{"as_of":"2026-08-22T02:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4092b9f78f5b7fa79839cfd1824eb3efa2d89b67d726573c1cf01d1d22109acd","coverage":[{"denominator":30,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":30,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T19:06:47.147410Z","state":"measured"},{"denominator":32,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":32,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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":"2026-08-01T11:20:12.173672Z","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":"2607.17125","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":"2026-08-13T18:39:35.524507Z","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":"sha256:5defa6e7984c9f9d690595b12c012fa8a7e38e7fcc0f12aedf4e0805f21b5f44","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":{"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":"2026-08-01T05:22:31.472131Z","title":"Damele,Simple skew braces with cyclic Sylow subgroups, arXiv:2607.17125(2026)","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":6,"source":"pdf_text","source_observed_at":"2026-08-01T05:22:31.472131Z"},"links":{"cited_paper":"/paper/2607.17125","citing_paper":"/paper/2607.22795"},"observation_digest":"sha256:3cb31cccfe9125494d4684ec53deae9b8544909c3d085f48974a95b8bfa58a5b","observation_id":"c62bd288-624f-4bd2-bb13-8b4491baaae2","resolution":{"observed_at":"2026-08-01T05:22:31.472131Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2607.17125/citation-record","integrity":"/paper/2607.17125/integrity","json":"/paper/2607.17125/citation-record.json","paper":"/paper/2607.17125"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T19:06:43.945519Z","title":"Bachiller, Extensions, matched products, and simple braces,J","venue":null,"work_id":null,"year":2018},"citing_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},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:43.945519Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:3faeef10e58d171cbdbba8ec33bc36455ef9f01bac8951a7bca2315576d1fe8c","observation_id":"bf21b0d2-93ff-4127-a91b-3b974a55a8ac","resolution":{"observed_at":"2026-08-01T19:06:43.945519Z","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":"2026-08-01T19:06:44.029094Z","title":"Bachiller, F","venue":null,"work_id":null,"year":2019},"citing_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},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:44.029094Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:b84f714027c9ba8443dc3cefa4b1c96adae2b8fc3179e8ff4e653989c80d7e9b","observation_id":"1e603746-f731-47d1-a3c9-d7db958c4d40","resolution":{"observed_at":"2026-08-01T19:06:44.029094Z","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":"2026-08-01T19:06:44.111426Z","title":"Ballester-Bolinches, R","venue":null,"work_id":null,"year":2025},"citing_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},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:44.111426Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:c5f90f4746df4155eed892c247508c59a1eb7923dd22cc71f06484b02000a858","observation_id":"5df37008-55ce-4269-8609-5e2c64135b5b","resolution":{"observed_at":"2026-08-01T19:06:44.111426Z","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":"2026-08-01T19:06:44.192908Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_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},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:44.192908Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:7d77b9f0cd80162fdefbc78d69054192edc63b1b17b96948f104a7c6d593aefa","observation_id":"d3e23886-52d7-4e37-be6c-ef2e6b0ff6cc","resolution":{"observed_at":"2026-08-01T19:06:44.192908Z","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":"2026-08-01T19:06:44.281855Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_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},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:44.281855Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:8df11d9cad15df4fa85d045193e75841e3300d9f32d0bb33a0c8855290805e37","observation_id":"20165c8a-20a7-4ed8-9d8d-618d898e1f4a","resolution":{"observed_at":"2026-08-01T19:06:44.281855Z","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":"2026-08-01T19:06:44.339189Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_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},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:44.339189Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:64d29def0669548e2bd86533efcef2eae46a0c4403bc623e8094c1356e29206a","observation_id":"8c5d6856-0d9d-4723-ba65-ef4ac0a829cd","resolution":{"observed_at":"2026-08-01T19:06:44.339189Z","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":"