{"as_of":"2026-08-11T11:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:628806d197e1e2cecddf754fd7bf0e86d77f729f86ef1af6682a87c356704705","coverage":[{"denominator":46,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":46,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T05:36:53.995157Z","state":"measured"},{"denominator":46,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":46,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2509.05516/citation-record","integrity":"/paper/2509.05516/integrity","json":"/paper/2509.05516/citation-record.json","paper":"/paper/2509.05516"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T05:36:49.131078Z","title":"write newline","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:49.131078Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:03ba41140e9f92102e0ac3fde38001663dbc86b8432ad903df1d700a6fe7b864","observation_id":"322707a6-504b-44c3-aedd-7301ecb21ab0","resolution":{"observed_at":"2026-08-05T05:36:49.131078Z","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":"2026-08-05T05:37:01.092222Z","title":"Monoidal functors, species and Hopf algebras , volume 29","venue":null,"work_id":"7306cf88-7403-4606-9d67-b648d1075820","year":2010},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:49.195443Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:266f6b94d1d5d838ca6bb843aa0cfd5d56cddd2025b4ab048aa224bbe18d6f05","observation_id":"dce38227-6db5-4815-aece-04f7f446755f","resolution":{"observed_at":"2026-08-05T05:37:01.144052Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:37:00.919520Z","title":"Deloopings of H urwitz spaces","venue":null,"work_id":"d75996f1-d068-447d-87e0-bf4f7af5670d","year":2024},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:49.295040Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:739bc80a9e07de0b52cc8390028dfa84a3e9cb86ae25642c5956da9801256495","observation_id":"829a1675-3a4b-40a7-9355-348084845414","resolution":{"observed_at":"2026-08-05T05:37:01.008602Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:37:00.751057Z","title":"Polynomial stability of the homology of H urwitz spaces","venue":null,"work_id":"830f3fcf-76e0-48a5-8b28-1a11d5b94405","year":2025},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:49.399419Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:1601c91081296e4cde788f4711339aedc09d13cc5d30071b15c57d46f496994c","observation_id":"706b9198-27f0-4b58-abc5-714577f5e89d","resolution":{"observed_at":"2026-08-05T05:37:00.852109Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:37:00.620052Z","title":"FI -modules and stability for representations of symmetric groups","venue":null,"work_id":"d034fa19-53fe-4e1d-8f21-ca92a96ffeeb","year":2015},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:49.552180Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:68a6ac5afec1b2de3d6f6ba4d5f1cc26dea772f89715b91312ec012799c399d3","observation_id":"811ad8cc-aba3-45e3-a5bf-811d19608e46","resolution":{"observed_at":"2026-08-05T05:37:00.670220Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:37:00.445371Z","title":"Representation theory and homological stability","venue":null,"work_id":"83d9d539-a7d1-4a8b-8f6d-087230e05b49","year":2013},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:49.626152Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:ca60352c98f4b1375650611cd3d0800186ceb0f613e7b21461ce7d7dd42a8bc5","observation_id":"e3680a07-16af-4e4b-ba33-4298aeacbea0","resolution":{"observed_at":"2026-08-05T05:37:00.523755Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:37:00.264223Z","title":"The braid group and the arc complex","venue":null,"work_id":"1252472f-98b1-4fab-8da7-8c0e0828b859","year":2013},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:49.674894Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:23dd4d8f05ddc8d9e3c2606c074f50ee1204f5a0cf162b7b174d063ab8c74242","observation_id":"8defe7e7-a46f-47f4-b1c9-0441de17a19b","resolution":{"observed_at":"2026-08-05T05:37:00.355096Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:37:00.128020Z","title":"On closed categories of functors","venue":null,"work_id":"e96997af-6f13-4805-9b3b-7667e364d964","year":1970},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:49.731264Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:5cb920a2287e71fbadcf589a861f8f8a00fc94105d572406b8434d0a822d668c","observation_id":"1a1a8234-25d6-4059-b650-97aa18b1212e","resolution":{"observed_at":"2026-08-05T05:37:00.183651Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:59.962239Z","title":"On closed categories of