{"as_of":"2026-08-15T16:49:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f526e48943cb7c5644edbe89762afd5711c082122d35d325fa05128282e3e9e6","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T12:49:50.179534Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-10T01:37:19.106477Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-11T13:31:01.854657Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"cited_work":{"arxiv_id":"1908.06796","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1908.06796","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"19e8a3e1-34f7-4a45-a085-cf31d3d40e3f","year":2025},"citing_paper":{"arxiv_id":"2604.19549","last_updated":"2026-04-21T15:06:40Z","snapshot_observed_at":"2026-08-08T12:44:49.970739Z","submitted_at":"2026-04-21T15:06:40Z","title":"Fuzzy Geometries with an Internal Space","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-10T01:37:19.106477Z"},"links":{"cited_paper":"/paper/1908.06796","citing_paper":"/paper/2604.19549"},"observation_digest":"sha256:916281df4a82b7657ad4bc9d54ef2bb20fc6cd5bf2e3f70de2366461a9db278d","observation_id":"0a2b9f74-3ad2-4135-a9e9-a91800476180","resolution":{"observed_at":"2026-05-11T13:31:01.865306Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1908.06796/citation-record","integrity":"/paper/1908.06796/integrity","json":"/paper/1908.06796/citation-record.json","paper":"/paper/1908.06796"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:49:50.100244Z","title":"Noncommutative geometry and reality,","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.100244Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:1173c0968fe503d5321c7703c393bbaaeceacde4d231cae77d146ec14e1475ed","observation_id":"e89e021e-cf55-4921-b6d0-ceb5d098b471","resolution":{"observed_at":"2026-08-14T12:49:50.100244Z","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":"2026-08-14T12:49:50.434672Z","title":"Noncommutative geometry,","venue":null,"work_id":"4c8a57a4-3175-48d6-be20-159446b0ab33","year":1994},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.104364Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:b2b2c6c0134da57977d8cefeb7128c1dc4af5fc9395da9d8041bc4325637a76b","observation_id":"a731e905-afee-4172-9921-5befbf426195","resolution":{"observed_at":"2026-08-14T12:49:50.437812Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9603053","last_updated":"1996-03-08T20:50:40Z","snapshot_observed_at":"2026-07-07T05:10:19.924629Z","submitted_at":"1996-03-08T20:50:40Z","title":"Gravity coupled with matter and foundation of non-commutative geometry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/9603053","snapshot_observed_at":"2026-08-14T12:49:50.107860Z","title":"Gravity coupled with matter and foundation of non- commutative geometry,","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.107860Z"},"links":{"cited_paper":"/paper/hep-th/9603053","citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:dfa524b65d90473bfad4241ac2e9132d2b0fd197db7648cd1a9634d4b11cb2fd","observation_id":"6de3bdb8-d3d3-4496-8cb9-a01ecfafbb01","resolution":{"observed_at":"2026-08-14T12:49:50.107860Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1502.05383","last_updated":"2015-07-28T16:48:03Z","snapshot_observed_at":"2026-08-15T11:03:04.289356Z","submitted_at":"2015-02-18T20:46:40Z","title":"Matrix geometries and fuzzy spaces as finite spectral triples","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1502.05383","snapshot_observed_at":"2026-08-14T12:49:50.111840Z","title":"Matrix geometries and fuzzy spaces as finite spectral triples,","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.111840Z"},"links":{"cited_paper":"/paper/1502.05383","citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:ee092458c8a8f096f5416744bde564d907ffd738a0463ddadc770a9d60f89013","observation_id":"15930161-f89d-4b39-9aac-476fe421e248","resolution":{"observed_at":"2026-08-14T12:49:50.111840Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0007131","last_updated":"2000-07-21T14:05:15Z","snapshot_observed_at":"2026-08-15T14:20:42.693561Z","submitted_at":"2000-07-21T14:05:15Z","title":"Dependence on the spin structure of the Dirac