{"as_of":"2026-08-13T05:29:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c0e039e704591b0caa1043db243d5c0364584040ed0bc1f7b7580ff40354b759","coverage":[{"denominator":44,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":44,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T10:53:59.322360Z","state":"measured"},{"denominator":44,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":44,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.20135/citation-record","integrity":"/paper/2607.20135/integrity","json":"/paper/2607.20135/citation-record.json","paper":"/paper/2607.20135"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2510.01346","last_updated":"2025-10-10T20:12:14Z","snapshot_observed_at":"2026-08-12T00:45:27.441386Z","submitted_at":"2025-10-01T18:21:13Z","title":"Aristotle: IMO-level Automated Theorem Proving","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2510.01346","snapshot_observed_at":"2026-08-01T10:53:53.851072Z","title":null,"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":1,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:53.851072Z"},"links":{"cited_paper":"/paper/2510.01346","citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:23c2fd5eeef50ca71b5b51a7bd3e79a25e97495bb47530d46a63e2ed2076f494","observation_id":"bd241e8a-0de7-4137-aba9-0388e895eb29","resolution":{"observed_at":"2026-08-01T10:53:53.851072Z","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":"2026-08-01T10:53:53.994762Z","title":"Akhtiamov and A","venue":null,"work_id":null,"year":2022},"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":2,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:53.994762Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:670d7a4a8cebc7fce5a98f1a60a21825eca74aeefdfbcaf2e579440c7a3e5343","observation_id":"7fbfb90f-7a7a-4e7b-814c-2c993b6ae777","resolution":{"observed_at":"2026-08-01T10:53:53.994762Z","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":"2026-08-01T10:53:54.138012Z","title":"Bachner, A","venue":null,"work_id":null,"year":2026},"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":3,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:54.138012Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:f0136db315a295eec5a5a4e6546008de48d3eb2b1003819ea2e77daf1fec5d69","observation_id":"b42149ca-88e0-4f72-b677-22f3d50cc852","resolution":{"observed_at":"2026-08-01T10:53:54.138012Z","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":"2026-08-01T10:53:54.298965Z","title":"Barenboim and M","venue":null,"work_id":null,"year":2013},"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":4,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:54.298965Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:4673a786b66814e5f021430c72bf182e19d3ceed737a5d17f8b5404be30d1a60","observation_id":"e90ff2f5-9173-4dd4-8f4a-f10e6ccf1caf","resolution":{"observed_at":"2026-08-01T10:53:54.298965Z","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":"2026-08-01T10:53:54.505803Z","title":"Becker and A","venue":null,"work_id":null,"year":2020},"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":5,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:54.505803Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:0ad2ab1d65e70be05744df0821b7f2ec297d1df1586e53ff418beb3a18818174","observation_id":"b5181119-9da1-4bea-ae01-199c0b12fb5b","resolution":{"observed_at":"2026-08-01T10:53:54.505803Z","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":"2026-08-01T10:53:54.587116Z","title":"Becker, A","venue":null,"work_id":null,"year":2019},"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":6,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:54.587116Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:1ee13bce4b35e25f634b529c15dbb4245c2df9e6c06265fe5906dbf63d55c05a","observation_id":"4b85d1da-9ea8-47d5-a506-8e90677e2c20","resolution":{"observed_at":"2026-08-01T10:53:54.587116Z","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":"2026-08-01T10:53:54.779578Z","title":"Becker and J","venue":null,"work_id":null,"year":2021},"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":7,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:54.779578Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:af1b01ca5fa0942bbdaa8aa83b4857203b18190a70e1a897e815b547671091b2","observation_id":"8ce81bcb-fcfb-47b5-b9c3-81df118ca30c","resolution":{"observed_at":"2026-08-01T10:53:54.779578Z","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":"2026-08-01T10:53:54.896937Z","title":"Bekka and P","venue":null,"work_id":null,"year":2020},"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":8,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:54.896937Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:1081f5c950f7362e976136b8066a4b31e5ea72f0ed4ae5d96f07f17520d8e358","observation_id":"80331d0a-af67-4957-8c74-e64d85512599","resolution":{"observed_at":"2026-08-01T10:53:54.896937Z","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":"2026-08-01T10:53:55.009875Z","title":"Bernshteyn,Descriptive combinatorics and distributed algorithms, Notices of the American Mathematical