{"as_of":"2026-08-12T18:46:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:90e504b1ed9eb1fcdc6e133893371af6081ae8f932d914444e296a07fccefb6f","coverage":[{"denominator":59,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":59,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T16:19:06.734507Z","state":"measured"},{"denominator":60,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":60,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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":"2026-08-01T10:53:59.322360Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.14113","snapshot_observed_at":"2026-08-01T10:53:59.322360Z","title":"Yaari,Density of finitely supported invariant measures for automorphisms of compact abelian groups, arXiv preprint arXiv:2507.14113 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20135","last_updated":"2026-07-22T13:39:10Z","snapshot_observed_at":"2026-08-08T23:12:20.702412Z","submitted_at":"2026-07-22T13:39:10Z","title":"Polynomial Hilbert-Schmidt stability of the lamplighter group","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:59.322360Z"},"links":{"cited_paper":"/paper/2507.14113","citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:03bf4a390d21016ad7d2935b0807cc83dcaaa5a44d84fdfb3be8a34661518df5","observation_id":"24d79f42-0758-4b99-aff8-3c65bd39d071","resolution":{"observed_at":"2026-08-01T10:53:59.322360Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.14113/citation-record","integrity":"/paper/2507.14113/integrity","json":"/paper/2507.14113/citation-record.json","paper":"/paper/2507.14113"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:19:22.866504Z","title":null,"venue":null,"work_id":"cdb25076-e5dd-4b3b-bdfe-be201325ecc4","year":2011},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:57.083029Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:a73915d16dbcee86f5c02025c224d565c1e0eb68b014327500f0abc256059d2e","observation_id":"89b9d1ae-7a0a-445b-8614-210ad91b22c5","resolution":{"observed_at":"2026-08-06T16:19:23.005348Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:22.529070Z","title":null,"venue":null,"work_id":"19573266-f9fb-4542-95ca-ea715114510f","year":1982},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:57.240083Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:ae126d3c1f6318bd85787f14a57298412fb803ae768f215cb5e0309baf99a60d","observation_id":"3510aaa7-c543-4e90-9213-3d76f6f9b0be","resolution":{"observed_at":"2026-08-06T16:19:22.739445Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:22.187641Z","title":null,"venue":null,"work_id":"58ce46b7-561f-46d1-8e7f-4b50be04bf18","year":1981},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:57.389172Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:8854af60804e8ec34be8f825c37ea96f99cab255da7d71c7832a59f74abeb997","observation_id":"b861ff39-3ff4-4f42-b3af-3df1b1dd64e3","resolution":{"observed_at":"2026-08-06T16:19:22.310712Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:21.910204Z","title":null,"venue":null,"work_id":"ea5dd56c-da80-45d6-b3a2-508d3b75aa9e","year":1984},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:57.522854Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:e686a9b5f6d0e79368a9d6a64b552b6b59000107a65e12ff1b4a968382424c7f","observation_id":"a70183dc-1041-4873-8ea6-32a3bcadf669","resolution":{"observed_at":"2026-08-06T16:19:22.022200Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:21.677036Z","title":null,"venue":null,"work_id":"ab2ac7f7-5312-4baf-9004-d7536c34e8ef","year":1971},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:57.639508Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:9f57def0286d8c7a799be240c5e571b1f3912e4c826575fe90689778063b233e","observation_id":"328f3103-8d23-46bc-b1ff-05ab4dcd301b","resolution":{"observed_at":"2026-08-06T16:19:21.771545Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:21.378180Z","title":null,"venue":null,"work_id":"015a6027-f2b3-4c7d-a84d-e0a681ef2812","year":2010},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:57.797913Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:f0a1f5d43ff4153d030b95620e56e2d08c7f2f9dbb527667ab3eb3a7cf229a93","observation_id":"d96940a0-5f8b-4961-bbb4-50859ec9e88e","resolution":{"observed_at":"2026-08-06T16:19:21.512221Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:21.133481Z","title":null,"venue":null,"work_id":"fad988a3-fe20-4eb6-ba91-59e0cb1991c1","year":1990},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:57.903750Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:3865c9453baf2476ef4abe4d44c17a76a376023531e9762ebaca91e91653808b","observation_id":"6ff45f8d-63b7-4f73-a834-1af4893a913a","resolution":{"observed_at":"2026-08-06T16:19:21.212283Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:20.820665Z","title":"D\\'iaz, Katrin