spectrum","version":1},"cited_work":{"arxiv_id":"math/0007131","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0007131","snapshot_observed_at":"2026-08-14T12:49:50.346307Z","title":"Dependence on the spin structure of the Dirac spectrum","venue":"math.DG","work_id":"8243a0e4-bdad-4ea2-b8d4-7cb28b6e656a","year":2000},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.115908Z"},"links":{"cited_paper":"/paper/math/0007131","citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:f57c379c6a878c05429d0d9778457007ce29d84e1fb7aa64a4c8b770213844f4","observation_id":"b623e87e-373c-4db5-88bd-e85143d87761","resolution":{"observed_at":"2026-08-14T12:49:50.349483Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9912130","last_updated":"1999-12-15T15:13:13Z","snapshot_observed_at":"2026-07-07T05:21:43.545091Z","submitted_at":"1999-12-15T15:13:13Z","title":"From Large N Matrices to the Noncommutative Torus","version":1},"cited_work":{"arxiv_id":"hep-th/9912130","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-th/9912130","snapshot_observed_at":"2026-08-14T12:49:50.332022Z","title":"From Large N Matrices to the Noncommutative Torus","venue":"hep-th","work_id":"4510620c-e695-43b5-81d6-64e3882cfe6a","year":1999},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.119774Z"},"links":{"cited_paper":"/paper/hep-th/9912130","citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:7381aed1d0c395c12be3e998687fc0ca47afd80761353def68833e0b68ffbbc3","observation_id":"71199ceb-afee-4661-8ca4-dac13407ec34","resolution":{"observed_at":"2026-08-14T12:49:50.336646Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1305.7479","last_updated":"2013-10-17T04:40:45Z","snapshot_observed_at":"2026-08-15T16:33:13.750133Z","submitted_at":"2013-05-31T16:26:15Z","title":"Generalized Fuzzy Torus and its Modular Properties","version":3},"cited_work":{"arxiv_id":"1305.7479","doi":null,"metadata_source":"pith","pith_arxiv_id":"1305.7479","snapshot_observed_at":"2026-08-14T12:49:50.318550Z","title":"Generalized Fuzzy Torus and its Modular Properties","venue":"hep-th","work_id":"24919032-c19e-410a-990a-bac8c9c65960","year":2013},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.123609Z"},"links":{"cited_paper":"/paper/1305.7479","citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:4aaa6bcca811bd5811fc37cc7dde8f4c3461d5c7323b811f1417101bedcf12f9","observation_id":"ef93cbc5-65b6-4f2d-bee3-00047dad24a0","resolution":{"observed_at":"2026-08-14T12:49:50.322179Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0103192","last_updated":"2001-04-12T11:04:21Z","snapshot_observed_at":"2026-07-07T04:39:30.623701Z","submitted_at":"2001-03-22T17:22:07Z","title":"Noncommutative Gauge Theories on Fuzzy Sphere and Fuzzy Torus from Matrix Model","version":2},"cited_work":{"arxiv_id":"hep-th/0103192","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-th/0103192","snapshot_observed_at":"2026-08-14T12:49:50.305435Z","title":"Noncommutative Gauge Theories on Fuzzy Sphere and Fuzzy Torus from Matrix Model","venue":"hep-th","work_id":"3bb16efc-8e65-485c-b760-5b9b9206fa9a","year":2001},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.127629Z"},"links":{"cited_paper":"/paper/hep-th/0103192","citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:69ccf68e4becbf779d5339b38f0eddb310a9ef55c88edbffc622c3be1b05e951","observation_id":"d2cd325c-39f9-4bb5-9192-a0bb45d2ae93","resolution":{"observed_at":"2026-08-14T12:49:50.309380Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1515/crll.1981.328.1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:49:50.244788Z","title":"Classification of C∗-algebras admitting ergodic actions of the two-dimensional torus","venue":null,"work_id":"80de6a66-05ab-471f-a97a-fc94c87386f3","year":1981},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.131838Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:75e7e3c8fa09b0bda70fea87b3198b0e61425b22dacd66ed60e114cdf8cac37e","observation_id":"13f04a22-acde-49c6-ade9-39b4f4eb974d","resolution":{"observed_at":"2026-08-14T12:49:50.249048Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/0605191","last_updated":"2006-05-08T09:12:43Z","snapshot_observed_at":"2026-07-07T05:57:00.712906Z","submitted_at":"2006-05-08T09:12:43Z","title":"On Spin Structures and Dirac