{"as_of":"2026-08-14T20:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e6eb7199212e6befbe5d2804af73c596bb3fe83402c943876251088dceb79365","coverage":[{"denominator":43,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":43,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T05:21:49.264644Z","state":"measured"},{"denominator":43,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":43,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/1909.01633/citation-record","integrity":"/paper/1909.01633/integrity","json":"/paper/1909.01633/citation-record.json","paper":"/paper/1909.01633"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:21:49.838539Z","title":"Ab \\'e rt and D","venue":null,"work_id":"17509a89-9908-4ef4-95a0-5012a43d36fc","year":2020},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.114618Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:427e67a9942922c10ffd19a8278e1436018d3a24750f353ceaa0e9ef0cfee197","observation_id":"6e27f7fb-fd67-487b-bb20-d8477dea1755","resolution":{"observed_at":"2026-08-14T05:21:49.842228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.825758Z","title":null,"venue":null,"work_id":"d8f2a9c4-4fe6-48d1-afbc-ea877489c04b","year":1974},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.118885Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:e09b5edddae581ddc90b8f8e604d9f24d09eac20e4565f105178fbb835aa6c49","observation_id":"2d24c2c5-c83c-4c4b-8fac-ab6c5262d115","resolution":{"observed_at":"2026-08-14T05:21:49.830063Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.812346Z","title":"Bartholdi","venue":null,"work_id":"87e15b93-3932-48dc-854b-e69d4ae02282","year":2016},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.123004Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:901659cda4b63d018083f46aaf88ea3c69413607c5ec20549d27066ef4cf4c1a","observation_id":"5340b51e-d69f-4a72-b87e-15dd3de7cae2","resolution":{"observed_at":"2026-08-14T05:21:49.816323Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.795048Z","title":"Baumslag","venue":null,"work_id":"0fd9451e-24b9-4641-bba1-111fa5f14b15","year":1963},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.127032Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:21e4d51bb9ea6db3be08e57911eed546e679c8e84c8f018095e1756eaec397bd","observation_id":"f21dd8df-ae59-4aa6-87c2-36103486caf5","resolution":{"observed_at":"2026-08-14T05:21:49.801850Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.775939Z","title":"Besson, M","venue":null,"work_id":"b1470281-c7b6-45da-85ce-6029b6eb6d86","year":2010},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.130550Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:362a4ef5e7bd19524cfaa1aad7ad0aa2ca60ce02ea90e83d7035d0d1b158377a","observation_id":"2a8ba84e-35c5-43d9-b3e0-d569d32b2f80","resolution":{"observed_at":"2026-08-14T05:21:49.779071Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.764978Z","title":"Bestvina, K.-U","venue":null,"work_id":"45201640-bf07-4638-a2ca-b4ef5da52bd9","year":2007},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.134105Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:dffc9fff9ff407f778ef32ad01d0b651c1605a782fe10dfb61d089ea043e35f2","observation_id":"6d0540be-a23b-470d-a0ff-9eff87890021","resolution":{"observed_at":"2026-08-14T05:21:49.768172Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.754678Z","title":"Bartholdi and D","venue":null,"work_id":"929ca27e-c446-42ac-b9aa-d414448b911e","year":2020},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.138245Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:80a922f1e01e1f74c7c1ac9b4b2f18303eacbcb9a54e39d2d193728321a4f369","observation_id":"25584bef-f08e-4e0d-ac8b-a820899a6850","resolution":{"observed_at":"2026-08-14T05:21:49.758058Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.743389Z","title":"Bestvina, M","venue":null,"work_id":"70d45ffe-3df4-4dc5-8577-5751e4b6bee7","year":2002},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.142004Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:a5ba825d8922df9612e83402ae3401f6a94870b9e450383ec2ce162710238227","observation_id":"90757056-e0ad-4ca6-bc9a-af580feee6e8","resolution":{"observed_at":"2026-08-14T05:21:49.747403Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.733688Z","title":null,"venue":null,"work_id":