{"as_of":"2026-08-13T10:06:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d412703b8da0163e4ed50c46b3b2f0cc2384e0106f3afa0f5b28647eb905765a","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-27T05:39:18.225910Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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":"2026-06-30T09:04:17.979029Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-06-30T09:04:32.520210Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"cited_work":{"arxiv_id":"2606.13270","doi":null,"metadata_source":"pith","pith_arxiv_id":"2606.13270","snapshot_observed_at":"2026-06-30T09:04:32.520210Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","venue":"math.DS","work_id":"6ac24115-d002-4ce1-8ff6-de1263d2100e","year":2026},"citing_paper":{"arxiv_id":"2606.28681","last_updated":"2026-06-27T01:46:12Z","snapshot_observed_at":"2026-08-01T04:48:23.976611Z","submitted_at":"2026-06-27T01:46:12Z","title":"Dimensional entropy of amenable group actions over stable sets and fibres","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-06-30T09:04:17.979029Z"},"links":{"cited_paper":"/paper/2606.13270","citing_paper":"/paper/2606.28681"},"observation_digest":"sha256:97b0ab157272670f5eff9de00f4844eb2235e74971eb34ffda003e20bc61ddbf","observation_id":"df4703b8-b77f-41ec-96a9-5652793dd5b6","resolution":{"observed_at":"2026-06-30T09:04:32.521610Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2606.13270/citation-record","integrity":"/paper/2606.13270/integrity","json":"/paper/2606.13270/citation-record.json","paper":"/paper/2606.13270"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Entropy-expansive maps","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:67ca40da91528d6f7a297c0a641230c71a79856879d506c14e536fcbdcddac8e","observation_id":"45abcac8-bda4-46b8-8a3c-5bd622ab9d79","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Zero-dimensional and symbolic extensions of topological flows","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:5671b73042ffe668ec87fed4546ce812c9411fccabe77b5f8c6b1c042bb616d2","observation_id":"3668b892-9bdc-4249-95f9-dacba2e5e8e9","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Variational principles for amenable metric mean dimensions","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:e1132479c670e83c965f23396858bf046512b688c74b28f67b6ef572a3c9f8d6","observation_id":"58e5e0db-12ac-483f-bb01-9f741eafc023","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Minimal subshifts of arbitrary mean topological dimension","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:3416e46d5dbc590fd4eebe67dbe7f2e1fe9c800ad7d514cae634fb6e2d4eb3f6","observation_id":"b0128e22-a858-4dfc-a4dc-0077e1740fa1","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"New characterizations of topological conditional entropy for actions of amenable groups","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:da662ac479123dcb838fc8f789f17aaeb911ebe5e59292795e48d0ab8069f06c","observation_id":"1ecf6e9f-de54-4a94-bd4b-e7536b9d1741","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Packing topological entropy for amenable group actions","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:6a0d73d19cd0937d052dfcfeb85a1f7ccfbcafa9a2a3d20f07093ddf5c3cbb0d","observation_id":"ceb80ea5-8a3b-4bf3-a003-4b590b849214","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Mean dimension of Z ^k -actions","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:98f1ee8ca5419bbe776b73e8624db693ef12bef9ede86513388e51f3b7989a34","observation_id":"c1fd61f0-9376-43b0-9c72-817934658ebb","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Application of signal analysis to the embedding problem of Z^k -actions","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:fdb79b0ab5f5b50c299f826686d8dee02e4347d1284b689b207840c8bf97c25c","observation_id":"44ba90f4-8747-4d2b-b83a-acdd539d38a1","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Topological invariants of dynamical systems and spaces of holomorphic maps","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:7798e561799a983e185a6e3a90c1cd952cad9545f10ef01355c7d92a9645eabf","observation_id":"ad59c7ae-90c8-4bb4-bf62-4c73aedd45d6","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Embedding minimal dynamical systems into H ilbert cubes","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:b18624f41c6a95522f4f8986b1747c922f29a4435be5121b79c26c0550767100","observation_id":"c5fdad17-93b4-47aa-834b-ddc8268d1659","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Embedding Z^k -actions in cubical shifts and Z^k -symbolic extensions","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:a113e55680851f0ceb84b247892f048ef943cf0553ce9dde9338a42c0c2ac92a","observation_id":"8acf0d98-01de-4372-995b-6f50e4cf8e6b","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Metric mean dimension for algebraic actions of sofic groups","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:a08eaaa376af49fb8794e57e31bfce11452b1359d5da72952baa8d430d9e4132","observation_id":"aac1843d-dd4a-4b2b-a463-d6eace02e6e3","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Sofic mean dimension","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:b2f8d2d1acb4b8ace0700b0008b23ace5d7179d94e2a8ef7da267adfa22b1878","observation_id":"53a2271f-5b42-4da2-bd9e-0a2c1944bd5e","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Amenable