"observed_at":"2026-08-15T17:13:34.478231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:34.411357Z","title":null,"venue":null,"work_id":"7e8b5679-735b-4ea8-8949-be11fc61c38c","year":2023},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.313402Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:4264102e19c6138373cac6afc58b108f4c53c1d7d8601af5ed89471b03a83db4","observation_id":"2e4544bb-cd82-492b-8675-2fc187220f63","resolution":{"observed_at":"2026-08-15T17:13:34.415354Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:34.298631Z","title":"3, 929–985","venue":null,"work_id":"a28e364b-4854-4336-9775-fca9f9fa8738","year":2022},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.399820Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:c580a24676deb516d4f1d8c2e3d2e57cc8946986a02e3cbb9c472ea375046cd9","observation_id":"8a714960-1793-4ba0-94cb-12b2cce34010","resolution":{"observed_at":"2026-08-15T17:13:34.403818Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:34.224313Z","title":null,"venue":null,"work_id":"00c77c3e-3434-47dc-a382-6edbe2d6e334","year":2014},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.474374Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:f7576316bce2cd6d19518fb2c0e3dbbae5b3032b092720168d29e5deced7611e","observation_id":"21f8ef1f-d42a-43b8-8600-ee5a5280b57a","resolution":{"observed_at":"2026-08-15T17:13:34.289893Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:34.159899Z","title":null,"venue":null,"work_id":"2d12b254-6d2b-48b9-a93c-15b527f3381e","year":2006},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.515426Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:665f7c4f1ff9be48898256f5bead4d7be5802de671cdcf1bd4f3b0834e9f4cde","observation_id":"e273ea23-69e0-4686-8025-c7e218f0b088","resolution":{"observed_at":"2026-08-15T17:13:34.163211Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.01466","last_updated":"2022-01-04T15:41:14Z","snapshot_observed_at":"2026-07-06T08:54:55.249405Z","submitted_at":"2020-02-04T18:44:12Z","title":"Separable boundaries for non-hyperbolic groups","version":4},"cited_work":{"arxiv_id":"2002.01466","doi":null,"metadata_source":"pith","pith_arxiv_id":"2002.01466","snapshot_observed_at":"2026-08-15T17:13:32.689246Z","title":"Separable boundaries for non-hyperbolic groups","venue":"math.OA","work_id":"e61a2692-77f5-4929-84b7-a9e567f98732","year":2020},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.554747Z"},"links":{"cited_paper":"/paper/2002.01466","citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:3a0b35d2d77eaced6ace5c5297e83b56892ff0d6f1a34af4a47d0c64dd951ffd","observation_id":"757df631-bfce-4f2b-92a0-a8509558ac11","resolution":{"observed_at":"2026-08-15T17:13:32.747209Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:34.147499Z","title":null,"venue":null,"work_id":"1c29d6f9-8e39-46fb-bafd-d6ce570aff9e","year":2021},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.594688Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:9cb51e24704552715db849a3059990eb8d31a5ca6701f35a84382b6471c851ba","observation_id":"5496f93c-90d8-45e0-acc3-9ee9abe94907","resolution":{"observed_at":"2026-08-15T17:13:34.152367Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:34.030463Z","title":null,"venue":null,"work_id":"b716d89e-2620-4fc7-835e-a1d547c31fca","year":2023},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.598081Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:10bba623f185134ef98bd1226010446e0243fedb306914113c5645e225acdb4d","observation_id":"274a8d46-ec80-4c85-8a11-5edb15a9a6e7","resolution":{"observed_at":"2026-08-15T17:13:34.097648Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:34.018299Z","title":"Brown and Narutaka Ozawa,C∗-algebras and finite-dimensional approximations, Graduate Studies in Mathematics, vol","venue":null,"work_id":"45be6ff5-654f-4454-9c34-a6e00f3b4058","year":null},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.665695Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:9bcf166846e3df7edfb1133db22efb3460b6b8ae37cf7924f5ef459cbe7c4659","observation_id":"0f788d65-45d7-476e-87df-226a9d5721f8","resolution":{"observed_at":"2026-08-15T17:13:34.022805Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.973943Z","title":"Danilenko, Entropy theory from the orbital point of view , Monatsh","venue":null,"work_id":"9dfe9638-4965-4bed-90dc-4f5d69e6bc28","year":2001},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.717543Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:bf6a16f5416d703108c2aec4eac5fe145428098cdf0d2de4a57ae54f038b87cb","observation_id":"c4f35834-3042-4fca-b514-8cfdd2768caf","resolution":{"observed_at":"2026-08-15T17:13:34.010765Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.947548Z","title":null,"venue":null,"work_id":"87d0dae7-22b0-4aa9-93ca-64fc9b33c4a6","year":1963},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.748201Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:7825dbd800ac1775cb6f006d1b5789cce565efc54fd68f72918e28e83fa929a4","observation_id":"7a4f9475-32d1-4470-8c9b-fa3c8ac178d0","resolution":{"observed_at":"2026-08-15T17:13:33.951546Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.870648Z","title":null,"venue":null,"work_id":"82958d39-0ffe-4c78-94cb-5f3707126b9a","year":1963},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.787471Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:40315de1972b1bd001be687a7a2c011eea4f72392b93319163b15986c9488ee8","observation_id":"ab6047d8-7aab-4854-8685-3924829bdb97","resolution":{"observed_at":"2026-08-15T17:13:33.939794Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.857927Z","title":"Systems Theory 1 (1967), 1–49","venue":null,"work_id":"641a505e-af28-414f-b3a2-ce02f10ce3ca","year":1967},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.817040Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:a97981980b0712428e326311e7919eca2a499fa05a37e97dadac7039755f825a","observation_id":"fbd63e54-4374-4b38-ae63-44393f8c6c8f","resolution":{"observed_at":"2026-08-15T17:13:33.862312Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.773324Z","title":"3, 453–466","venue":null,"work_id":"80cfef20-b817-4e99-b21b-3712ffb660c9","year":1996},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.821017Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:e8c88e1ab0a2194c3990f2b90e70f52b2c591c136d413212b3a70bf1ef1bf87c","observation_id":"5ae640e0-2071-43f0-b142-c52303440036","resolution":{"observed_at":"2026-08-15T17:13:33.850055Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.687637Z","title":"101, American Mathematical Society, Providence, RI, 2003","venue":null,"work_id":"97471667-c8a4-400e-ad5f-37317fe3b8f0","year":2003},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.852102Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:366a3c214478a7a768a5999e070c89b096ab24ba3b2caab0cd2d441e9a7d1681","observation_id":"8a57d801-43fe-4492-9dda-f2aa1c6dc410","resolution":{"observed_at":"2026-08-15T17:13:33.729793Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.674444Z","title":"Thouvenot, and Benjamin Weiss, Entropy theory without a past , Ergodic Theory Dynam","venue":null,"work_id":"78c8d874-519a-48d6-8989-32b1585c4ba7","year":2000},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.936492Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:bd1f8a6517619f874bfb32fd2c4224ab48bdbe91411ef12032fa2a86b9e17a3f","observation_id":"c9402856-a4c4-4ac7-8ba5-8c3e4e37d83f","resolution":{"observed_at":"2026-08-15T17:13:33.679473Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.03329","last_updated":"2025-06-17T07:40:29Z","snapshot_observed_at":"2026-08-16T14:37:14.617060Z","submitted_at":"2023-12-06T07:35:53Z","title":"On intermediate factors of a product of disjoint systems","version":4},"cited_work":{"arxiv_id":"2312.03329","doi":null,"metadata_source":"pith","pith_arxiv_id":"2312.03329","snapshot_observed_at":"2026-08-15T17:13:32.610330Z","title":"On intermediate factors of a product of disjoint systems","venue":"math.DS","work_id":"f7f8a0cf-2948-4bb0-9007-2c2abc3955b0","year":2023},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:31.998848Z"},"links":{"cited_paper":"/paper/2312.03329","citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:e823eb0f78a09428aaea342f5c6e14a4696c4bb52c269a37599d6ad0dd0c5192","observation_id":"9a583a42-0f33-4be5-ae1a-ee319294507f","resolution":{"observed_at":"2026-08-15T17:13:32.669731Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.572754Z","title":"3, 279–293","venue":null,"work_id":"c1505932-f550-4048-a46c-cf7adc420ea4","year":1978},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.053927Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:4bb7894fe8884267b09f4f88050f36ff8ba8a7e6ea984fd0e7161116e4cb9693","observation_id":"ab544fd3-bd48-4982-bec0-0507c98aa7c3","resolution":{"observed_at":"2026-08-15T17:13:33.625355Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1712.10133","last_updated":"2020-11-08T16:06:08Z","snapshot_observed_at":"2026-08-14T19:59:23.124833Z","submitted_at":"2017-12-29T07:15:22Z","title":"Stationary