Society69(2022), no","venue":null,"work_id":null,"year":2022},"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":9,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:55.009875Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:d9664f5b7b83e53ba68cd1c6574a5a28f020ab1224bccd5b5ce144e78688abde","observation_id":"9fb7fe44-53dd-448b-9889-8a1a485bcf38","resolution":{"observed_at":"2026-08-01T10:53:55.009875Z","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":"2026-08-01T10:53:55.213716Z","title":"Math.233 (2023), no","venue":null,"work_id":null,"year":2023},"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":10,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:55.213716Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:efc1c36de18a6eed413f142ed5618f33ded37d1709618f7aa16b2ef1115fc05e","observation_id":"c963bedf-10d8-4e5c-8393-6ecfeba0612f","resolution":{"observed_at":"2026-08-01T10:53:55.213716Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2604.14903","last_updated":"2026-04-16T11:47:18Z","snapshot_observed_at":"2026-08-06T12:10:57.364729Z","submitted_at":"2026-04-16T11:47:18Z","title":"Groups with arbitrarily poor permutation stability","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.14903","snapshot_observed_at":"2026-08-01T10:53:55.352850Z","title":"Bradford,Groups with arbitrarily poor permutation stability, arXiv preprint arXiv:2604.14903 (2026)","venue":null,"work_id":null,"year":2026},"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":11,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:55.352850Z"},"links":{"cited_paper":"/paper/2604.14903","citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:cb998fb88d2b2f02b820b8753acba7015362da03e356efed75c84d9b12389cac","observation_id":"ce107d76-68b0-47cc-a965-74574aaf4cdf","resolution":{"observed_at":"2026-08-01T10:53:55.352850Z","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":"2026-08-01T10:53:55.423237Z","title":null,"venue":null,"work_id":null,"year":2017},"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":12,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:55.423237Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:4030d947de01b843b70d619fcf492adefff6483d91753de20c09a2323a172d2a","observation_id":"047f3991-635a-4cce-8dfc-0b014e8dc386","resolution":{"observed_at":"2026-08-01T10:53:55.423237Z","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":"2026-08-01T10:53:55.500675Z","title":null,"venue":null,"work_id":null,"year":2026},"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":13,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:55.500675Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:0e6055f40338280addadf77294e66074a2266e4dd8020cb381f46bb975ab0bc0","observation_id":"942bb7a5-6092-43c0-9cae-8baa439acc4c","resolution":{"observed_at":"2026-08-01T10:53:55.500675Z","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":"2026-08-01T10:53:55.564035Z","title":"De Chiffre, L","venue":null,"work_id":null,"year":2020},"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":14,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:55.564035Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:82eca1f79ecf566f222562c050516fb9cc7bb20e65c6c363ec736aefe1669214","observation_id":"656db0fc-6b5e-4467-87a7-4007ad86512c","resolution":{"observed_at":"2026-08-01T10:53:55.564035Z","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":"2026-08-01T10:53:55.618845Z","title":"De Chiffre, N","venue":null,"work_id":null,"year":2019},"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":15,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:55.618845Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:8b78de38dcd0e26426e4e9fbf3dadacf50a446b8d3cb0e0178427a9328a4066e","observation_id":"17284a14-f49c-4e07-ad48-b3ca47467313","resolution":{"observed_at":"2026-08-01T10:53:55.618845Z","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":"2026-08-01T10:53:55.679300Z","title":"de la Salle,Spectral gap and stability for groups and non-local games, arXiv preprint arXiv:2204.07084 (2022)","venue":null,"work_id":null,"year":2022},"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":16,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:55.679300Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:13a4441b336e32e4cca9b964ed365ccb4727edea0b6a597243222aceb755da35","observation_id":"3d8e635b-d95d-4db1-a016-c929fdadc7ce","resolution":{"observed_at":"2026-08-01T10:53:55.679300Z","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":"2026-08-01T10:53:55.735118Z","title":"Dogon,Stability and approximation of groups and operator algebras, 2021, M.Sc","venue":null,"work_id":null,"year":2021},"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":17,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:55.735118Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:0dead62f3a3e65aab85111a16df6fb1333d8fb15c42f2fc1d9a0c44b6b7077ed","observation_id":"2fde1ee0-eb86-452c-bbb5-6481040af499","resolution":{"observed_at":"2026-08-01T10:53:55.735118Z","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":"2026-08-01T10:53:55.893313Z","title":"Z.305(2023), no","venue":null,"work_id":null,"year":2023},"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":18,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:55.893313Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:3f909c65d7c4412f32a0adea5af1e4f708e37f5330e2cdb39d1c63c34185ab0d","observation_id":"ace1e110-7d94-482d-ba44-825013a8b9e3","resolution":{"observed_at":"2026-08-01T10:53:55.893313Z","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":"2026-08-01T10:53:56.045843Z","title":"Dogon