upper mean dimensions","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:207c11fc60ccd94667e245655ad41c88b10d8d449ba3711ba602e56112968a71","observation_id":"75497be8-c52e-42b3-90e8-2379dc4e632a","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Mean dimension, small entropy factors and an embedding theorem","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:9675d78fb1e4194b24e48b2e56ccb7367d52c66d42ab962f672892108d05c12a","observation_id":"e7abaaec-372c-4476-ac24-0b5f698f09ad","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Pointwise theorems for amenable groups","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:51ff01ee83141eeab7d6a713852689bb82eb535eaa1b08bd68d517515d79d39f","observation_id":"513eb7f3-bf72-443a-b6f3-234734a7bca0","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Mean dimension, mean rank, and von N eumann-- L \\\"uck rank","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:2d1228f33497db5ed3c98b1f3d822a700b6e48a467a9a4266574b40c9a463878","observation_id":"56861f4b-1786-4934-87b0-17b4d7b038bf","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Mean topological dimension","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:b9479f9a12ced4c5611ca08030a3f47cebc909d5894b129c9e6b915e0cba935d","observation_id":"32a8e1b6-76a7-4e42-8770-f7e15c065315","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Brody curves and mean dimension","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:976cc8bf7a30153ebe0177f61c2edcc70aca01f7a4e525fda3ef20745f236a76","observation_id":"91a2ae6e-21c7-4ab7-bc75-47ba1bc64f24","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Radius of comparison and mean topological dimension: Z^d -actions","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:069d9191d649a6ebd4b35965f7311c6fcbe83ff95afc59cd8e494a30de1ba4db","observation_id":"08fb2529-27a7-47c9-bd14-e5c1211f4167","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Ornstein and Benjamin Weiss","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:d3ea56bd3e1789a4cd220606d3433122c7dcdebbd7cdcc88b28ed7422c3aa1f0","observation_id":"3ef720db-f58d-4fd6-ae17-c70c28d0251d","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Mean dimension of the dynamical system of B rody curves","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:d210b0f87c3a8aa59ace683f75b9dfe945c8f412de2db71d259ddef8ded63ace","observation_id":"28e09441-8d50-47ce-83ff-56867a4d9503","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Remark on the local nature of metric mean dimension","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:e545ab8f49fc6c520f63652a6a47a35af35745d1d9d8f06f7f8b5c546a3d7505","observation_id":"0bf95c99-925f-4034-a66a-0b20c6846f2f","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Bowen's equations for upper metric mean dimension with potential","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:8c7770d86dc0f986fa7a3a602bce6e9e8623bc3eea34a0f521db0d0d4cbeacdd","observation_id":"0f23a07b-cfe8-4e7e-9804-341d6497fc79","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.08330","last_updated":"2024-09-04T09:54:49Z","snapshot_observed_at":"2026-08-13T02:17:47.965375Z","submitted_at":"2023-05-15T03:44:27Z","title":"Upper metric mean dimensions with potential of $\\epsilon$-stable sets","version":5},"cited_work":{"arxiv_id":"2305.08330","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2305.08330","snapshot_observed_at":"2026-07-03T16:28:39.094848Z","title":"Upper metric mean dimensions with potential of \\( \\)-stable sets","venue":null,"work_id":"4037bbbc-4089-4c31-925a-e4790421b699","year":2024},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"cited_paper":"/paper/2305.08330","citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:ffd60bc32eeb1318ac2250d76d6acfd83733157d955d52dc68ffbc77e3a14803","observation_id":"8e37b537-3620-4ba5-a4d9-79e252486a9f","resolution":{"observed_at":"2026-07-03T16:28:39.096538Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Entropy points and applications","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:d41d04090358aa838f8938497c444c292976ba03173c2dd989fcd884931f5fbf","observation_id":"bcb3c77f-a815-478f-813e-d94af2d8c6e8","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T05:39:18.225910Z","title":"Bowen entropy for actions of amenable groups","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-06-27T05:39:18.225910Z"},"links":{"citing_paper":"/paper/2606.13270"},"observation_digest":"sha256:efde23ce89dc92797010a0f6b9576f0da31dbe75eb15a15533fcff2118b66683","observation_id":"cec0e36c-11e4-4194-9cf5-7201a2f66527","resolution":{"observed_at":"2026-06-27T05:39:18.225910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.13270","last_updated":"2026-06-11T12:24:54Z","latest_version":1,"primary_category":"math.DS","snapshot_observed_at":"2026-08-03T12:33:32.379289Z","submitted_at":"2026-06-11T12:24:54Z","title":"Metric mean dimension of amenable group actions: localization and non-uniformity"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":26,"verified_exact":1,"verified_fuzzy":0},"total_outbound_references":27},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:2606.13270."}