functors","venue":null,"work_id":"ae7fb529-f3ee-454d-ae19-6456bfdde273","year":1972},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:49.858796Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:55b5fbfdc4a61c2d4177557050f738e3e2c54057a3ba596fded1935f9a3c702f","observation_id":"edc1013d-3251-4276-b5bd-fb0741f877a8","resolution":{"observed_at":"2026-08-05T05:37:00.041844Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:59.797328Z","title":"Abstract algebra , volume 3","venue":null,"work_id":"d86a4a1f-1be3-4b05-9ff4-ff10730b2bce","year":2004},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:49.948248Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:27b025457a38e63ac8b1e78900b71fc4f7c3e2c3f82155709a3fedc61a2f2871","observation_id":"068c12f5-b415-4b9d-9fb1-d64252a92e03","resolution":{"observed_at":"2026-08-05T05:36:59.873537Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2304.08314","last_updated":"2023-04-17T14:31:54Z","snapshot_observed_at":"2026-07-06T15:16:31.335505Z","submitted_at":"2023-04-17T14:31:54Z","title":"The Hilbert Polynomial of Quandles and Colorings of Random Links","version":1},"cited_work":{"arxiv_id":"2304.08314","doi":null,"metadata_source":"pith","pith_arxiv_id":"2304.08314","snapshot_observed_at":"2026-08-05T05:36:55.124302Z","title":"The Hilbert Polynomial of Quandles and Colorings of Random Links","venue":"math.GT","work_id":"0407b64f-8767-48c2-90cc-e0158ee634ae","year":2023},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:50.038851Z"},"links":{"cited_paper":"/paper/2304.08314","citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:56b6c26fd4366a466fcbbe0807b1f570626a953a532221f1399a6ed62e503788","observation_id":"4350670c-6a8d-45dd-8dec-a6a485b4b032","resolution":{"observed_at":"2026-08-05T05:36:55.202048Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:59.644420Z","title":"A primer on homotopy colimits","venue":null,"work_id":"b3445d8a-3f8c-4c63-9715-c6081f1ed859","year":null},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:50.101701Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:032e6f77906bf53f7282e7ffa817fde2a264b9f21fe4c146a97b2a09cd18f4df","observation_id":"7c1df661-ca26-4d91-a6e5-0368de9f2de9","resolution":{"observed_at":"2026-08-05T05:36:59.724795Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2310.16286","last_updated":"2026-07-07T16:25:57Z","snapshot_observed_at":"2026-08-09T07:08:04.639777Z","submitted_at":"2023-10-25T01:41:20Z","title":"Homological stability for generalized Hurwitz spaces and Selmer groups in quadratic twist families over function fields","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.16286","snapshot_observed_at":"2026-08-05T05:36:50.190505Z","title":"Ellenberg and Aaron Landesman","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:50.190505Z"},"links":{"cited_paper":"/paper/2310.16286","citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:b953f6fbb60bbe92522ecfceee20febd56dd2d3d1e6d12645a0d777efe49000d","observation_id":"a50381d8-ce20-4548-9512-a0ede6ec5a85","resolution":{"observed_at":"2026-08-05T05:36:50.190505Z","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":"2026-08-05T05:36:59.465924Z","title":"Semisimplicial spaces","venue":null,"work_id":"bdab2bec-0514-4331-9f9f-804feb611138","year":2099},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:50.330287Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:913bc52d8231742bbd3218a38fd282a0cd6b07792f9e5da1ded1b830d52b0126","observation_id":"f54c79a9-656d-4bb8-ab5f-eaa5ec1fc60b","resolution":{"observed_at":"2026-08-05T05:36:59.554123Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:59.341631Z","title":"Averages of arithmetic functions over conductors of function fields","venue":null,"work_id":"94a136f4-bad1-46d8-8bf9-19b1add02210","year":null},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:50.389627Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:f57e364270bfd78516cc93ff40b55f0ddde479697de9f89169d3d3a201d09b8a","observation_id":"67c537fe-6781-464d-b11f-2e63638fd855","resolution":{"observed_at":"2026-08-05T05:36:59.397484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1701.04541","last_updated":"2023-03-05T15:59:47Z","snapshot_observed_at":"2026-08-10T07:34:12.579845Z","submitted_at":"2017-01-17T06:07:16Z","title":"Fox-Neuwirth-Fuks cells, quantum shuffle algebras, and Malle's conjecture for function fields","version":2},"cited_work":{"arxiv_id":"1701.04541","doi":null,"metadata_source":"pith","pith_arxiv_id":"1701.04541","snapshot_observed_at":"2026-08-05T05:36:54.918923Z","title":"Fox-Neuwirth-Fuks cells, quantum shuffle algebras, and