Gelfert, and Bruno Santiago, Weak * and entropy approximation of nonhyperbolic measures: a geometrical approach , Math","venue":null,"work_id":"9ddd8c92-4d21-4841-a44d-767794b007b7","year":2020},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:58.013017Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:ce4dbef272dc9d207fce1b5ea1c03e314cac955de2ebf68ac6749172660b5588","observation_id":"0e1ddc71-fa75-401d-a408-6eb27ba22730","resolution":{"observed_at":"2026-08-06T16:19:20.942496Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:20.582865Z","title":"Systems 30 (2010), no","venue":null,"work_id":"4556ace9-2cec-43e2-af0b-bad0fd8282b8","year":2010},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:58.158316Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:6d6999842fd71521ddb33e5f6af82e22249f58c2e6bdeef3938b36d4282aa19b","observation_id":"edfaeeef-5735-49e9-850e-e77d5044dca9","resolution":{"observed_at":"2026-08-06T16:19:20.683248Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.11608","last_updated":"2025-07-10T13:54:40Z","snapshot_observed_at":"2026-07-06T18:47:04.659942Z","submitted_at":"2024-07-16T11:16:25Z","title":"Characters of diagonal products and Hilbert-Schmidt stability","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.11608","snapshot_observed_at":"2026-08-06T16:18:58.315548Z","title":"Dogon, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:58.315548Z"},"links":{"cited_paper":"/paper/2407.11608","citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:dfac3f5ab9b38d7b5e08ee97024ce60d7769adbb87ca76cbd94f6a301fc28c17","observation_id":"f26382d2-4753-4899-84d3-d610e907ff31","resolution":{"observed_at":"2026-08-06T16:18:58.315548Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.07791","last_updated":"2025-02-21T01:49:18Z","snapshot_observed_at":"2026-08-10T20:33:31.146220Z","submitted_at":"2025-01-14T02:19:21Z","title":"Residually finite amenable groups that are not Hilbert-Schmidt stable","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.07791","snapshot_observed_at":"2026-08-06T16:18:58.456312Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:58.456312Z"},"links":{"cited_paper":"/paper/2501.07791","citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:a59a32da1ef7c6dbe5b2b4b883988bbd6c68f1e4e6f71e2fb7f08ebb2ceeadd1","observation_id":"e4c90a5e-41a7-43e2-bec7-76c4d0716092","resolution":{"observed_at":"2026-08-06T16:18:58.456312Z","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":"2026-08-06T16:19:20.343419Z","title":"Systems 42 (2022), no","venue":null,"work_id":"9bc9139d-0a60-4915-847e-22ac1ce46be2","year":2022},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:58.584236Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:e0dfcd1d102f38eb8d6ee440b95f1422ff3937f041d98102bbe149154c63b64e","observation_id":"d10718ce-0e5b-4461-ad7b-929b9adbc8ce","resolution":{"observed_at":"2026-08-06T16:19:20.431668Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:20.061279Z","title":null,"venue":null,"work_id":"8ef9bc24-7f5b-4b3a-8bf7-40d69fd22e70","year":2023},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:58.743893Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:a4562432f8e2662131df9b199b83e6cdf97a747baf3e26dfeccfdc0659cdfb3f","observation_id":"b20ec2e4-ce8d-40b9-90fd-36e86d932d7e","resolution":{"observed_at":"2026-08-06T16:19:20.207436Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:18:58.896570Z","title":"259, Springer-Verlag London, Ltd., London, 2011","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:58.896570Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:5b481a2823686c2ea800a9a0f8b8b736a85c1f31474c9b5a756da46b2b82af40","observation_id":"d50604c2-3e57-4840-9da3-5c222408ee21","resolution":{"observed_at":"2026-08-06T16:18:58.896570Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:18:59.125303Z","title":"Pytheas