"5c37cd75-b9c5-41eb-a0ee-b98a06e9625f","year":1985},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.145519Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:1bd576b1fde71aa0831fb4407588d12865b15528e1d438167868cde5dd29c078","observation_id":"6e552948-56e3-4b9d-9438-57e75bffcb3b","resolution":{"observed_at":"2026-08-14T05:21:49.737079Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.723574Z","title":null,"venue":null,"work_id":"8679eb74-a5ae-4879-af6e-d185189e6e71","year":1982},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.148906Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:489d8c18af9861f0e4930ec66eb0265bd13622adb8da948d5db1d4bf75032ff3","observation_id":"5cd4d39b-1d25-4e54-9aff-92292f554a3f","resolution":{"observed_at":"2026-08-14T05:21:49.727138Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.712215Z","title":null,"venue":null,"work_id":"fb4139d0-256b-4cbe-b297-ac87bfd4ee7e","year":2006},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.152831Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:e9456c20b5e7a6a9f404614d7e2d78674d425c38265ee495220303910c355e6e","observation_id":"3cdc0715-fd3d-4107-bc4b-1bc7ead20f42","resolution":{"observed_at":"2026-08-14T05:21:49.715795Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.03543","last_updated":"2020-07-13T13:35:59Z","snapshot_observed_at":"2026-08-14T16:07:55.532553Z","submitted_at":"2019-07-08T12:11:13Z","title":"The Euler characteristic of $\\operatorname{Out}(F_n)$","version":2},"cited_work":{"arxiv_id":"1907.03543","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.03543","snapshot_observed_at":"2026-08-14T05:21:49.312647Z","title":"The Euler characteristic of $\\operatorname{Out}(F_n)$","venue":"math.GR","work_id":"37ff92a7-2cb1-4c77-b0ea-3a10939975cb","year":2019},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.157875Z"},"links":{"cited_paper":"/paper/1907.03543","citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:610f9d748240f37a2d5c459d75bbb27fa9d7bb8db66c18dbcb70c94e478177a6","observation_id":"c42a91fb-548a-46b2-8a20-d47f9474ff72","resolution":{"observed_at":"2026-08-14T05:21:49.317834Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.701788Z","title":"Cheeger and M","venue":null,"work_id":"9fef5b5b-1155-4613-a901-287ec6e6f77e","year":1986},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.161775Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:ea7202e3561763697f7723091b9aad59bc9616b7e463cf5112ad7749c8f38b9f","observation_id":"b4d9683f-cbfc-4a42-90a2-b8e52b82a3c9","resolution":{"observed_at":"2026-08-14T05:21:49.705676Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.690158Z","title":null,"venue":null,"work_id":"83f9ce5d-0f5a-4a30-8c5d-d053703a5697","year":null},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.165315Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:afd580fb45754a2e9f723630813e8cfe3a1aba54e7023e93bb5187caa5cd50a5","observation_id":"84885732-40ab-49a5-8071-0aa8b882dd0c","resolution":{"observed_at":"2026-08-14T05:21:49.694145Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.679317Z","title":null,"venue":null,"work_id":"b748f1df-9a03-488f-8838-d56ea0fb47d3","year":1978},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.168983Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:82a185629339e94ad1be1fc6e41ebca10f2e0e3bcc22efe0bd5705a889282f94","observation_id":"347e052b-f1ee-4ab7-9de2-aea2a291f6dd","resolution":{"observed_at":"2026-08-14T05:21:49.683074Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.669482Z","title":"Culler and K","venue":null,"work_id":"8b1e65b4-052f-4ee1-8516-001df62d2220","year":1986},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.172227Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:34f7f642b8f2d73bbed338205de732c08c19cd84211e04e6c20480affb4354ee","observation_id":"9a0040b7-5f2c-48ce-a5ff-c19857c0c4d8","resolution":{"observed_at":"2026-08-14T05:21:49.673181Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.659294Z","title":null,"venue":null,"work_id":"d1ffbd71-7859-4200-b31d-4d97c7f3932a","year":1969},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.175835Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:c8da4728bf87c760afca0acf7fb49b9bb5e39c75efba2f65364d66570e81789b","observation_id":"5b5b29fb-2b5c-43b8-95e9-a3db7d616b