{"as_of":"2026-08-22T07:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5b70c3090765134c831cc3152eb60f6f039fb3f3e56cbf4b21c7b8e8d8084b14","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-20T23:05:46.145278Z","state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"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":"2026-08-01T19:06:44.783858Z","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":"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":"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":"2026-08-01T05:22:31.683653Z","title":"Damele and A","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":8,"source":"pdf_text","source_observed_at":"2026-08-01T05:22:31.683653Z"},"links":{"cited_paper":"/paper/2605.07609","citing_paper":"/paper/2607.22795"},"observation_digest":"sha256:94c7b8b68dedf9fd1ead58cdb6152ba4d90d836d661d5135a854023e9b682e23","observation_id":"4c20bd73-0ffa-4084-88e0-f65261da6fa3","resolution":{"observed_at":"2026-08-01T05:22:31.683653Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2605.07609/citation-record","integrity":"/paper/2605.07609/integrity","json":"/paper/2605.07609/citation-record.json","paper":"/paper/2605.07609"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Auslander,Simply transitive groups of affine motions, Amer","venue":null,"work_id":"6bc68058-c25e-4bd2-83b2-08049c5c706f","year":1977},"citing_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},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-20T23:05:46.145278Z"},"links":{"citing_paper":"/paper/2605.07609"},"observation_digest":"sha256:81539fdb4d50c84b38a70abb506e087851e4523239c14f050cd8f4b679d79aa0","observation_id":"bd83ceb7-69d6-42aa-8b3e-2992d5f8785f","resolution":{"observed_at":"2026-05-20T23:14:13.062060Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Baues,Infra-solvmanifolds and rigidity of subgroups in solvable linear algebraic groups, Topology43(2004), no","venue":null,"work_id":"7e9ebf7f-e840-4acf-8ec9-ae90a21f0f3f","year":2004},"citing_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},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-20T23:05:46.145278Z"},"links":{"citing_paper":"/paper/2605.07609"},"observation_digest":"sha256:fcd81e8739e77bd3a4e382a2d4c2e9190c333404752b8a580f4176e6a94c432f","observation_id":"72cda146-b4b7-4a9d-9adf-33189e8e5fcf","resolution":{"observed_at":"2026-05-20T23:14:13.058971Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"2f517f56-0df3-4f6d-befe-a47f5cc33bfb","year":1973},"citing_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},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-20T23:05:46.145278Z"},"links":{"citing_paper":"/paper/2605.07609"},"observation_digest":"sha256:7b9d1bdfafe5649f954ceec7c3842ea35f558098d6d2142314c5f40399877f5a","observation_id":"475c342b-27ce-487c-b84e-a0221b94c067","resolution":{"observed_at":"2026-05-20T23:14:13.055398Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Deré,NIL-affine crystallographic actions of virtually polycyclic groups, Transform","venue":null,"work_id":"77f8fd40-7937-42d5-acf1-752fd8c00a40","year":2021},"citing_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},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-20T23:05:46.145278Z"},"links":{"citing_paper":"/paper/2605.07609"},"observation_digest":"sha256:6fb18fc868d4f0a79ff6e3a764c087001879cb654fd3892292525371ed6c0301","observation_id":"d191a2d8-9476-4ee7-a31e-e8a5f5a0f9c6","resolution":{"observed_at":"2026-05-20T23:14:13.052550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jalgebra.2026.01.048","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Damele and A","venue":"Journal of Algebra","work_id":"9945d378-7cf5-4777-9d79-684f8aeee57f","year":2026},"citing_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},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-20T23:05:46.145278Z"},"links":{"citing_paper":"/paper/2605.07609"},"observation_digest":"sha256:f6877bc166c01c206b5c0d1f5c333eb4987f995ea9632c4a56faffddfece9a7f","observation_id":"8f5cc13c-b632-4a66-a06d-af09ea58b171","resolution":{"observed_at":"2026-05-20T23:09:11.683932Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Gorshkov and