Fogg, Substitutions in dynamics, arithmetics and combinatorics, Lecture Notes in Mathematics, vol","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:59.125303Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:5e80b928bf8e59480b74bdc78b75b63fcd576490798bd35ab980299ba9287768","observation_id":"bacde0ca-2f3f-4ff0-b06e-94db9e89073b","resolution":{"observed_at":"2026-08-06T16:18:59.125303Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:18:59.304759Z","title":"Systems Theory 1 (1967), 1--49","venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:59.304759Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:7191d165802fd61cd04a73d9d4ec872e7f7e1a8d1cf162b1eba039d43e1d8914","observation_id":"a709491c-a1e3-4219-9fbe-15ef11e2f5c1","resolution":{"observed_at":"2026-08-06T16:18:59.304759Z","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":"2026-08-06T16:19:19.730008Z","title":null,"venue":null,"work_id":"9ca905bb-88a0-4a8f-9697-7bd602f5690b","year":1990},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:59.520278Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:10e9491379d9e786ae39b08c7db593471d818ce0b71a6a9b6974d5d64770ae60","observation_id":"a748d467-13ad-4d19-92b8-e1a2511dac9f","resolution":{"observed_at":"2026-08-06T16:19:19.861079Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:19.496459Z","title":"Systems 38 (2018), no","venue":null,"work_id":"60ce9e9c-7c5f-4e3f-81f0-b61d7d2a4006","year":2018},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:59.655794Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:1502614a1e6b9d746140e74d5d5316f60e48864c00f49b40176cd0108b4ee2d1","observation_id":"cb05dea6-eeec-4c86-b1f4-321bdebfb689","resolution":{"observed_at":"2026-08-06T16:19:19.617136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:19.192769Z","title":null,"venue":null,"work_id":"f09619ad-837d-48a9-8e8c-befe786296fc","year":2010},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T16:18:59.859495Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:73dbae282ea2c62e5848bcd4e8407ad296ff9ece791e539923208f3941ef8c0a","observation_id":"09e49150-c4f0-4199-8775-f1066a54cb43","resolution":{"observed_at":"2026-08-06T16:19:19.381883Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0804.2234","last_updated":"2016-12-28T12:32:29Z","snapshot_observed_at":"2026-07-06T01:38:39.607460Z","submitted_at":"2008-04-14T18:31:21Z","title":"Lectures on Lie groups over local fields","version":5},"cited_work":{"arxiv_id":"0804.2234","doi":null,"metadata_source":"pith","pith_arxiv_id":"0804.2234","snapshot_observed_at":"2026-08-06T16:19:06.964387Z","title":"Lectures on Lie groups over local fields","venue":"math.GR","work_id":"77188fe8-bdbb-43e0-9f04-4421ce244f60","year":2008},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:00.050915Z"},"links":{"cited_paper":"/paper/0804.2234","citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:5883ac1b382955afb7f3b94e28366bd15f8026ab42de0be9631f1240d68f9c04","observation_id":"5bbb5d19-b8de-432b-abef-4fbe28185bd9","resolution":{"observed_at":"2026-08-06T16:19:07.104043Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:18.854536Z","title":null,"venue":null,"work_id":"22bc6a3e-45f6-4974-aecf-607e5355f5b7","year":1963},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:00.212895Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:432b547971a67f22e7c41d40175eb66298f85aadc5da50fb52695f0decd86318","observation_id":"c977c650-b96a-49cc-8cfa-1579e59e5619","resolution":{"observed_at":"2026-08-06T16:19:19.034896Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:18.599608Z","title":"Halmos, On automorphisms of compact groups, Bull","venue":null,"work_id":"b0a9c623-1d2a-4022-b964-23da2da246f1","year":1943},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:00.408487Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:8084000ceae49f0ad6cb7f834cdb4081955916da6d05d939aeb6999b566f5c79","observation_id":"6ba1ebfb-4a1f-40ad-b8ae-dea66e965422","resolution":{"observed_at":"2026-08-06T16:19:18.712329Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:18.371294Z","title":"Hall, Finiteness conditions for soluble