Malle's conjecture for function fields","venue":"math.NT","work_id":"791b8eaa-149a-43e6-97f5-c265c8216bc1","year":2017},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:50.497296Z"},"links":{"cited_paper":"/paper/1701.04541","citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:3eb0361d5d98121f3cc17c1ebefd85c20fcdbacd07504d7aaa3692fe99df89a4","observation_id":"8868a3b9-91ad-4c4b-947d-06a75e674c0e","resolution":{"observed_at":"2026-08-05T05:36:55.000347Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1212.0923","last_updated":"2013-11-19T21:06:31Z","snapshot_observed_at":"2026-07-06T03:01:17.734180Z","submitted_at":"2012-12-05T03:17:05Z","title":"Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1212.0923","snapshot_observed_at":"2026-08-05T05:36:50.603497Z","title":"Ellenberg, Akshay Venkatesh, and Craig Westerland","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:50.603497Z"},"links":{"cited_paper":"/paper/1212.0923","citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:dea6d06e313136acb4e163afe4d854115c4ae6919a6ad50d294c712b33a637b5","observation_id":"84db9120-0138-4ad4-8e2a-d8e5fa4afba6","resolution":{"observed_at":"2026-08-05T05:36:50.603497Z","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":"2026-08-05T05:36:59.159133Z","title":"Ellenberg, Akshay Venkatesh, and Craig Westerland","venue":null,"work_id":"5fb614f3-28d7-4b69-bf26-0cb1b0c76e94","year":2016},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:50.724144Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:fc6799ead411ebb815bd7a27390b8915096cf251d68982864c040ce399f5d776","observation_id":"42514b7c-89e3-465e-b5e3-f26a09450361","resolution":{"observed_at":"2026-08-05T05:36:59.238878Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:50.872353Z","title":"Representation theory: a first course , volume 129","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:50.872353Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:d551cd077711bf999c066ca445abf5a94ce9bb6fbcf8a6c530dff1debf0585e7","observation_id":"324b46eb-013a-42d7-bd68-fcf28df990da","resolution":{"observed_at":"2026-08-05T05:36:50.872353Z","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":"2026-08-05T05:36:59.013245Z","title":"Midwest R epresentation S tability R esearch M eeting P roblem S ession, 2019","venue":null,"work_id":"c240bceb-61b3-4c8b-a9b9-4d3739422b8c","year":2019},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:51.003969Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:54fdc4d2ea17be2308812fe63adec55d6389f84634f945a74cbba145bcf32794","observation_id":"975a6eec-1cfb-4ee6-b1db-d12f6f169ba5","resolution":{"observed_at":"2026-08-05T05:36:59.103749Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1805.07184","last_updated":"2023-12-28T19:50:13Z","snapshot_observed_at":"2026-08-02T04:03:00.932894Z","submitted_at":"2018-05-18T13:01:55Z","title":"Cellular $E_k$-algebras","version":4},"cited_work":{"arxiv_id":"1805.07184","doi":null,"metadata_source":"pith","pith_arxiv_id":"1805.07184","snapshot_observed_at":"2026-08-05T05:36:54.722450Z","title":"Cellular $E_k$-algebras","venue":"math.AT","work_id":"f902c56c-0647-4e9c-bb45-5a7d4ad511b2","year":2018},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:51.120336Z"},"links":{"cited_paper":"/paper/1805.07184","citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:49e3fe0692698e5482617886d9890b68110b1c9f1695d40dd857e4128b20712d","observation_id":"e998c500-2ea0-4fbf-b962-009001fc11ed","resolution":{"observed_at":"2026-08-05T05:36:54.817461Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:58.726081Z","title":"Homological stability for moduli spaces of high dimensional manifolds","venue":null,"work_id":"4fb798b4-6824-4433-b54a-3df7591cda06","year":2018},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:51.269238Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:9881fac5ae3783d53062ab061eda5765f10ab4904c909e544967f7d3d7a2d109","observation_id":"5c87a1a0-f0c8-4e5d-ac8a-409279cda920","resolution":{"observed_at":"2026-08-05T05:36:58.876497Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:58.455812Z","title":"Hirschhorn","venue":null,"work_id":"3b3fbff6-bbbb-4586-bdc5-c01b3739c48d","year":2003},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:51.419723Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:0c06ec3a32af0e12540852a35513f04fca34e938ecdf3678428db96144cad297","observation_id":"47fc827f-a306-41c4-96f0-80319401e25d","resolution":{"observed_at":"2026-08-05T05:36:58.599498Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:58.144265Z","title":"Tethers and