2026-08-01T19:06:44.393282Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_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},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:44.393282Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:03784fa838858cfddb9ab86ec20b8f4126ae4967c5c0a1301499bbe0d17e9059","observation_id":"3369f9ec-ac86-47d7-955f-b8282cafceb1","resolution":{"observed_at":"2026-08-01T19:06:44.393282Z","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":"2026-08-01T19:06:44.478774Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_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},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:44.478774Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:a0d70830a241f45e0ead3c83884977685b54d00e8d63dca834b810e5450cc890","observation_id":"6cddb2f3-e1cf-4e75-ab0e-314c79dcd3a3","resolution":{"observed_at":"2026-08-01T19:06:44.478774Z","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":"2026-08-01T19:06:44.539754Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_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},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:44.539754Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:db5a19373bbc49e1322f495ed0c8c09aaf999b2494cc9653cc739394df1e056a","observation_id":"a3336290-db4f-41aa-934b-d613799aff3f","resolution":{"observed_at":"2026-08-01T19:06:44.539754Z","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":"2026-08-01T19:06:44.607990Z","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":"2607.17125","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},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:44.607990Z"},"links":{"cited_paper":"/paper/2605.22302","citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:249f301c9a2f4808a56a5635eb25dd241293aa1e48cc09bdf01a5ec9415909fc","observation_id":"29417059-31c5-42da-92e5-e3c8a065cb2f","resolution":{"observed_at":"2026-08-01T19:06:44.607990Z","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":"2026-08-01T19:06:44.673934Z","title":"Damele and A","venue":null,"work_id":null,"year":2026},"citing_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},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:44.673934Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:0e8e149b93ed59ca21fe408ccc2d4caebf016300242e5a6d46a079c6c516cd79","observation_id":"77067df7-5999-488d-990e-c94e49ba54bb","resolution":{"observed_at":"2026-08-01T19:06:44.673934Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2605.07609","last_updated":"2026-05-18T10:09:02Z","snapshot_observed_at":"2026-08-15T10:48:49.338856Z","submitted_at":"2026-05-08T11:35:51Z","title":"Solvability and Rigidity for Topological Skew Braces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.07609","snapshot_observed_at":"2026-08-01T19:06:44.783858Z","title":"Damele and A","venue":null,"work_id":null,"year":2026},"citing_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},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:44.783858Z"},"links":{"cited_paper":"/paper/2605.07609","citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:1e0e881c1fb262cb204dbd9c85d41de01b76488976e33030bf2eaa1b2c19c0bc","observation_id":"33aeb935-353c-4df1-a68d-4169ba79129b","resolution":{"observed_at":"2026-08-01T19:06:44.783858Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.29295","last_updated":"2026-07-13T10:01:07Z","snapshot_observed_at":"2026-08-13T17:24:30.093346Z","submitted_at":"2026-06-28T09:35:28Z","title":"A Schur--Zassenhaus Theorem for Finite Skew Braces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.29295","snapshot_observed_at":"2026-08-01T19:06:44.952085Z","title":"Damele, A Schur–Zassenhaus theorem for finite skew braces, Preprint, arXiv:2606.29295, 2026","venue":null,"work_id":null,"year":2026},"citing_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},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:44.952085Z"},"links":{"cited_paper":"/paper/2606.29295","citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:7019a60f9625f67f7f2b3395410c90275954ed79d3aeaf7f90dded842f9fe35c","observation_id":"45757222-2c99-4bf1-bcac-1494f6f50c89","resolution":{"observed_at":"2026-08-01T19:06:44.952085Z","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":"2026-08-01T19:06:45.086204Z","title":"Damele, Finite skew braces whose additive group is aZ-group,Arch","venue":null,"work_id":null,"year":2026},"citing_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},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:45.086204Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:3a70bf06e0fb46fd36eb198f1576faedf6b967b436ed3a683cc860ad92eae3e0","observation_id":"94cc7db1-a68f-465e-9eea-f65fca27f775","resolution":{"observed_at":"2026-08-01T19:06:45.086204Z","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":"2026-08-01T19:06:45.210604Z","title":"Feit