C*-dynamical systems","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1712.10133","snapshot_observed_at":"2026-08-15T17:13:32.124627Z","title":"to appear in Journal of the Euro- pean Mathematical Society","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.124627Z"},"links":{"cited_paper":"/paper/1712.10133","citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:eb046f306661cdc43b5864589efe625fd9ba90cefe2627a05a63c14eb2d89b27","observation_id":"d8335cf9-019d-439d-8f0c-d8e4f235f41a","resolution":{"observed_at":"2026-08-15T17:13:32.124627Z","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":"2026-08-15T17:13:33.562192Z","title":null,"venue":null,"work_id":"5d576317-cf67-41db-a2b8-b2bbbe96b61e","year":2021},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.158587Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:5b7fb2554c1d2f19ac2012149e1fd7c4ac4fc77209c7eca2c69ffef85387501f","observation_id":"e461bde6-c942-4318-9daf-4e984ceb15b7","resolution":{"observed_at":"2026-08-15T17:13:33.565782Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.527810Z","title":"1, 203–230","venue":null,"work_id":"ecbc3865-12c8-4d84-841b-63103d5d942f","year":2021},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.191251Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:4324b005673b1656a39eebcc2a705a4f354c0a06d3636d7d61c631047019a0f6","observation_id":"3fc5481f-a849-401f-9d31-dccc682caa55","resolution":{"observed_at":"2026-08-15T17:13:33.552856Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.431912Z","title":null,"venue":null,"work_id":"1f7f129c-8986-4c7c-b95d-a40e7aaebe66","year":2021},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.204343Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:33e70abbb45ba3dca80e41255d6b8d979c38cf2c2015d1b08a11cd2e8746df73","observation_id":"32661293-2fa4-4873-a749-6a9dd02ebdcf","resolution":{"observed_at":"2026-08-15T17:13:33.494517Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.419705Z","title":"10, 3341–3353","venue":null,"work_id":"b580220e-ef5b-412c-b90b-51fa596a2587","year":2023},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.272824Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:e1de5d56f64ccfc5ba49861290e8dd6b172354ae6fd10269eb5a544fbf077ef9","observation_id":"ffba2ca6-4e36-46fa-9554-db4627c22915","resolution":{"observed_at":"2026-08-15T17:13:33.424199Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.372056Z","title":"Ka˘ ımanovich and Anatoly M","venue":null,"work_id":"c618fbc2-3047-4a82-93c9-b08ebacee45f","year":1983},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.341672Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:da6111e1168baa99f3e3e050718d91cf9c716498b0e120f38a9f0de990f95040","observation_id":"148ec7ec-3a64-47bb-b74d-81a80df9398e","resolution":{"observed_at":"2026-08-15T17:13:33.411210Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.337120Z","title":null,"venue":null,"work_id":"6d33cece-0080-4693-a17a-13701d332466","year":2014},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.351927Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:35273f96b8ccb4e0adab508625017ed10d2702b3d3e0bbbf1a3ae649b2a5557d","observation_id":"008ccb6d-f1b8-4a18-82ca-6536300e8e1e","resolution":{"observed_at":"2026-08-15T17:13:33.342137Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.202635Z","title":"2, 229–252","venue":null,"work_id":"f9f1b8b9-42e9-43e3-9af7-f3f83536154d","year":1999},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.356772Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:c5e766950e556d0f5a6c2e51da233d52a76f3fff8ca32b19517164f026a6acb4","observation_id":"3b5f12ce-f609-4e97-b599-cd152c1cc7e4","resolution":{"observed_at":"2026-08-15T17:13:33.267779Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.183292Z","title":"Zimmer, Rigidity of Furstenberg entropy for semisimple Lie group actions, Ann","venue":null,"work_id":"4eb91cc7-478b-409d-908f-4afd5edf0713","year":2000},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.360506Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:6452a6e19610915352766be15d2f167b51c9ed5c09f875cc2695aa59c3919a53","observation_id":"ddfe93dc-66cf-4730-82e3-aadab8d33e1b","resolution":{"observed_at":"2026-08-15T17:13:33.188858Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:33.067009Z","title":"1, 