{"as_of":"2026-08-22T11:40:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6b344877d87ce95e58adc3427b1c8cb00479b7e3eb026322863f3d66591b8b78","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T11:20:13.513191Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T19:06:06.462660Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.19955","snapshot_observed_at":"2026-08-01T05:22:31.571241Z","title":"Damele and G","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.22795","last_updated":"2026-07-24T13:54:02Z","snapshot_observed_at":"2026-08-07T16:33:54.621931Z","submitted_at":"2026-07-24T13:54:02Z","title":"A Counterexample to Byott's Conjecture for Finite Skew Braces","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T05:22:31.571241Z"},"links":{"cited_paper":"/paper/2607.19955","citing_paper":"/paper/2607.22795"},"observation_digest":"sha256:18f0d3ae1ab4980db3087e4b15ee1dbc1ec300d1cc978a70bde3f1afa35266fc","observation_id":"7ed383c9-ee61-4d57-b5a4-d99f78746c7a","resolution":{"observed_at":"2026-08-01T05:22:31.571241Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.19955","snapshot_observed_at":"2026-08-04T19:06:06.462660Z","title":"Damele and G","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.01884","last_updated":"2026-08-03T08:25:33Z","snapshot_observed_at":"2026-08-07T11:47:57.045201Z","submitted_at":"2026-08-03T08:25:33Z","title":"Powerful multiplicative groups do not force right nilpotence in finite braces","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T19:06:06.462660Z"},"links":{"cited_paper":"/paper/2607.19955","citing_paper":"/paper/2608.01884"},"observation_digest":"sha256:192f367ca4399f5f4d57b017aaf812b3cc9bd81be65ba7b3b88a34dd1b06048e","observation_id":"4e2d0e59-3fef-4e3f-9e95-68c677692bbd","resolution":{"observed_at":"2026-08-04T19:06:06.462660Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2607.19955/citation-record","integrity":"/paper/2607.19955/integrity","json":"/paper/2607.19955/citation-record.json","paper":"/paper/2607.19955"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T11:20:10.438640Z","title":"Amberg, O","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:10.438640Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:fd8c9ea9514d18ad32b82d2509b252bcb2024339a51e8e6835b7061672cc7c74","observation_id":"eba649ac-7319-4d50-8d2e-034c55026a35","resolution":{"observed_at":"2026-08-01T11:20:10.438640Z","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":"2026-08-01T11:20:10.504084Z","title":"Bachiller, Extensions, matched products, and simple braces,J","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:10.504084Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:d6a505b6d60ebc50f8992a9de1c721c50ec8fc5cd2f676ccd229487b049b1eb8","observation_id":"282d13fa-e5b0-4c84-92ce-dc5400d65d7a","resolution":{"observed_at":"2026-08-01T11:20:10.504084Z","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":"2026-08-01T11:20:10.594861Z","title":"Bachiller, F","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:10.594861Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:0e718831f19796c4c9c23334683664d04ae248ff85588f1ec67f3ec613d4b923","observation_id":"9ae3de09-5465-4f23-8092-1756bf7fa85c","resolution":{"observed_at":"2026-08-01T11:20:10.594861Z","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":"2026-08-01T11:20:10.709489Z","title":"Ballester-Bolinches, R","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:10.709489Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:90dc4de0474f56108ccea029a7c8a595e5358a1106e167e839a9109fc33a1bb5","observation_id":"6bb09922-cb18-4237-b36e-9dbeb10ad1ee","resolution":{"observed_at":"2026-08-01T11:20:10.709489Z","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":"2026-08-01T11:20:10.887579Z","title":"Ballester-Bolinches, R","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:10.887579Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:d6789fd800251c25fec35fa414769f44dabcf94cc6169cfa3540e5fe6da2b50d","observation_id":"2241ef57-2e06-4bb1-9146-07c5b699f9d1","resolution":{"observed_at":"2026-08-01T11:20:10.887579Z","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":"2026-08-01T11:20:11.001419Z","title":"Burnside, On groups of