and T","venue":null,"work_id":null,"year":2026},"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":19,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:56.045843Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:3365cdc1f40668979dd894364b15123c2f55c7a5c0359e7475390bbbcf0cdc8c","observation_id":"a9cdc3b3-c3fd-4994-abb0-b48140f49fc4","resolution":{"observed_at":"2026-08-01T10:53:56.045843Z","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":"2026-08-01T10:53:56.211584Z","title":null,"venue":null,"work_id":null,"year":2026},"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":20,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:56.211584Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:bd1ff6fd4f9f4e5777d6e6ac4fdcd1078b80504181c065b26ba30e5e7e5131c4","observation_id":"78c7e8db-67b9-44e1-94a1-4245c5d6fe4f","resolution":{"observed_at":"2026-08-01T10:53:56.211584Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.11608","last_updated":"2025-07-10T13:54:40Z","snapshot_observed_at":"2026-08-12T23:21:13.028232Z","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":"2026-08-01T10:53:56.307886Z","title":null,"venue":null,"work_id":null,"year":2024},"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":21,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:56.307886Z"},"links":{"cited_paper":"/paper/2407.11608","citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:ca02f593134d7e6b91461839f9f50d3020e8d3751ab0a9ab6021442954ea52fd","observation_id":"4b91fe20-047d-4221-869a-49f3db210eb7","resolution":{"observed_at":"2026-08-01T10:53:56.307886Z","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":"2026-08-01T10:53:56.495174Z","title":"Eckhardt and T","venue":null,"work_id":null,"year":2023},"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":22,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:56.495174Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:a06b69c0c82b68139366162d6ac375cdd468c29caa47cc2ecbf273214768ef97","observation_id":"50351a6e-8d6e-4716-879a-eb119bd6078e","resolution":{"observed_at":"2026-08-01T10:53:56.495174Z","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":"2026-08-01T10:53:56.630525Z","title":null,"venue":null,"work_id":null,"year":1995},"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":23,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:56.630525Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:115890b814900cc8f20dc1a598681529e289279fca6aded0c9ca97aa24af3a3b","observation_id":"3aa346bd-3a54-4c12-b823-edacaa1638eb","resolution":{"observed_at":"2026-08-01T10:53:56.630525Z","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":"2026-08-01T10:53:56.761753Z","title":"Gao and S","venue":null,"work_id":null,"year":2015},"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":24,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:56.761753Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:86ff0b8c7121ae770a1fd5e28c4dc95052fd18401f5d8853d2712e6134ea101e","observation_id":"03c7ef5f-4c31-45df-bf97-be5e599e15b3","resolution":{"observed_at":"2026-08-01T10:53:56.761753Z","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":"2026-08-01T10:53:56.927476Z","title":null,"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":25,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:56.927476Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:2e993d47f1f05e29e221e7d2f24ab97d112875ea1954203f7ef999ef719122b6","observation_id":"4aa9f05f-7c92-4fac-8c91-36a4a5a31c10","resolution":{"observed_at":"2026-08-01T10:53:56.927476Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1002.3082","last_updated":"2010-02-16T13:32:01Z","snapshot_observed_at":"2026-08-05T21:16:22.003968Z","submitted_at":"2010-02-16T13:32:01Z","title":"Almost commuting matrices with respect to normalized Hilbert-Schmidt norm","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1002.3082","snapshot_observed_at":"2026-08-01T10:53:57.057001Z","title":"Glebsky,Almost commuting matrices with respect to normalized hilbert-schmidt norm, arXiv preprint arXiv:1002.3082 (2010)","venue":null,"work_id":null,"year":2010},"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":26,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:57.057001Z"},"links":{"cited_paper":"/paper/1002.3082","citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:afbe02930ea6bae70b3fd6de3d2de36bf106696f6e114943aeaae69daba106fd","observation_id":"633794f2-c8b3-43dd-a02c-a17076ec4e83","resolution":{"observed_at":"2026-08-01T10:53:57.057001Z","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":"2026-08-01T10:53:57.151594Z","title":null,"venue":null,"work_id":null,"year":2017},"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":27,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:57.151594Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:1786ae292b5480df5aed0351a3aeede36013930f38a6f7c2aef171c28942b8e7","observation_id":"0974d842-eb80-44fe-8287-11a96486da0f","resolution":{"observed_at":"2026-08-01T10:53:57.151594Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.15347","last_updated":"2025-02-21T10:01:36Z","snapshot_observed_at":"2026-08-07T17:59:11.641644Z","submitted_at":"2025-02-21T10:01:36Z","title":"From