and J","venue":null,"work_id":null,"year":1963},"citing_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},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:45.210604Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:a76aa51722b084e415e72d0eb8be5abd912d7c4f386cb7244cc9bd3b8d85b8bf","observation_id":"3792d9a4-504f-4011-a412-30a7d3a57b94","resolution":{"observed_at":"2026-08-01T19:06:45.210604Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.30453","last_updated":"2026-07-01T11:08:48Z","snapshot_observed_at":"2026-08-17T00:50:04.291440Z","submitted_at":"2026-06-29T15:22:13Z","title":"The Schur--Zassenhaus Theorem and Sylow's Third Theorem for Finite Skew Braces","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.30453","snapshot_observed_at":"2026-08-01T19:06:45.330899Z","title":"Ferrara and M","venue":null,"work_id":null,"year":2026},"citing_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},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:45.330899Z"},"links":{"cited_paper":"/paper/2606.30453","citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:2a3c658ac9dba05b86c28a8440d104a96e3d77b8011e4ed621a40ef811c3a494","observation_id":"218035bc-65a6-4f7e-9940-988e2b0a153c","resolution":{"observed_at":"2026-08-01T19:06:45.330899Z","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":"2026-08-01T19:06:45.485414Z","title":"Gorshkov and T","venue":null,"work_id":null,"year":2021},"citing_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},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:45.485414Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:9a44f97e31441e742e153c6931770f06ac4b4f4894080869b2f443a95f6a2fd6","observation_id":"463efe68-bb82-41e7-a81f-3c8433728937","resolution":{"observed_at":"2026-08-01T19:06:45.485414Z","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":"2026-08-01T19:06:45.622720Z","title":"Guarnieri and L","venue":null,"work_id":null,"year":2017},"citing_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},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:45.622720Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:cebaf0b9d2b5497061ef0ab2cfdfec4b8cb36f2919d922eff230edd5e70e824c","observation_id":"48d028b8-d2b8-4eab-9838-5bdb85eb6360","resolution":{"observed_at":"2026-08-01T19:06:45.622720Z","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":"2026-08-01T19:06:45.780017Z","title":"Hall, Jr.,The Theory of Groups, The Macmillan Company, New York, 1959","venue":null,"work_id":null,"year":1959},"citing_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},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:45.780017Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:3e40ee13d1317b2c1707917b822ca84cc91c41c7653a67c985f7da7c588b53e1","observation_id":"07b3ef4f-d7f8-4215-a0a5-484feaf6cef3","resolution":{"observed_at":"2026-08-01T19:06:45.780017Z","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":"2026-08-01T19:06:45.908951Z","title":"Huppert,Endliche Gruppen I, Grundlehren der Mathematischen Wis- senschaften, vol","venue":null,"work_id":null,"year":1967},"citing_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},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:45.908951Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:ef9c4ce038db061122f0c3d111eb1bca2bc38bcd24c982605aed833d9b76995b","observation_id":"bdde51a9-c949-4d3b-9127-85d6d7571ae4","resolution":{"observed_at":"2026-08-01T19:06:45.908951Z","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":"2026-08-01T19:06:45.983298Z","title":"Kohl, Classification of the Hopf–Galois structures on prime power radical extensions,J","venue":null,"work_id":null,"year":1998},"citing_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},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:45.983298Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:ce6f21eb40892a6ec0bcd51280fec4b8a53929d16005029c6535400be88486c7","observation_id":"f8b2bdb8-c89f-4eb1-b9dc-71bcbefdb9ae","resolution":{"observed_at":"2026-08-01T19:06:45.983298Z","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":"2026-08-01T19:06:46.095957Z","title":"Konovalov, A","venue":null,"work_id":null,"year":2021},"citing_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},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:46.095957Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:ad263f9c3b3c7f14f81a5d24d71f117278967202c7cf9a84251c8d2d73761480","observation_id":"f969d2cd-6bff-417e-ae6f-d5055303fa78","resolution":{"observed_at":"2026-08-01T19:06:46.095957Z","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":"2026-08-01T19:06:46.242218Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_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},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:46.242218Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:45043b3196f44b4953a96589cff65ea2624f63f192919c8776577d86770ed8f3","observation_id":"cbc424de-2736-499b-891a-05beeaa34733","resolution":{"observed_at":"2026-08-01T19:06:46.242218Z","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":"2026-08-01T19:06:46.383416Z","title":"Rump, Braces, radical