orderpαqβ,Proc","venue":null,"work_id":null,"year":1904},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:11.001419Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:fcefb6e1a6ba9c08998e3f32037c4c3df61d449d9dbbb4c43d657060876766d1","observation_id":"e6cd151d-8a48-4d49-82e2-53288e02f73e","resolution":{"observed_at":"2026-08-01T11:20:11.001419Z","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":"2026-08-01T11:20:11.115224Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:11.115224Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:16163502ff32f2b95bd91fa647ddb02cece2746aead250c220510f3c11c0aa35","observation_id":"9c6edeff-4ac2-4ce9-b07e-e04aca79a07b","resolution":{"observed_at":"2026-08-01T11:20:11.115224Z","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":"2026-08-01T11:20:11.256805Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:11.256805Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:e9da603b68c85c6134343db4aeca22db6de0d8133755d07db6b25c601a19f5cf","observation_id":"db3dea75-0fec-4980-977c-4f03195dfcd3","resolution":{"observed_at":"2026-08-01T11:20:11.256805Z","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":"2026-08-01T11:20:11.431957Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:11.431957Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:cef253cd29e513e7fbc1bc5d9d0bdb33707613a67625617ff04440aca0d6c3c2","observation_id":"366820e6-fd5f-4bd3-9611-f75472b01fbb","resolution":{"observed_at":"2026-08-01T11:20:11.431957Z","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":"2026-08-01T11:20:11.595917Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:11.595917Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:21ed209ae9251491999e6445ada0637dea8708db6f60f8dd0ce70ac44eadcd11","observation_id":"bb0617ac-3d8d-4a1e-b567-ebb3f7a4957c","resolution":{"observed_at":"2026-08-01T11:20:11.595917Z","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":"2026-08-01T11:20:11.704390Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:11.704390Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:c85c07964044532b627c8a0c047490e1d1e77b5df910eb6628585393fc78cf90","observation_id":"be3beac1-8530-4884-94ae-fc16ea1d4256","resolution":{"observed_at":"2026-08-01T11:20:11.704390Z","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":"2026-08-01T11:20:11.818750Z","title":"Cedó and L","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:11.818750Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:49487787d9a2292ef6594b7418e35b5b8872161ea97fe7fcdf6f1f42485b76c1","observation_id":"88c77c4d-0818-4273-bc95-410d152ef705","resolution":{"observed_at":"2026-08-01T11:20:11.818750Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.24287","last_updated":"2026-06-23T08:08:29Z","snapshot_observed_at":"2026-08-06T02:39:49.970658Z","submitted_at":"2026-06-23T08:08:29Z","title":"On Simply Connected Simple Lie Skew Braces with Nilpotent Multiplicative Group","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.24287","snapshot_observed_at":"2026-08-01T11:20:11.910494Z","title":"Damele and A","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:11.910494Z"},"links":{"cited_paper":"/paper/2606.24287","citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:d6528740d4fa5839d37f18ab8d20e483f84f7e66457ae5fa34813af08f60dbab","observation_id":"34bcc762-7bae-4267-8df8-8def9f95afd0","resolution":{"observed_at":"2026-08-01T11:20:11.910494Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2605.22302","last_updated":"2026-05-21T10:48:35Z","snapshot_observed_at":"2026-08-16T03:04:08.974210Z","submitted_at":"2026-05-21T10:48:35Z","title":"On finite perfect two-sided skew braces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.22302","snapshot_observed_at":"2026-08-01T11:20:12.022397Z","title":"Damele, On finite perfect two-sided skew braces, Preprint, arXiv:2605.22302, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:12.022397Z"},"links":{"cited_paper":"/paper/2605.22302","citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:428860d36d69a17b540b097589f7b0beac75ab9a2a75046ccff250bd69e96b93","observation_id":"a32c8e01-3f27-4ac4-84cc-0d5c288f15ac","resolution":{"observed_at":"2026-08-01T11:20:12.022397Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2607.17125","last_updated":"2026-07-21T09:36:31Z","snapshot_observed_at":"2026-08-14T19:06:17.864206Z","submitted_at":"2026-07-19T08:24:06Z","title":"Simple Skew Braces with Cyclic Sylow Subgroups","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.17125","snapshot_observed_at":"2026-08-01T11:20:12.173672Z","title":"Damele, Simple skew braces with cyclic Sylow subgroups, Preprint, arXiv:2607.17125 [math.GR], 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:12.173672Z"},"links":{"cited_paper":"/paper/2607.17125","citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:7391f2e1afbf9148038e409b20b4f2297096ed8031bd8df788ca9797891d1e6c","observation_id":"91b70c96-9938-4350-b229-73dff8a5ee99","resolution":{"observed_at":"2026-08-01T11:20:12.173672Z","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":"2026-08-01T11:20:12.282340Z","title":"Damele, Finite skew braces whose additive group is aZ-group,Arch","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:12.282340Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:2cedeabd50f081ab965d20f405d7d89edb69ba5bee52afa6c3ab393611b402ff","observation_id":"c794d41d-31f4-4f7f-8c7c-cfd6c3883bde","resolution":{"observed_at":"2026-08-01T11:20:12.282340Z","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":"2026-08-01T11:20:12.385009Z","title":"Feit