homology stability for surfaces","venue":null,"work_id":"6ed8b566-4c9e-4374-91c7-be3960cecc54","year":1916},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:51.545378Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:4062d3923a2f0abbd4f585575c79ccc2fd1d6bb48dce67c98cd7d705f7d2686a","observation_id":"5bdc2bb0-bdb4-4c5d-8fde-01afe1a830d6","resolution":{"observed_at":"2026-08-05T05:36:58.276761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.08081","last_updated":"2024-08-26T11:23:53Z","snapshot_observed_at":"2026-08-08T12:31:12.625100Z","submitted_at":"2024-08-15T11:13:49Z","title":"Scissors automorphism groups and their homology","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.08081","snapshot_observed_at":"2026-08-05T05:36:51.652180Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:51.652180Z"},"links":{"cited_paper":"/paper/2408.08081","citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:0c89f032d3c52bf19f35ab48c597b2dd1f4fbd7ab9bcd30ad47ad3ee203a20a3","observation_id":"ff694e98-19d2-46bb-8daf-e8cd4a55c1d9","resolution":{"observed_at":"2026-08-05T05:36:51.652180Z","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":"2026-08-05T05:36:57.871356Z","title":"Homological stability of topological moduli spaces","venue":null,"work_id":"bd8f9351-9c7e-4a22-a833-29c8390dbb45","year":2019},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:51.779077Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:39b7d71f9e8cde40fa1a94ca7222b991a79cdb200599b2d1425138d94ab0fbb9","observation_id":"5c27a9d7-a634-4317-b14f-93d7a1ae8d5e","resolution":{"observed_at":"2026-08-05T05:36:57.984229Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.22222","last_updated":"2024-10-29T16:52:50Z","snapshot_observed_at":"2026-07-06T19:41:41.942153Z","submitted_at":"2024-10-29T16:52:50Z","title":"An alternate computation of the stable homology of dihedral group Hurwitz spaces","version":1},"cited_work":{"arxiv_id":"2410.22222","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.22222","snapshot_observed_at":"2026-08-05T05:36:54.530867Z","title":"An alternate computation of the stable homology of dihedral group Hurwitz spaces","venue":"math.NT","work_id":"8682ca8f-ca3d-4fc3-b75b-39364c28df6d","year":2024},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:51.910960Z"},"links":{"cited_paper":"/paper/2410.22222","citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:be1cdd17caed3cd9a0259cbc29e4a4b037736d0a80276bed70a93cf237594068","observation_id":"d5ffa506-cee8-4107-8126-53f193428d76","resolution":{"observed_at":"2026-08-05T05:36:54.634999Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:52.036728Z","title":"The C ohen-- L enstra moments over function fields via the stable homology of non-splitting H urwitz spaces","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:52.036728Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:8fa819dd7d95a8f4018f3d8edd9df6dee3bd102805ec80bcbaf28af0d617b83b","observation_id":"3b564ea5-1ac8-4c4b-8d04-95e2613b778b","resolution":{"observed_at":"2026-08-05T05:36:52.036728Z","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":"2026-08-05T05:36:52.198235Z","title":"Homological stability for H urwitz spaces and applications","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:52.198235Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:1bc36ee6f137d9a15adc924c16c7216f51ea9a462e91d34747467d34264944d4","observation_id":"202384fa-6af7-42e2-97b5-f3cba2548f9e","resolution":{"observed_at":"2026-08-05T05:36:52.198235Z","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":"2026-08-05T05:36:57.601705Z","title":"The stable homology of H urwitz spaces and applications","venue":null,"work_id":"f0e21226-4bac-4215-a192-8c72c0063a0a","year":null},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:52.340402Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:1c95f7aa7c889cec345107778a3eda3594b18d965dbeb03d7e2ef740eda76f76","observation_id":"95a77747-3644-46c5-b664-79efe7529b72","resolution":{"observed_at":"2026-08-05T05:36:57.715769Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:57.435572Z","title":"Symmetric functions and H all polynomials","venue":null,"work_id":"391fee84-a4d9-4efa-a1cb-7e9959f04b0a","year":1998},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:52.435101Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:4b7a30b8371af0e25c144364e568625de68f8777b84ca5ae52800b05d84f98c9","observation_id":"bac1f684-4f68-408d-964b-ff15806f7dbc","resolution":{"observed_at":"2026-08-05T05:36:57.512256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:57.288363Z","title":"The