rings, and the quantum Yang–Baxter equation,J","venue":null,"work_id":null,"year":2007},"citing_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},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:46.383416Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:ed3c90432824e4995713011393649d4c71aaf87756bb68a669a0a0fdbed24337","observation_id":"b9bd8ae8-75b6-4b32-80eb-a4872ee4bd4e","resolution":{"observed_at":"2026-08-01T19:06:46.383416Z","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":"2026-08-01T19:06:46.526384Z","title":"Smoktunowicz and L","venue":null,"work_id":null,"year":2018},"citing_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},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:46.526384Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:5cbcb73d6227d234a4cf2dbf84e6d9cca3c84085dad34281903810c3b639638a","observation_id":"a0978f42-5ba3-4be7-853f-8d504395b14d","resolution":{"observed_at":"2026-08-01T19:06:46.526384Z","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":"2026-08-01T19:06:46.670571Z","title":"Trappeniers, On two-sided skew braces,J","venue":null,"work_id":null,"year":2023},"citing_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},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:46.670571Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:366e2ea89e44b492443faf89411be5ccfdff4de2ff55dd3749f1379ec9ee8cc6","observation_id":"83f0fc1c-0a1e-4727-be6b-2ecbfaec814e","resolution":{"observed_at":"2026-08-01T19:06:46.670571Z","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":"2026-08-01T19:06:46.782175Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_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},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:46.782175Z"},"links":{"cited_paper":"/paper/2606.18414","citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:fd3f95d231a39652a19919e9ee00c2a1318f3f8f9e42be3d1a0e43a60f61adb3","observation_id":"4d632035-3277-4f98-905c-e0d07096231e","resolution":{"observed_at":"2026-08-01T19:06:46.782175Z","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":"2026-08-01T19:06:46.922740Z","title":"Tsang, Non-abelian simple groups which occur as the type of a Hopf–Galois structure on a solvable extension,Bull","venue":null,"work_id":null,"year":2023},"citing_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},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:46.922740Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:d4f302cc9ffc7ce6b6c42e1535d7fe588da0040a2c1581fa9074f7309b347026","observation_id":"b9f55eeb-dd63-4e67-8e47-867fd82d4813","resolution":{"observed_at":"2026-08-01T19:06:46.922740Z","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":"2026-08-01T19:06:47.067623Z","title":"Tsang and C","venue":null,"work_id":null,"year":2020},"citing_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},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:47.067623Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:5c9b9b8c46c62c7e035964a7eaeaca4b0371e0cf7d02040b7b6a6faf05a4b0e6","observation_id":"ef4be01e-94c0-4c48-b4f7-caa02cc5a0a4","resolution":{"observed_at":"2026-08-01T19:06:47.067623Z","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":"2026-08-01T19:06:47.147410Z","title":null,"venue":null,"work_id":null,"year":1966},"citing_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},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T19:06:47.147410Z"},"links":{"citing_paper":"/paper/2607.17125"},"observation_digest":"sha256:3b99e0932fd8a24cc94f8fe4bb83c6fbab1c9ad404b10925acca26af429f8f49","observation_id":"9589895c-54d9-4616-a20f-5330ab619f38","resolution":{"observed_at":"2026-08-01T19:06:47.147410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.17125","last_updated":"2026-07-21T09:36:31Z","latest_version":2,"primary_category":"math.GR","snapshot_observed_at":"2026-08-14T19:06:17.864206Z","submitted_at":"2026-07-19T08:24:06Z","title":"Simple Skew Braces with Cyclic Sylow Subgroups"},"reference_resolution":{"displayed":30,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":30,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":30},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 2 inbound Pith citation observations for arXiv:2607.17125."}