93–104","venue":null,"work_id":"f71b6940-5934-4ffe-8340-3b72eefc680f","year":2002},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.364551Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:024d4962cea1487a9a5be8386824c9d45740d5fbe2b992e306476cd241df6de7","observation_id":"ebf62449-971b-465f-8d1b-999ad1934963","resolution":{"observed_at":"2026-08-15T17:13:33.113372Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:13:32.369347Z","title":null,"venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.369347Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:e080648942b7cb4b0c35fde0b5e2ab05df344626ad56f15aa9a1aa555a16abd2","observation_id":"5f28f8bc-a953-4cc0-8393-43ff28b77d88","resolution":{"observed_at":"2026-08-15T17:13:32.369347Z","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":"2026-08-15T17:13:33.037140Z","title":null,"venue":null,"work_id":"834aed83-1e1e-4eb2-9b5b-0bc6670fc0a2","year":2020},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.374087Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:2d1fd86b70a02c9dfb9ef4d1269dc2fac155a522ce9ae35e8b3e7b91403d3cdd","observation_id":"8a93b06a-d8f8-439e-bc8e-55fc90c6f688","resolution":{"observed_at":"2026-08-15T17:13:33.041775Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:32.916964Z","title":"I, Encyclopaedia of Mathematical Sciences, vol","venue":null,"work_id":"03e17bce-4fcf-4f70-be69-075c26df761e","year":1979},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.434084Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:284be4e961496ee0674c373fa18aa60e3a844dedcfc1705118cf21b6abe6ec3c","observation_id":"2bbcee29-dcd7-4a15-98eb-ab93e47ab12f","resolution":{"observed_at":"2026-08-15T17:13:32.999257Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:32.903424Z","title":"II , Encyclopaedia of Mathematical Sciences, vol","venue":null,"work_id":"3c71b12a-76e2-4cad-931d-faa8ce524a18","year":2003},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.489938Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:fb751d7e24ecb9e84b70822e367681dcf6d65c351acbbbabe693bd3cb1acc8ca","observation_id":"ce12b8df-879d-4802-bd31-e484b2d7f5ed","resolution":{"observed_at":"2026-08-15T17:13:32.908337Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T17:13:32.832295Z","title":null,"venue":null,"work_id":"c3a7c7eb-071d-41ef-92c6-d7c0995eae07","year":2024},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.535593Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:c0eeff8f978d05b4be3279261ca963e3bfd3885ab4f977d05d9c1bbd86137e60","observation_id":"c2192903-8a2a-4349-8579-0bc6e4ef8ceb","resolution":{"observed_at":"2026-08-15T17:13:32.895654Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.10905","last_updated":"2025-07-28T08:11:07Z","snapshot_observed_at":"2026-08-16T13:34:04.170279Z","submitted_at":"2024-07-15T16:59:18Z","title":"Noncommutative topological boundaries and amenable invariant random intermediate subalgebras","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.10905","snapshot_observed_at":"2026-08-15T17:13:32.539473Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.539473Z"},"links":{"cited_paper":"/paper/2407.10905","citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:feeb8d7e98bfed8672d9f7086f663e4752527be0e9d0373bbe3e7f9fb4ed7f77","observation_id":"6a97ce98-52f3-47df-b77d-a3e6983a6622","resolution":{"observed_at":"2026-08-15T17:13:32.539473Z","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":"2026-08-15T17:13:32.816655Z","title":"7, 2001–2006","venue":null,"work_id":"5d3b9764-a0b2-4b02-80e9-e10bbb7740a3","year":2000},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.543732Z"},"links":{"citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:34563d9bb07937a6f183b16f6ccd2637f86379ad7aca4010dc326050ea7e58f3","observation_id":"3f21bee4-1925-4e2f-af24-41a58b22dd02","resolution":{"observed_at":"2026-08-15T17:13:32.821637Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","latest_version":1,"primary_category":"math.OA","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":2,"verified_fuzzy":21},"total_outbound_references":38},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 1 inbound Pith citation observation for arXiv:2508.18978."}