groups, Proc","venue":null,"work_id":"b8a426bf-5814-415c-a7f3-e557998e3929","year":1954},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:00.566681Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:7d26787ca8b457711ce0f76d5895f75133aab53ad1fbe52b20cd90ca54e9a5ac","observation_id":"1a4aa17d-67cb-4202-a1bb-ebff83480ed1","resolution":{"observed_at":"2026-08-06T16:19:18.459144Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:18.090184Z","title":null,"venue":null,"work_id":"a5832e97-eba1-4b3f-8f1a-7aeba486cd83","year":1971},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:00.764327Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:224800b50a207932b165e87c63ed717c811da675ef42ab59b7e839af5b776e62","observation_id":"ff82f6cb-65bc-41fe-8e70-e2488d2c0bfd","resolution":{"observed_at":"2026-08-06T16:19:18.210721Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:17.808835Z","title":null,"venue":null,"work_id":"11b6dac6-54b8-4bfd-bd2f-57b6ab774162","year":2018},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:00.882496Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:92cb045d241208a1036f1c09f20f4ed8fd750556cc805025f07cee46f0319d1d","observation_id":"11d25948-5cfe-411f-9824-dd47a6ab2d41","resolution":{"observed_at":"2026-08-06T16:19:17.952913Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:17.468952Z","title":null,"venue":null,"work_id":"88bf0818-ef28-49cb-bceb-952d658d6ee4","year":2012},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:01.033894Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:9f7bf3afb24f234a4bab31ece5875337c105bfc232f69d34d46fbde40da8055f","observation_id":"98dc7481-d042-4efb-9405-72cadd0b02cc","resolution":{"observed_at":"2026-08-06T16:19:17.599452Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:17.229243Z","title":"30, American Mathematical Society, Providence, RI, 2003","venue":null,"work_id":"ee4fee8c-b6d7-4963-9334-db4e07b7af1e","year":2003},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:01.145552Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:636971137a52130eecc52bce36b7c45d99c750e4b0b4b2111cd0256ba7951f18","observation_id":"90cb2308-267b-4515-bb60-21cd60bd8ef4","resolution":{"observed_at":"2026-08-06T16:19:17.355080Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:16.946455Z","title":null,"venue":null,"work_id":"83c04193-922b-4443-9ad1-e82eb40fdfd2","year":2014},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:01.268004Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:a172c07e51b84c15c781b0d95b12bb1ede668fec3145c8f5c5c6dbe57ffa4a3b","observation_id":"02d83d91-a22e-4722-a371-f576793641aa","resolution":{"observed_at":"2026-08-06T16:19:17.115138Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:16.581480Z","title":"Math., vol","venue":null,"work_id":"fb2f4db3-2a4d-4bd8-b186-e6293f509ae3","year":2016},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:01.396297Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:99fa34a4a7f5dfc1e7d98ef06d61d18845c292b0757a9ca6a7ca7bb5bed190a6","observation_id":"fcf465e6-0c6e-4980-8b41-e55d82d20728","resolution":{"observed_at":"2026-08-06T16:19:16.747565Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:16.244591Z","title":"Systems 9 (1989), no","venue":null,"work_id":"1073dfb1-6eb9-4f23-a9cb-46144469d1b9","year":1989},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:01.513101Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:9f4a7f808ec22c83e23cc1ec481b80c9dbec17901cb294cda669fb563a6390a9","observation_id":"d8123e9c-9112-48d6-92bc-185efcccc6d2","resolution":{"observed_at":"2026-08-06T16:19:16.372775Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:15.873388Z","title":null,"venue":null,"work_id":"48afab7b-b471-4693-9205-f2286c61602d","year":1972},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:01.614900Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:879c4133a6a340ba70381a76206bbb36b01f8a879d0676ce63b2d84324520191","observation_id":"9d61c83c-c56f-4e41-94f4-6d895c046455","resolution":{"observed_at":"2026-08-06T16:19:16.059778Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:15.572195Z","title":null,"venue":null,"work_id":"a8105443-ffe6-4674-8236-1dc5fc36d2c8","year":1977},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:01.721869Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:34b1bd7f69cf052c4f30981c1afdde2c346d57dd35415a3274d0eaa3eba958f8","observation_id":"3f489c0d-972b-415f-9ec6-6b9bdf88a617","resolution":{"observed_at":"2026-08-06T16:19:15.706976Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:15.165664Z","title":null,"venue":null,"work_id":"65f20fe7-a425-44f6-b4b3-b03b41f3c5bd","year":1978},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:01.883746Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:56b5157a6c912f570a933839e08de6d8974bd73533a5599c5673af2b99191180","observation_id":"ce9a94b0-1736-49c5-8f8b-f533587c0902","resolution":{"observed_at":"2026-08-06T16:19:15.357383Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:14.777813Z","title":"C