T","venue":null,"work_id":"0881d3af-ebe7-4431-9933-5d14e665e2b3","year":2021},"citing_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},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-20T23:05:46.145278Z"},"links":{"citing_paper":"/paper/2605.07609"},"observation_digest":"sha256:15c96d884248944fc66b88e0fa47dc87e3ed64840d52cf98db76b9416f635e4d","observation_id":"f10111b4-4a33-4ce6-9482-c221450d85bc","resolution":{"observed_at":"2026-05-20T23:14:13.049355Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/mcom/3161","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Guarnieri, L","venue":"Mathematics of Computation","work_id":"3c7e798b-05ba-4828-b1c2-f98d25f80312","year":2017},"citing_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},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-20T23:05:46.145278Z"},"links":{"citing_paper":"/paper/2605.07609"},"observation_digest":"sha256:72caa467d12dbd5814309b50423bfdfa40ccafb941ddfd19ab757f5f1e5d1369","observation_id":"2e71da91-57f0-4ef9-90d8-02d76602fa04","resolution":{"observed_at":"2026-05-20T23:09:11.679528Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-07-16T21:50:49.350829+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-16T21:50:49.350829+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"638eba6c-08e4-477d-b49e-e46ea4cdeb72","year":2015},"citing_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},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-20T23:05:46.145278Z"},"links":{"citing_paper":"/paper/2605.07609"},"observation_digest":"sha256:ab2d419955c597587981e6f2df2fed537369c3bd91ffb7ee04ef4d83340db43b","observation_id":"b9cf6851-9b46-417b-b3c0-c6f95e9d9c40","resolution":{"observed_at":"2026-05-20T23:14:13.046280Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b1d0e8da-07ff-498e-9a9b-9252c1556e5f","year":2007},"citing_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},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-20T23:05:46.145278Z"},"links":{"citing_paper":"/paper/2605.07609"},"observation_digest":"sha256:40a841a80208cf486045ae422047eb88e4ca949dabf4f2c3155aebc93d0d9441","observation_id":"013b0127-b1d4-4d06-975b-f1dc39e3c2ac","resolution":{"observed_at":"2026-05-20T23:14:13.043332Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"bc0ea4b7-86ab-4684-9f6c-a87d4aa5ba45","year":2013},"citing_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},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-20T23:05:46.145278Z"},"links":{"citing_paper":"/paper/2605.07609"},"observation_digest":"sha256:2fe34fdbe58b660be6b0be3ccc324820143b870e83b20e961a69226aac41ee4d","observation_id":"64df09e3-e3e7-4deb-870b-0adcf77eff0a","resolution":{"observed_at":"2026-05-20T23:14:13.039951Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Nasybullov,Connections between properties of the additive and the multiplicative groups of a two-sided skew brace, J","venue":null,"work_id":"1397248d-a428-4c7d-8184-26143ea831e3","year":2019},"citing_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},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-20T23:05:46.145278Z"},"links":{"citing_paper":"/paper/2605.07609"},"observation_digest":"sha256:3e3f527e07134e7d1abeaa88327e81139f8f5d1036abfe21e6f74d0edf2f86c9","observation_id":"745ce7f1-8321-4483-bb55-7d18b236b31c","resolution":{"observed_at":"2026-05-20T23:14:13.036716Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/jca/2-1-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Smoktunowicz and L","venue":"Journal of Combinatorial Algebra","work_id":"87b13760-8fba-4529-9569-332018da3d04","year":2018},"citing_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},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-20T23:05:46.145278Z"},"links":{"citing_paper":"/paper/2605.07609"},"observation_digest":"sha256:86062a786e52c7d9a3ee231fbe607fa97d6cdbc8b0ce66519988f9d0c5fc4e8b","observation_id":"a2306949-71b8-48a5-94dd-6abbabb9dac9","resolution":{"observed_at":"2026-05-20T23:09:11.688483Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-05-22T09:52:56.528348+00:00","source":"crossref_status_cache"},{"observed_at":"2026-05-22T09:52:56.528348+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2605.07609","last_updated":"2026-05-18T10:09:02Z","latest_version":2,"primary_category":"math.GR","snapshot_observed_at":"2026-08-15T10:48:49.338856Z","submitted_at":"2026-05-08T11:35:51Z","title":"Solvability and Rigidity for Topological Skew Braces"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":3,"verified_fuzzy":5},"total_outbound_references":12},"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 12 of 12 outbound references and 2 inbound Pith citation observations for arXiv:2605.07609."}