descriptive to distributed","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.15347","snapshot_observed_at":"2026-08-01T10:53:57.367142Z","title":"Grebík and Z","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":28,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:57.367142Z"},"links":{"cited_paper":"/paper/2502.15347","citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:c846a67319323f1e6e2085a550d13b52aee3a9591f48c69c26053c013dd8bf64","observation_id":"0fab2676-5b34-4241-8e71-f110e6523a2f","resolution":{"observed_at":"2026-08-01T10:53:57.367142Z","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":"2026-08-01T10:53:57.521562Z","title":"Hadwin and T","venue":null,"work_id":null,"year":2018},"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":29,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:57.521562Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:dc738e59b5352b87088cf21d5deccac4d7778b6e877eb44c4b1ebc3aebf889c7","observation_id":"c14ccab6-7774-42f5-bc91-925fd38df96f","resolution":{"observed_at":"2026-08-01T10:53:57.521562Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2009.12982","last_updated":"2020-09-27T23:45:58Z","snapshot_observed_at":"2026-08-08T23:12:06.197640Z","submitted_at":"2020-09-27T23:45:58Z","title":"Quantum soundness of the classical low individual degree test","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2009.12982","snapshot_observed_at":"2026-08-01T10:53:57.614426Z","title":null,"venue":null,"work_id":null,"year":2009},"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":30,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:57.614426Z"},"links":{"cited_paper":"/paper/2009.12982","citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:bfefed14a76d153545d543de0ad9dbec3c8c7279e01769528d465f4f90749592","observation_id":"1ba7c025-a146-42df-b237-7b97227c4bbd","resolution":{"observed_at":"2026-08-01T10:53:57.614426Z","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":"2026-08-01T10:53:57.767015Z","title":"11, 131–138","venue":null,"work_id":null,"year":2021},"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":31,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:57.767015Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:68707c79eebeaa73fee00f66e4ac31a30bcb14383da1f5fd31a8fe0c1fa8f409","observation_id":"3cf97b19-f145-488d-afbc-e7a26236a399","resolution":{"observed_at":"2026-08-01T10:53:57.767015Z","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":"2026-08-01T10:53:57.970091Z","title":"Lazarovich, A","venue":null,"work_id":null,"year":2024},"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":32,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:57.970091Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:db3327eef11b8f1d6536b398ae181146e4358f9d15da3f548d063be8c11c2498","observation_id":"125c03f8-951c-434e-8653-cfb4c3c93a6f","resolution":{"observed_at":"2026-08-01T10:53:57.970091Z","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":"2026-08-01T10:53:58.194477Z","title":"Levit and A","venue":null,"work_id":null,"year":2022},"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":33,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:58.194477Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:d3b45f4ce4d41bae7744d36b5994549025a12d7098e42f726e1ed15e306c03ec","observation_id":"1f0123ae-5066-403e-afdd-75d9ecc63280","resolution":{"observed_at":"2026-08-01T10:53:58.194477Z","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":"2026-08-01T10:53:58.385141Z","title":"Levit and I","venue":null,"work_id":null,"year":2023},"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":34,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:58.385141Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:0a03ab3283da67e91cb5a936879f7ef9f935b5b916529b0dc36b7fb9f24457c2","observation_id":"6ad6e1bd-5214-4b6c-8b45-010f65c4c903","resolution":{"observed_at":"2026-08-01T10:53:58.385141Z","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":"2026-08-01T10:53:58.625503Z","title":"Linial,Locality in distributed graph algorithms, SIAM Journal on Computing21(1992), no","venue":null,"work_id":null,"year":1992},"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":35,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:58.625503Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:0740e833d21965ec46e7aa8657ad3c767069105986ea84a5da1e02ad7ba3b9d5","observation_id":"9fa7ff77-c6ae-4380-8c81-630bfd0405a2","resolution":{"observed_at":"2026-08-01T10:53:58.625503Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.01757","last_updated":"2024-10-21T10:04:16Z","snapshot_observed_at":"2026-08-12T22:32:19.744487Z","submitted_at":"2024-10-02T17:12:22Z","title":"URP, comparison, mean dimension, and sharp shift