onf., M ath","venue":null,"work_id":"33c1112c-0739-471a-852b-ca889e8b5428","year":1978},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:01.999737Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:9b02c2fb19e3e4a41f5271760aa3563587047fd1d02d9d3702e25d2ac7854cba","observation_id":"0f989262-6baf-4a50-b187-86b1c3e6fa32","resolution":{"observed_at":"2026-08-06T16:19:14.998532Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:14.348113Z","title":"Systems 2 (1982), no","venue":null,"work_id":"131ef6af-c55b-4582-9987-ca86532ddf19","year":1982},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:02.136562Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:f4c9adb0ad5fb3fced86ebe72bcaac84b3f85b9f8a8f05cc405a775c1c9929a9","observation_id":"01d541b1-b2b2-43a9-a284-4b83f8584b79","resolution":{"observed_at":"2026-08-06T16:19:14.526450Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:13.934375Z","title":null,"venue":null,"work_id":"42d8d5eb-a20e-422d-ad61-cf119f3b4437","year":1982},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:02.372601Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:9caaa09ba97697458fefd121e80ceb2fc7b03af0fa5bf3fddef95a4eea1fd6b8","observation_id":"a513cc8e-71c7-4f9c-abb8-3065c92f6b49","resolution":{"observed_at":"2026-08-06T16:19:14.107349Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:13.536363Z","title":null,"venue":null,"work_id":"c23181f4-a2d0-458d-a9c1-9c498431e2ce","year":1971},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:02.506532Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:faa68c18b143d63e5d9ee7a3c505c1d0cf809a994a0615a2ea4485b936a1c14c","observation_id":"26860abd-ef5a-4099-b771-3d1c9c6cf22b","resolution":{"observed_at":"2026-08-06T16:19:13.713849Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:13.180388Z","title":null,"venue":null,"work_id":"8b0226b3-c988-4bd3-a1a4-c7393db7cc35","year":1972},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:02.661725Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:29c642dfa294f9244858d65b9f351536ac188671cf6f3baf7981beb5030f66a7","observation_id":"8e612f70-b15b-4844-b0a9-6f6f66edbaf7","resolution":{"observed_at":"2026-08-06T16:19:13.317554Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:12.841689Z","title":"Systems 42 (2022), no","venue":null,"work_id":"50ae9997-48fd-4bae-89d6-a4cb4ea330d6","year":2022},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:02.826307Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:763bc04253cf6fd60a8b7e632188f1f5785867b72004748bfd3ad7368193c1c7","observation_id":"f162fc7c-8400-4c99-8221-4c9539c51018","resolution":{"observed_at":"2026-08-06T16:19:12.996344Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:12.436243Z","title":"3, 388--393","venue":null,"work_id":"375bf8ce-6fd0-417d-9e98-0ca6032f59f8","year":1967},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:03.001025Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:8d8cee5abdeb2693a3763252add24e8adc921dc009cf821495ee93635d9975b6","observation_id":"5d453720-fe7c-47b3-907e-001c9a339aa3","resolution":{"observed_at":"2026-08-06T16:19:12.618436Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:11.991061Z","title":null,"venue":null,"work_id":"efaab338-f073-4fc5-8a02-40ee3f5a8aa8","year":2024},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:03.153054Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:8b7cd7abd8adef8deb29472b480fa2135a2a494193c26a19d9d6d12a3a40160a","observation_id":"9cd7029b-a69d-48e6-a771-885dfaf2d1e3","resolution":{"observed_at":"2026-08-06T16:19:12.201146Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:11.621717Z","title":null,"venue":null,"work_id":"a8b00dda-84c0-4eae-8dcd-5a78a5c89e7a","year":1988},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:03.371693Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:b90c85504e8429a126b52747c8123d0dac1057c0613e6e840726c0acad4b02b2","observation_id":"ad2e1dc3-cb38-47b1-ae85-359a871d9bfd","resolution":{"observed_at":"2026-08-06T16:19:11.808505Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:11.234181Z","title":null,"venue":null,"work_id":"3b58cf86-f213-4372-ba0e-1f0117ee1388","year":1980},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:03.512374Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:b94c6d7d3bb17fc38ca79ae4a76cfe82c0d4da365426be1c13d329cf08d05693","observation_id":"c4994f4e-205d-4f61-a5a1-cbdb5482c889","resolution":{"observed_at":"2026-08-06T16:19:11.368255Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:03.684726Z","title":null,"venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:03.684726Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:0fe5056cd29acfb84391aac72107ffc7b1f540ed1f1a56e0c0992ab02501578d","observation_id":"8185ccf5-6593-4306-b7bb-1776c8672a25","resolution":{"observed_at":"2026-08-06T16:19:03.684726Z","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":"2026-08-06T16:19:10.906397Z","title":"Miles and R","venue":null,"work_id":"a4dd69a0-49e9-4515-bb82-756e7090e72d","year":1978},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:03.836912Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:df2ac05cf86b703d47e0fc6c4e616dd4ac2683767f8f438e73d5e52ce9fa795e","observation_id":"b42b0d76-be43-482c-a515-fd18456c52ad","resolution":{"observed_at":"2026-08-06T16:19:11.043077Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:10.562527Z","title":null,"venue":null,"work_id":"3e364545-d400-496a-9b84-18847d87ff0d","year":1961},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:04.006649Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:7a0981494745cf39ea82313e3f52abc51580072e688e1f6b57f5467c8efa2354","observation_id":"b638b285-22d3-43e1-b723-c77b55cd5648","resolution":{"observed_at":"2026-08-06T16:19:10.716929Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:10.142153Z","title":"Pestov, Hyperlinear and sofic groups: a brief guide, Bull","venue":null,"work_id":"99a4bad4-e10f-4e0f-8af0-90ac20118960","year":2008},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:04.190690Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:ee43275ae3abf213c502f695f3bf3403d31978a771a64ff1ff3f2b2788a8ba36","observation_id":"5f0f3d5a-0325-4622-953c-78062e38abce","resolution":{"observed_at":"2026-08-06T16:19:10.325819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:09.878073Z","title":"Phelps, Lectures on C hoquet's theorem , second ed., Lecture Notes in Mathematics, vol","venue":null,"work_id":"3ed74247-f9d8-45a0-a15e-c4b7f13c31f4","year":2001},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:04.419086Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:7480d4d33a339329c76631a66b7345c95c3b54487d4122b661f820650da0b0c3","observation_id":"7430c3c2-aaaf-450e-86b1-9d215bb46b58","resolution":{"observed_at":"2026-08-06T16:19:10.002499Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:09.602631Z","title":"Pfister and W","venue":null,"work_id":"a49f32ba-fd3c-4894-a9af-08ff170d0d6f","year":2005},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:04.635667Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:b97ff9ef5c268856c4ba1f99cb37c8a47ef4dbffa2e2d997bf4be486b815bd1a","observation_id":"7cb7a809-3852-498c-b027-ee3263fc6a95","resolution":{"observed_at":"2026-08-06T16:19:09.756784Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:09.389782Z","title":"1294, Springer-Verlag, Berlin, 2010","venue":null,"work_id":"f201c39b-9160-413f-8592-e8df5516dd43","year":2010},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:04.826309Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:cb75925f396b64e31fd335fedae767c32f4dcd6d921d5f972bc1eef32ed89e95","observation_id":"fa616d2d-c192-4051-909c-6110ea34c59c","resolution":{"observed_at":"2026-08-06T16:19:09.472589Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:05.062468Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:05.062468Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:edb96a7386562b0d35414355a0fd0a8b3f4f4d22671a5e2e5c978cacc1d643ae","observation_id":"80bd08b4-fbb2-4a9f-862d-6fa6b3294646","resolution":{"observed_at":"2026-08-06T16:19:05.062468Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:19:05.275042Z","title":"auser