1c","resolution":{"observed_at":"2026-08-14T05:21:49.662201Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.650617Z","title":null,"venue":null,"work_id":"e901cc95-3a01-491d-ad0c-ddf7d55f8f81","year":1979},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.180041Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:58f499dafefcec5affc9c2f84f0b303fdbf2c715545100df388e0a5a77b28b6f","observation_id":"2f2ebc1c-1cbb-4c75-ac33-26fe0185969b","resolution":{"observed_at":"2026-08-14T05:21:49.653696Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.640850Z","title":null,"venue":null,"work_id":"11bd6d1c-e904-4958-b01d-71d3d6040bf6","year":2000},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.183763Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:f119e25abde68a83e7f3666152a3edbf9416dece9504a81089c6ece208da6320","observation_id":"652923d8-6331-4784-8b65-400d8b05f19a","resolution":{"observed_at":"2026-08-14T05:21:49.644324Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.630334Z","title":"Eilenberg and T","venue":null,"work_id":"c692cdbb-e04b-4b42-9df3-87200749b1f5","year":1957},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.187136Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:a481c02799f56f3cecedeafc21e6c5fff7c5bc559f72850a4b78a6bfb530b5c7","observation_id":"8e5a9802-ddc2-40e0-adf0-2b2476bb526f","resolution":{"observed_at":"2026-08-14T05:21:49.633895Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.620406Z","title":"Gaboriau","venue":null,"work_id":"8286c762-7240-4da8-a4d7-8892d3b03083","year":2002},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.190761Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:0387097044a2586b5c4d86091bb79fdf31e8af180314fa7d2f6094d2a8134979","observation_id":"3b12770b-12f6-4031-a4dd-6d45f793dd1a","resolution":{"observed_at":"2026-08-14T05:21:49.623964Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.610983Z","title":"Gaboriau","venue":null,"work_id":"a3e872ff-639e-4d4f-80fa-02addeb59647","year":2020},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.193863Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:70547a1f377461ac155eaa00387749bb48058109accbbe45d5c2f76b2dc7a657","observation_id":"ae907654-01a7-49df-9231-bd8825b855c6","resolution":{"observed_at":"2026-08-14T05:21:49.614235Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.600789Z","title":"Gaboriau and R","venue":null,"work_id":"2039aa03-c3a4-4910-a8e2-6fa63203eab8","year":2009},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.196719Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:3c12baaf92d312c4751010609fde6dac65b02a629eba26cbc56612b00f3e9422","observation_id":"d58ffeb7-7303-49f1-8694-d87fe668e9fa","resolution":{"observed_at":"2026-08-14T05:21:49.604734Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.489438Z","title":null,"venue":null,"work_id":"dbff4780-084d-458c-9e52-60e96637576b","year":1974},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.199781Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:941857062533c2666c2b0975b997fa31a28e8b8e7ae8f78191819bfe4f1417be","observation_id":"847ab0ec-410b-4a3c-90b8-892d3f8ad559","resolution":{"observed_at":"2026-08-14T05:21:49.493097Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.480379Z","title":null,"venue":null,"work_id":"76b18e64-3a99-45a5-9db7-4225b4ac1a08","year":1995},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.202748Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:459540f117f9e13d1edc3ff6be96a1bd734462f0d6eb8f2e9a0634809caec6d2","observation_id":"639de0f2-f4a9-47bb-bef3-2083b6cd1851","resolution":{"observed_at":"2026-08-14T05:21:49.483594Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.471026Z","title":"Kammeyer","venue":null,"work_id":"9730460f-bff5-4c5f-a977-5b9aeeddb292","year":2019},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.205770Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:63e2661781834dfc2b1364cb519165db8e93d4d4a60d1e780b67d8a749f84468","observation_id":"15e7e8fb-7713-4eac-a21e-cf3ac04c7d63","resolution":{"observed_at":"2026-08-14T05:21:49.474482Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.461078Z","title":null,"venue":null,"work_id":"34b7ce0b-820a-499a-a07e-675a49b971ec","year":2008},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.209189Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:e108b200e6139307af9e02919619b55038b39c7121fd4032aeb2c79e3d7cb5bb","observation_id":"f1b64276-70d4-427a-89ec-b037fa2ca6a1","resolution":{"observed_at":"2026-08-14T05:21:49.464410Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.452397Z","title":"Kleiner