and J","venue":null,"work_id":null,"year":1963},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:12.385009Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:0585a1079aff2db89034a67638dbbe775bc736a0a73190aef22a12f3101315b5","observation_id":"17056de3-75f5-49fc-885d-5f1ecea93629","resolution":{"observed_at":"2026-08-01T11:20:12.385009Z","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":"2026-08-01T11:20:12.504774Z","title":"Guarnieri and L","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:12.504774Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:8e3ff3f8b5b6094404dd3e5516d1b16bfe554cfb2fe473735e84b9f95184af8c","observation_id":"2f4c685e-0ad9-4809-aea8-074888c8bb71","resolution":{"observed_at":"2026-08-01T11:20:12.504774Z","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":"2026-08-01T11:20:12.584114Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:12.584114Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:80689ec190c8470c3c2182bc3f58f3aaca9cc867c1b974149497f62c219a33b1","observation_id":"0f257cf2-07aa-4723-a6f8-159996cf0d6e","resolution":{"observed_at":"2026-08-01T11:20:12.584114Z","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":"2026-08-01T11:20:12.747373Z","title":"Nasybullov, Connections between properties of the additive and the multi- plicative groups of a two-sided skew brace,J","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:12.747373Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:9bea4ba5b56200bcaed3ed773b6c16387b61b2a879fbb5761e72d8fce7336d50","observation_id":"17eba1c8-34eb-4fe3-b5df-69747d67f5ee","resolution":{"observed_at":"2026-08-01T11:20:12.747373Z","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":"2026-08-01T11:20:12.910187Z","title":"Rump, Braces, radical rings, and the quantum Yang–Baxter equation,J","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:12.910187Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:a37749d6fc6ca2e455fd12c1ff6e6933c64632f32325a2efeb701df3bff7e512","observation_id":"d736ecfb-bf4c-4395-929b-e87684193104","resolution":{"observed_at":"2026-08-01T11:20:12.910187Z","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":"2026-08-01T11:20:13.074310Z","title":"Smoktunowicz and L","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:13.074310Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:dc42fad36aaa800342749dd0bfbe9ec3dbb27cabc3a6ef430a7a97d930923cdf","observation_id":"bf804dc0-a9ed-41d1-ac0c-1a26863c6f90","resolution":{"observed_at":"2026-08-01T11:20:13.074310Z","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":"2026-08-01T11:20:13.232703Z","title":"Trappeniers, On two-sided skew braces,J","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:13.232703Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:9fd520a31e561b013b328890c899eb973ab2af29d0d4c0a32100fd42c4760497","observation_id":"01ea0f2e-606b-4eed-b392-6532f6d773d5","resolution":{"observed_at":"2026-08-01T11:20:13.232703Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.18414","last_updated":"2026-06-30T10:19:55Z","snapshot_observed_at":"2026-08-17T13:42:20.754300Z","submitted_at":"2026-06-16T19:09:43Z","title":"Analogues of Sylow's first theorem, Cauchy's theorem, and Hall's theorem for skew braces","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.18414","snapshot_observed_at":"2026-08-01T11:20:13.367010Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:13.367010Z"},"links":{"cited_paper":"/paper/2606.18414","citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:6fb0fb9d0ff79e1c7cd6e31dc02240162e018b8e7284db6a6ab2e32a8afdaa61","observation_id":"e79d5b82-41d6-4f6d-aa4f-ce872337cf85","resolution":{"observed_at":"2026-08-01T11:20:13.367010Z","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":"2026-08-01T11:20:13.513191Z","title":"Tsang and C","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T11:20:13.513191Z"},"links":{"citing_paper":"/paper/2607.19955"},"observation_digest":"sha256:75b3ae6e81695203ec97d7b29dcf6a4b51a3efc2ced791dd3e41dd49d5721d0b","observation_id":"1ee2b7d5-84b2-4b10-bd7a-c935330425c8","resolution":{"observed_at":"2026-08-01T11:20:13.513191Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.19955","last_updated":"2026-07-22T09:30:15Z","latest_version":1,"primary_category":"math.GR","snapshot_observed_at":"2026-08-22T04:03:54.781440Z","submitted_at":"2026-07-22T09:30:15Z","title":"Ideals and Solvability in Skew Braces"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":25,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":25},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 2 inbound Pith citation observations for arXiv:2607.19955."}