Operators on the Noncommutative Torus","version":1},"cited_work":{"arxiv_id":"math/0605191","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0605191","snapshot_observed_at":"2026-08-14T12:49:50.290928Z","title":"On Spin Structures and Dirac Operators on the Noncommutative Torus","venue":"math.QA","work_id":"d25759d2-0be1-4887-9cc1-7dfd88a54d2a","year":2006},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.135082Z"},"links":{"cited_paper":"/paper/math/0605191","citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:43c2e5025db3288f95aa64f601e35bc2ea4379217c3d26f4480c5355fd446c09","observation_id":"f88bec2c-f463-4b0d-83ad-0096353bc91b","resolution":{"observed_at":"2026-08-14T12:49:50.295639Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1003.5156","last_updated":"2011-12-28T10:14:49Z","snapshot_observed_at":"2026-08-15T05:23:12.913850Z","submitted_at":"2010-03-26T15:11:26Z","title":"Classification of spin structures on the noncommutative n-torus","version":4},"cited_work":{"arxiv_id":"1003.5156","doi":null,"metadata_source":"pith","pith_arxiv_id":"1003.5156","snapshot_observed_at":"2026-08-14T12:49:50.277966Z","title":"Classification of spin structures on the noncommutative n-torus","venue":"math.OA","work_id":"77b83958-65b1-4abd-b9c7-f9e125b203ce","year":2010},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.138451Z"},"links":{"cited_paper":"/paper/1003.5156","citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:f4fcbc5a3ab1cc6b2fd0e81c3e953c055307bcae2ca3b809a7fdface73421919","observation_id":"b80f2368-58cf-4e38-b5fe-f3ead6cdd311","resolution":{"observed_at":"2026-08-14T12:49:50.281710Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1804.06803","last_updated":"2018-05-07T13:28:28Z","snapshot_observed_at":"2026-08-14T19:24:35.868222Z","submitted_at":"2018-04-18T16:28:16Z","title":"Spin geometry of the rational noncommutative torus","version":2},"cited_work":{"arxiv_id":"1804.06803","doi":null,"metadata_source":"pith","pith_arxiv_id":"1804.06803","snapshot_observed_at":"2026-08-14T12:49:50.264613Z","title":"Spin geometry of the rational noncommutative torus","venue":"math.QA","work_id":"67078207-8607-4264-9e67-9cecc4d242ff","year":2018},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.142117Z"},"links":{"cited_paper":"/paper/1804.06803","citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:b00a65031eae1335ab6f84536962547a43af81edb7c2418f38ef088207d5d0ca","observation_id":"57342a16-a01e-4a35-a046-d31639320675","resolution":{"observed_at":"2026-08-14T12:49:50.268072Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/owr/2018/32","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:49:50.233226Z","title":"Non-commutative spectral triples for space-time","venue":null,"work_id":"66a77270-ff10-4fd8-82b4-9a79f7037b76","year":2018},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.145482Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:5fee05bdca180a4abb898494dd43573a89632e0695aea1963fcfad1b885407ad","observation_id":"abff65a7-dd69-4c30-ab53-6732e7f5301e","resolution":{"observed_at":"2026-08-14T12:49:50.236942Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T12:49:50.424411Z","title":"Aspects of the noncommutative torus","venue":null,"work_id":"22e72f80-a5b5-4cbb-9cff-49d49309215d","year":2019},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.149352Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:867d1d1d0cb1a87bba2bb2152078b43385d69714688b6e4a8a4d9312990db87e","observation_id":"b573ca7a-fe6c-4973-9c05-e3e9dafdbb0e","resolution":{"observed_at":"2026-08-14T12:49:50.427931Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T12:49:50.413404Z","title":"The theory of groups and quantum mechanics,","venue":null,"work_id":"c0b0d2c2-a41d-4730-a2a6-4ba77bb5b1ff","year":1950},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.152513Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:aeb9dd7e6f2a775458812aa7f8566f843ea4797072ced132dd9e3927309fa039","observation_id":"68a9635b-130d-4ec3-b062-f4ec2c1b9b5d","resolution":{"observed_at":"2026-08-14T12:49:50.417634Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/s0002-9939-1965-0177064-5","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:49:50.221435Z","title":"Some