and J","venue":null,"work_id":"f683c012-ac78-4294-acc7-e6f5771d43f9","year":2008},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.212710Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:5ccfeaa43a6996efc25ef99f4d6b97f613048986a5a2de760b7949a9f442cc0c","observation_id":"e827b2f6-7059-4b92-b41f-f0a075f0dabe","resolution":{"observed_at":"2026-08-14T05:21:49.455272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.444353Z","title":null,"venue":null,"work_id":"25d599bd-ade6-4c61-9bf9-ddc33217634e","year":1929},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.216603Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:734b77b8eff9f27aba669fedb270ada602dfae510917d4a65cef5dffb1d49ee5","observation_id":"ed89d310-b093-4528-a49f-dfffbd2377a7","resolution":{"observed_at":"2026-08-14T05:21:49.447098Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.436054Z","title":"Lott and W","venue":null,"work_id":"2145462e-aef1-4e4b-9449-a87e93f72ce9","year":1995},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.220011Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:daf76aac4cc12401a4894f5eee7c3e8cc7a56a0cd0325e181beaa5c5c509b4de","observation_id":"60fcada9-6b90-4f0d-8760-e56b723f9707","resolution":{"observed_at":"2026-08-14T05:21:49.439058Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.426950Z","title":"L \\\"u ck","venue":null,"work_id":"2c94f3e5-654c-4b6c-bf85-e71ceeb026a8","year":1994},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.223278Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:93b2cd420d961331b7b66223d23abcf66db1bf9a70d1d1a8e50e1d8a59056672","observation_id":"0e27cf12-c278-4ef7-aa9b-d86bc7eaf863","resolution":{"observed_at":"2026-08-14T05:21:49.430189Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.417414Z","title":"L \\\"u ck","venue":null,"work_id":"53f9663f-87a4-465f-8d45-e5e89615266c","year":1998},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.226626Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:125028e267ce923ce674b9ab1c6d6367fcf90534cd21cceebb91df9a66ddf1e1","observation_id":"09ae66fe-b6f2-4cdd-8596-a8597ba04b24","resolution":{"observed_at":"2026-08-14T05:21:49.420914Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.408198Z","title":"L \\\"u ck","venue":null,"work_id":"6bb2ee10-3b57-49e5-a795-eabb9330d072","year":2002},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.229987Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:1a46e9c71be75e640cedd8b7c519c6b41daf21dbfd6922707e417581f9705a8a","observation_id":"e6c08f56-9471-40e1-a8be-edb424b8f788","resolution":{"observed_at":"2026-08-14T05:21:49.411571Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.398156Z","title":null,"venue":null,"work_id":"985fc950-20ee-44bc-a265-0bb73cde9171","year":1935},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.233174Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:6bcc7ea77767e8bb36124e6047fea9f0b03e074c1686bd80d8c3ab007ffdec7a","observation_id":"99e503a1-b22a-4cea-aa6c-3b7bd3aef175","resolution":{"observed_at":"2026-08-14T05:21:49.401810Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.388046Z","title":null,"venue":null,"work_id":"e4db61ed-0258-4a56-8b1d-8d81801e46d0","year":1962},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.236447Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:0a8b1544a8d7c3a9daac4c0572aedded0d217e9e4658e97c205b14695608580d","observation_id":"33164700-d598-454b-92cf-08afe25b558d","resolution":{"observed_at":"2026-08-14T05:21:49.391633Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.377066Z","title":null,"venue":null,"work_id":"9ee8579e-6614-4652-b7d8-71b31bfbcae6","year":1924},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.240063Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:334053f29e7f715c382b74068932856111e3b8be013c1bf607838d7d3182b753","observation_id":"378521a2-adb7-4d03-9791-598a1e6c6485","resolution":{"observed_at":"2026-08-14T05:21:49.380481Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.365950Z","title":null,"venue":null,"work_id":"a498792f-ba26-4b62-9116-e9d7b4793161","year":2008},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.243484Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:072b33a2fdfb2f0063b166b2d3a65ce7686542941cb9c117d551ad8eca503e3b","observation_id":"7c8f1c9c-23fe-447b-9347-cca805398d38","resolution":{"observed_at":"2026-08-14T05:21:49.370160Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.355464Z","title":"Ornstein