Classics, Birkh\\","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:05.275042Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:c656e6b4868fd53c976a3f7eb6f13ebd05c2c5bfc7831b570f4840d710e2490d","observation_id":"bbe78b2e-5f66-431c-8d6e-1de714e75035","resolution":{"observed_at":"2026-08-06T16:19:05.275042Z","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":"2026-08-06T16:19:09.092479Z","title":null,"venue":null,"work_id":"b62a0b4d-7842-4080-946d-71638e64e64f","year":2002},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:05.502957Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:69a5f2f0a3be482e1432b499871cef065e9162b8e73396c20723f12e741cb1e4","observation_id":"cf141119-b4dd-4600-af8a-5dd0ee8e771e","resolution":{"observed_at":"2026-08-06T16:19:09.206562Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:08.790313Z","title":null,"venue":null,"work_id":"89a5ee32-9e22-483a-8f28-85fef4fd36f6","year":1996},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:05.706156Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:df6eb95a3a4b0908683b454d7db5ebebbf59fe56acb90fb1e4132821304a0d61","observation_id":"65747084-a773-4330-b5db-ef748f091660","resolution":{"observed_at":"2026-08-06T16:19:08.941566Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:08.407162Z","title":null,"venue":null,"work_id":"7ff7e852-38bb-4e3a-bbce-6d4fae9ba824","year":1970},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:05.940477Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:312bf7f9e2b2ff92fa9bfe6b54907d18fae0111f60aeb489f7e025de78b7bfc4","observation_id":"f5a0833b-52c3-4c15-86be-1d7992031cf4","resolution":{"observed_at":"2026-08-06T16:19:08.616960Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:08.114959Z","title":"Veech, Periodic points and invariant pseudomeasures for toral endomorphisms, Ergodic Theory Dynam","venue":null,"work_id":"2049df14-fe17-466c-b19f-7e0b46efc529","year":1986},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:06.193045Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:d51d22c88e21071c309ab340741cf7d21cdbe8577eba7e8aeaa0fe8cc1572c22","observation_id":"73b75718-5d0a-4139-8513-8ba2dd35914e","resolution":{"observed_at":"2026-08-06T16:19:08.230371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:06.345216Z","title":"79, Springer-Verlag, New York-Berlin, 1982","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:06.345216Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:b1e2283f4b8306b2f0f9ab69a2611a0a0c47fc2864794fe7c85fc0b4cb73818b","observation_id":"72218069-823b-4b25-ba45-9defe5c285aa","resolution":{"observed_at":"2026-08-06T16:19:06.345216Z","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":"2026-08-06T16:19:07.749730Z","title":"Band 144, Springer-Verlag, New York-Berlin, 1974","venue":null,"work_id":"af750ea9-2133-4dee-84bd-a324aec941bf","year":1974},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:06.519564Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:5dc5062e32a1a7adfe5a5490127966afdd98e70b191f6605ddf825658e4fab7c","observation_id":"29f1797c-bdfe-45fc-a5f0-046ff06623f3","resolution":{"observed_at":"2026-08-06T16:19:07.873965Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T16:19:07.378029Z","title":"7, 1942--1972","venue":null,"work_id":"df755507-a8d2-4a24-8d37-20692002b6f8","year":2016},"citing_paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-06T16:19:06.734507Z"},"links":{"citing_paper":"/paper/2507.14113"},"observation_digest":"sha256:516a6ea87e52209329d322424a62feda9725b848d4696ad348235aad7e082f1b","observation_id":"a6d30c03-5b7e-43f0-8490-b2815eeef8a0","resolution":{"observed_at":"2026-08-06T16:19:07.573938Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.14113","last_updated":"2025-07-18T17:44:36Z","latest_version":1,"primary_category":"math.DS","snapshot_observed_at":"2026-08-09T05:20:14.848721Z","submitted_at":"2025-07-18T17:44:36Z","title":"Density of finitely supported invariant measures for automorphisms of compact abelian groups"},"reference_resolution":{"displayed":59,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":37,"verified_exact":1,"verified_fuzzy":21},"total_outbound_references":59},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 1 inbound Pith citation observation for arXiv:2507.14113."}