remarks on symplectic automor- phisms,","venue":null,"work_id":"34119eb5-556f-41ba-9a42-9ecae71fc6da","year":1965},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.155872Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:0f56b93fe0c7a83792b002a9258c3d773743de28074b731ffc75d06693dabe25","observation_id":"68df4d91-517b-49a2-81d1-40b2dbe05e02","resolution":{"observed_at":"2026-08-14T12:49:50.226485Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:49:50.160040Z","title":"Holonomy and path structures in general relativ- ity and Yang-Mills theory,","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.160040Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:9859f55a66760faa2b482a5b3e62d80ccede36a44f665e4b5a33de7ed914c7aa","observation_id":"38371dfd-b69c-42d0-b658-4716632b064c","resolution":{"observed_at":"2026-08-14T12:49:50.160040Z","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":"2026-08-14T12:49:50.403828Z","title":"Algebraic topology,","venue":null,"work_id":"4a023311-47ca-4371-a045-ced1f24ec717","year":2002},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.164037Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:2ecd412732b2c7bc3d4115436925d7f1ec81a4e37d55ea0f041698e475247ed9","observation_id":"e5bc9cd1-02f7-4c4e-96d8-7b7b106168a4","resolution":{"observed_at":"2026-08-14T12:49:50.407256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T12:49:50.393569Z","title":"The topology of 4-manifolds,","venue":null,"work_id":"adb9f8c9-5efe-49ab-a917-b9b38a2b6b54","year":1989},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.167200Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:742c89a3b4c19fad4c90f4676f026ff49c8e8ef7c63de2841971d243158dead9","observation_id":"85b12b16-0eb6-40b4-854b-8d3db4fcb9f2","resolution":{"observed_at":"2026-08-14T12:49:50.396739Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:49:50.170349Z","title":"Elements of Non- commutative Geometry,","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.170349Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:f8c274ab2478254d5675d247c6ea1f2163c8c598598c159ad791d177f434b291","observation_id":"8aa0d519-af52-46c8-8d9c-1cd206dfe36b","resolution":{"observed_at":"2026-08-14T12:49:50.170349Z","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":"2026-08-14T12:49:50.382543Z","title":"Noncommutative tori: a case study of noncommutative dif- ferential manifolds,","venue":null,"work_id":"1592a310-c505-4fb5-983c-6f1fc5d6b3d8","year":1990},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.173391Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:d01e1347ec27f9c946123cf1abac2baa6359ca28c9a95f8d76bae5d6c3a151a6","observation_id":"aba7297e-d50c-4182-8dc6-b148eb2a667a","resolution":{"observed_at":"2026-08-14T12:49:50.386818Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T12:49:50.372943Z","title":"Spin Geometry,","venue":null,"work_id":"8c582b9f-0ff3-4be9-aea7-da34cef5f884","year":1990},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.176395Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:ee57a1314e366ee156794af06222ad8eafe4e8a35305b871671854cba3e875c6","observation_id":"c3c1a3b1-8a12-4533-80eb-992a94efe229","resolution":{"observed_at":"2026-08-14T12:49:50.376103Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:49:50.179534Z","title":"Reduction of symplectic manifolds with sym- metry","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T12:49:50.179534Z"},"links":{"citing_paper":"/paper/1908.06796"},"observation_digest":"sha256:273063b042494da3b21528c6f6a7fcad3565edb1674f2886beb7fb3deb70415b","observation_id":"ebd8c3e8-f5cf-41e7-8aa4-e4a4d0fc65c8","resolution":{"observed_at":"2026-08-14T12:49:50.179534Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"1908.06796","last_updated":"2024-10-30T15:38:49Z","latest_version":2,"primary_category":"math.QA","snapshot_observed_at":"2026-08-15T12:47:00.023289Z","submitted_at":"2019-08-19T13:36:20Z","title":"Finite spectral triples for the fuzzy torus"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":10,"verified_fuzzy":7},"total_outbound_references":23},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 1 inbound Pith citation observation for arXiv:1908.06796."}