geometry of iterated loop spaces , volume 271","venue":null,"work_id":"7a68d73b-48a4-4ed0-bd03-0bc183b451b3","year":2006},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:52.552406Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:3693a58680ac98fc6472faee3dbc023ef47f6066cd3a6df7435620856d2976f9","observation_id":"f00352ee-138a-4eba-9cb0-f2730e969448","resolution":{"observed_at":"2026-08-05T05:36:57.354321Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:57.151428Z","title":"More concise algebraic topology: localization, completion, and model categories","venue":null,"work_id":"8606a76a-8176-40a9-87f7-cdf4934f8ad0","year":2011},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:52.664262Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:591f67c43f4bd853b33f37a2189daec8951777e130e76822bd9a038a7245dd7d","observation_id":"e4fc6c94-c7cd-4c71-9f14-37a4049139fc","resolution":{"observed_at":"2026-08-05T05:36:57.229901Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1910.05574","last_updated":"2021-06-21T11:40:01Z","snapshot_observed_at":"2026-07-06T08:29:01.140025Z","submitted_at":"2019-10-12T14:53:19Z","title":"Representation stability, secondary stability, and polynomial functors","version":3},"cited_work":{"arxiv_id":"1910.05574","doi":null,"metadata_source":"pith","pith_arxiv_id":"1910.05574","snapshot_observed_at":"2026-08-05T05:36:54.132695Z","title":"Representation stability, secondary stability, and polynomial functors","venue":"math.AT","work_id":"8d38d87c-6fc3-403f-b892-bcc21585bb5d","year":2019},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:52.801926Z"},"links":{"cited_paper":"/paper/1910.05574","citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:a50260bfacf8dc571489c4e9bc607eb1f2d3356d1c268e332849b0963732ced6","observation_id":"6d9b8a17-f30e-4e48-a4c6-14c4ecb27746","resolution":{"observed_at":"2026-08-05T05:36:54.249717Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.00354","last_updated":"2026-07-03T02:41:53Z","snapshot_observed_at":"2026-08-08T19:54:46.239590Z","submitted_at":"2024-02-01T05:51:17Z","title":"Uniform twisted homological stability","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.00354","snapshot_observed_at":"2026-08-05T05:36:52.918195Z","title":"Uniform twisted homological stability","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:52.918195Z"},"links":{"cited_paper":"/paper/2402.00354","citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:b518b2d16015944c2df09abaf367ef860b538c6972db869923e3d196a2d63802","observation_id":"9d6e6a16-77d8-46c9-908a-35346241ff14","resolution":{"observed_at":"2026-08-05T05:36:52.918195Z","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":"2026-08-05T05:36:57.020131Z","title":"Central stability homology","venue":null,"work_id":"5c22668f-1c00-4e72-a19b-61536b5110df","year":2020},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:53.045681Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:246fd034359effa650ffe8c3ebbe81d2b41d498f20814a959621ec55cb14872e","observation_id":"e808ae22-0a73-4a85-84f8-83ecaff6aa3c","resolution":{"observed_at":"2026-08-05T05:36:57.095485Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:56.808896Z","title":null,"venue":null,"work_id":"5c6e84b6-9e38-4d49-be39-f702951456c4","year":2017},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:53.181151Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:80856ebcceb3cff67a4d5a56637b51d87861b5a2c5c927ef77fd812e447b6029","observation_id":"ecfc42f8-26cb-48cd-8cdc-b5a871b16fdc","resolution":{"observed_at":"2026-08-05T05:36:56.899968Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:56.629329Z","title":"A new approach to twisted homological stability with applications to congruence subgroups","venue":null,"work_id":"562dda7b-8e8b-4c0f-acdc-ed63e2b9a87e","year":2023},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:53.184248Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:677a40e559042c5cca36f705d9444744c4a2a9e8ed52f9f9d0e03adbc9cff6f2","observation_id":"3dbcd428-e7a5-4aad-a37e-4f5df4d3b6f7","resolution":{"observed_at":"2026-08-05T05:36:56.727034Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:56.412621Z","title":"Homotopical algebra , volume 43","venue":null,"work_id":"2f722394-b081-41be-9b9d-fd5c9ee923d0","year":2006},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:53.187381Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:b2deb8f304b7580f27b438919e65f4de90035a8d2ebd37d01b3c14982870d38e","observation_id":"314fc210-01a2-4fe7-9071-82137f1a6dea","resolution":{"observed_at":"2026-08-05T05:36:56.504224Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:56.228548Z","title":"Generalized