and B","venue":null,"work_id":"ef40c268-1ea5-4783-a96b-3b89c0753751","year":1980},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.246744Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:d92aca0d49c30cef5f9c2fa2eedaa43d3c2c0ab81a129b6d88e375160c2cc25a","observation_id":"8f3e598e-a300-4c14-8b7c-187ed3fd96d2","resolution":{"observed_at":"2026-08-14T05:21:49.358903Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/0211159","last_updated":"2002-11-11T16:11:49Z","snapshot_observed_at":"2026-07-07T05:32:21.443158Z","submitted_at":"2002-11-11T16:11:49Z","title":"The entropy formula for the Ricci flow and its geometric applications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0211159","snapshot_observed_at":"2026-08-14T05:21:49.249986Z","title":"Perelman","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.249986Z"},"links":{"cited_paper":"/paper/math/0211159","citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:987ca87e4645efddc51e76df6d1956e3f129ac2f3cd45d277a8f810b6b2b91d7","observation_id":"5263739c-6e0e-472f-a1fa-3f0f0d3aeda7","resolution":{"observed_at":"2026-08-14T05:21:49.249986Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0303109","last_updated":"2003-03-10T16:44:35Z","snapshot_observed_at":"2026-07-07T05:34:01.844436Z","submitted_at":"2003-03-10T16:44:35Z","title":"Ricci flow with surgery on three-manifolds","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0303109","snapshot_observed_at":"2026-08-14T05:21:49.253828Z","title":"Perelman","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.253828Z"},"links":{"cited_paper":"/paper/math/0303109","citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:4c495eed4c9621ccf0a478227eddb0d8e29a140d50a57fbb1a5d66ad40633027","observation_id":"9e77a133-7259-420b-872e-5e5e91ef48e5","resolution":{"observed_at":"2026-08-14T05:21:49.253828Z","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":"2026-08-14T05:21:49.345523Z","title":null,"venue":null,"work_id":"8dc6ee6d-f5b1-4293-956b-5816f525abc0","year":1977},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.257423Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:3451876ef40450c5e9f5c961d941bfba61785c1b91472833ad248cd072d85653","observation_id":"53a1a144-6835-49be-a113-e98f736d185a","resolution":{"observed_at":"2026-08-14T05:21:49.348822Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.334469Z","title":"Sauer and A","venue":null,"work_id":"827f0f58-0fce-46c9-833c-4b70c7b026be","year":2010},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.261022Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:bed2bdd6bba777aaaedb7da38a7308581b95fcf4162c318d60eb74f3d506bd41","observation_id":"b369b985-5497-4820-a20c-07e9ec1da4e1","resolution":{"observed_at":"2026-08-14T05:21:49.337967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T05:21:49.324765Z","title":"Vogtmann","venue":null,"work_id":"f768dd68-dc19-47eb-8449-b541caa0a5af","year":2006},"citing_paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers","version":4},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-14T05:21:49.264644Z"},"links":{"citing_paper":"/paper/1909.01633"},"observation_digest":"sha256:8b29cd634eddb49813c8da46275106ecb458704d2acb0d5cebf12d64913f6481","observation_id":"698fe440-47ac-4333-a30e-d1aa4f4ffe51","resolution":{"observed_at":"2026-08-14T05:21:49.327945Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1909.01633","last_updated":"2022-06-27T06:49:52Z","latest_version":4,"primary_category":"math.GR","snapshot_observed_at":"2026-08-14T16:46:36.895391Z","submitted_at":"2019-09-04T09:05:32Z","title":"On the top-dimensional $\\ell^2$-Betti numbers"},"reference_resolution":{"displayed":43,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":1,"verified_fuzzy":22},"total_outbound_references":43},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:1909.01633."}