embeddability","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.01757","snapshot_observed_at":"2026-08-01T10:53:58.800859Z","title":"Naryshkin,URP, comparison, mean dimension, and sharp shift embeddability, arXiv preprint arXiv:2410.01757 (2024)","venue":null,"work_id":null,"year":2024},"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":36,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:58.800859Z"},"links":{"cited_paper":"/paper/2410.01757","citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:9de2b5c3fe7a61dfcbd6d81611a85955151e1fd1e4c534abd4b40bf29ffb0160","observation_id":"e6e6bd10-d13c-4c14-b86b-7de58271405e","resolution":{"observed_at":"2026-08-01T10:53:58.800859Z","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":"2026-08-01T10:53:58.924363Z","title":null,"venue":null,"work_id":null,"year":null},"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":37,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:58.924363Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:a15b7179a394ce10ee91dbdc1cee470c336af7ecdb3c6e0cad178343c8ccafb1","observation_id":"8dd4169a-270a-49ae-b9b9-a6e1738f1b65","resolution":{"observed_at":"2026-08-01T10:53:58.924363Z","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":"2026-08-01T10:53:58.958277Z","title":null,"venue":null,"work_id":null,"year":1961},"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":38,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:58.958277Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:562cc14e766dc30c536507003c8696862cd6c6159b7a613471c61227655ac3ee","observation_id":"da350a99-cc5e-424e-b184-82b7dce19973","resolution":{"observed_at":"2026-08-01T10:53:58.958277Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1308.5853","last_updated":"2013-10-19T21:36:04Z","snapshot_observed_at":"2026-08-10T23:12:50.075800Z","submitted_at":"2013-08-27T13:00:58Z","title":"Locally Nilpotent Groups and Hyperfinite Equivalence Relations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1308.5853","snapshot_observed_at":"2026-08-01T10:53:59.016697Z","title":null,"venue":null,"work_id":null,"year":2013},"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":39,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:59.016697Z"},"links":{"cited_paper":"/paper/1308.5853","citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:4d923c50874493e83f0a1a8289c176a8c86411eb46705ac5fc0096fcf1e47893","observation_id":"3372f0b8-3740-43bb-bb00-ccfd4dfa5956","resolution":{"observed_at":"2026-08-01T10:53:59.016697Z","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":"2026-08-01T10:53:59.072855Z","title":null,"venue":null,"work_id":null,"year":1960},"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":40,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:59.072855Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:4a17b20bc98690a1d4c1fc88f922ea7a6cfe99312b823d3ac4971244e31dfada","observation_id":"ba3639c5-4167-498e-8c51-26c41ee23023","resolution":{"observed_at":"2026-08-01T10:53:59.072855Z","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":"2026-08-01T10:53:59.141402Z","title":null,"venue":null,"work_id":null,"year":2022},"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":41,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:59.141402Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:6d74d90fc1a82058e500dfaac9809db1e770e2adc8d526708fd245c95d22bad5","observation_id":"2a7d5e1e-8c27-4d9a-abd4-44c0291a36b2","resolution":{"observed_at":"2026-08-01T10:53:59.141402Z","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":"2026-08-01T10:53:59.207205Z","title":"4996–5025, EMS Press, Berlin, Germany, 2023","venue":null,"work_id":null,"year":2023},"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":42,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:59.207205Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:3b89bf16b93eece7fd0894f9aa8b30756f2816c2114332ca5fd663d5aab6a8d7","observation_id":"2ea9e34e-67cf-48a2-ac1a-8a51f2e1dcc4","resolution":{"observed_at":"2026-08-01T10:53:59.207205Z","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":"2026-08-01T10:53:59.259183Z","title":"von Neumann,Beweis des Ergodensatzes und des H-Theorems in der neuen Mechanik, Z","venue":null,"work_id":null,"year":1929},"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":43,"source":"pdf_text","source_observed_at":"2026-08-01T10:53:59.259183Z"},"links":{"citing_paper":"/paper/2607.20135"},"observation_digest":"sha256:b60787c335afb8c9d509710bcb46a6b7335409fbb233f5851c86efe4db520f47","observation_id":"140a8649-73dc-4f15-ba3a-dd781fda6480","resolution":{"observed_at":"2026-08-01T10:53:59.259183Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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"}}],"paper":{"arxiv_id":"2607.20135","last_updated":"2026-07-22T13:39:10Z","latest_version":1,"primary_category":"math.GR","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"},"reference_resolution":{"displayed":44,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":44,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":44},"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 13 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2607.20135."}