representation stability and FI_d -modules","venue":null,"work_id":"033ee708-0089-4519-9951-085f6d778c13","year":2017},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:53.233848Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:c3068d7c718bf6116bbde75a66fe1c54839d0b7fb89302303235acdb8589b415","observation_id":"5a26b143-fa56-49c9-88e7-f1046ce15c08","resolution":{"observed_at":"2026-08-05T05:36:56.318513Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:56.041750Z","title":"Homology of H urwitz spaces and the C ohen- L enstra heuristic for function fields [after E llenberg, V enkatesh, and W esterland]","venue":null,"work_id":"3576fa5a-a36c-4cfa-a3f4-1f2f659135b1","year":2020},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:53.380165Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:441ee92dea2883e98884fee9af133f9c497cb336e9c048eb838d5686f1b4dfb6","observation_id":"7c967505-18f7-4eda-910a-a4b240f93404","resolution":{"observed_at":"2026-08-05T05:36:56.147644Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:55.888351Z","title":"Classical homological stability from the point of view of cells","venue":null,"work_id":"ea1f582c-ccec-46c3-8839-ecb2b7ffeb1c","year":2024},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:53.531091Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:1c95c0e61c72ba4cdd63b94d1c1fcf881ec416d8af03ec2e1d8d12ad2d4535e3","observation_id":"b95d4861-f650-4e00-8453-73cea04fc3e7","resolution":{"observed_at":"2026-08-05T05:36:55.951231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:55.675608Z","title":"Homological stability for automorphism groups","venue":null,"work_id":"d1f467ec-1970-42d4-abd2-39f15c2d064f","year":2017},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:53.601207Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:2571d47b76c407f3e25815b1f193bccaa0d5201616789754bbb6719c72159788","observation_id":"b28d8f46-f2a6-4f2d-9c2e-d3b5ad51fb51","resolution":{"observed_at":"2026-08-05T05:36:55.805966Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T05:36:55.512238Z","title":"The tamely ramified geometric quantitative minimal ramification problem","venue":null,"work_id":"a80cc780-e321-4597-b0a1-400be384770a","year":2024},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:53.717156Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:ba7715bb9d2640a3f0c7b85db4a556e791c47906839a08582c4f637bbd5990a2","observation_id":"c3545d0c-c851-4a67-abc1-6af621a48501","resolution":{"observed_at":"2026-08-05T05:36:55.603021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1209.5122","last_updated":"2012-09-23T22:45:41Z","snapshot_observed_at":"2026-07-06T02:56:09.683560Z","submitted_at":"2012-09-23T22:45:41Z","title":"Introduction to twisted commutative algebras","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1209.5122","snapshot_observed_at":"2026-08-05T05:36:53.836772Z","title":"Introduction to twisted commutative algebras","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:53.836772Z"},"links":{"cited_paper":"/paper/1209.5122","citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:7950f36c4ab45548da576ac5db80f61f52ab396eabfbb47e465dfc154fd02a07","observation_id":"03c6933e-e8e8-4107-8272-ccdb481326e0","resolution":{"observed_at":"2026-08-05T05:36:53.836772Z","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":"2026-08-05T05:36:55.314977Z","title":"A practical view of W : A guide to working with W eyl group representations, with special emphasis on branching rules","venue":null,"work_id":"32ee35db-320f-48f4-a119-1f84e4ba4716","year":2006},"citing_paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-05T05:36:53.995157Z"},"links":{"citing_paper":"/paper/2509.05516"},"observation_digest":"sha256:ca3ff2292204964d276741006d2204c6607f18e402902b9aeac41be28bd3f196","observation_id":"ede0a348-c11a-49f4-be40-513e8854bc86","resolution":{"observed_at":"2026-08-05T05:36:55.428456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2509.05516","last_updated":"2025-09-05T21:56:42Z","latest_version":1,"primary_category":"math.AT","snapshot_observed_at":"2026-08-07T18:23:38.498121Z","submitted_at":"2025-09-05T21:56:42Z","title":"Representation stability for ordered Hurwitz spaces"},"reference_resolution":{"displayed":46,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":10,"verified_exact":4,"verified_fuzzy":31},"total_outbound_references":46},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 0 inbound Pith citation observations for arXiv:2509.05516."}