{"as_of":"2026-08-13T10:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:54ccce25ce1a993462f0503737d56fec1333be6b1b139492da721625ef3bef59","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T12:23:09.165609Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2509.01843/citation-record","integrity":"/paper/2509.01843/integrity","json":"/paper/2509.01843/citation-record.json","paper":"/paper/2509.01843"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:23:13.751712Z","title":null,"venue":null,"work_id":"86bce39a-bfd1-4824-a1ea-6cbf65577ad3","year":1997},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:07.103078Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:75670eb2a332fe7960fe336faf9775eea8b821d80004f34de31478414a2c1f32","observation_id":"faf4eecc-01d6-4a6b-86f5-b4ab4a0f45b8","resolution":{"observed_at":"2026-08-05T12:23:13.829409Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:13.579142Z","title":null,"venue":null,"work_id":"f9bfc908-d3f8-44ec-a91a-fe0af7b79681","year":1973},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:07.164249Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:584f2a2eb10cf12e5db1dc1b832446c1c83ccbe14b59eadce0c492631fe608bb","observation_id":"e21eca8d-8fb4-4135-90cb-03d99135a48a","resolution":{"observed_at":"2026-08-05T12:23:13.650107Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:13.400656Z","title":null,"venue":null,"work_id":"f4d74780-679e-4f6b-bdf9-b1d7e325ec61","year":2023},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:07.240091Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:4d95e505eeb51870d2780948774d5d542bb27d481708ad2337d3bc827632ca09","observation_id":"067688f6-7245-427d-95f4-ba4a742dea89","resolution":{"observed_at":"2026-08-05T12:23:13.469112Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:13.208471Z","title":null,"venue":null,"work_id":"0ca30636-c5c4-46df-8bb1-507b7a4a2ff2","year":2014},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:07.314498Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:e793f0e2dbd370dcd4793b9f88db3a01eff6f6084e81c3ce6f0105da04863c73","observation_id":"1a8d7776-41a0-4722-b312-a195f088a035","resolution":{"observed_at":"2026-08-05T12:23:13.283515Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:12.981116Z","title":null,"venue":null,"work_id":"48de1c67-e743-4d5d-8551-7c42a83adac1","year":2002},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:07.391648Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:6306bb9acdf2c7f6875f62502e0c965236c48ce236a1c7099de1c38e68e3f1b2","observation_id":"dfd014ea-385a-43d8-a1d9-45ccd813d373","resolution":{"observed_at":"2026-08-05T12:23:13.067272Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:12.807930Z","title":null,"venue":null,"work_id":"e4617182-a94e-482c-b558-85decc905d45","year":2002},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:07.478175Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:4455d6e2e9c01aef04e8ee643da0ae05ab1f3a3829b2454715feffe4b114eebb","observation_id":"4c14b034-1532-46af-9d4c-9589b4b9b60b","resolution":{"observed_at":"2026-08-05T12:23:12.889421Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:12.657071Z","title":"21, Cambridge University Press, Cambridge, 1991","venue":null,"work_id":"d2d74ada-62e2-40e3-89bf-cfdd5ca3904c","year":1991},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:07.575070Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:e098a78ae2bf597992299752ec747c0043d797a55f0c829e516bcd7e7a63344a","observation_id":"e6736463-e452-4072-ae52-f5b1c7684eed","resolution":{"observed_at":"2026-08-05T12:23:12.728599Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:12.453676Z","title":null,"venue":null,"work_id":"9b0f4d4a-9561-4711-b022-279462020911","year":1987},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:07.640395Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:0fb417e17ee2fba8a50f7ebba52e00983081fd1ba592d58465b350708947e679","observation_id":"56361edf-6fda-4987-b4ac-db8111effc7d","resolution":{"observed_at":"2026-08-05T12:23:12.549140Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:12.240116Z","title":"16, American Mathematical Society, Providence, RI, 1999, With a preface and notes by Stephen DeBacker and Paul J","venue":null,"work_id":"412a512e-a603-4116-85b6-dfdd94a11052","year":1999},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:07.716030Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:c235fe9d92daaa3457dc98fdbdd673fb2f6a98ae288571d72a4ad942e0aae06c","observation_id":"9d3b6954-686f-4684-84cd-952a7d87025a","resolution":{"observed_at":"2026-08-05T12:23:12.341294Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:12.118878Z","title":null,"venue":null,"work_id":"1436e24e-bd3c-4370-8a83-a84f6832b31d","year":2024},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:07.804050Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:ccf6207182d299af372bd999d2d591a2304d9fb73831a2e7a5a97d4c3fb3b24e","observation_id":"ff835f4e-baf5-4ad4-a2ca-2d94df194c29","resolution":{"observed_at":"2026-08-05T12:23:12.185492Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:11.981631Z","title":null,"venue":null,"work_id":"88046260-1986-4e35-94b3-93db11e415b8","year":2025},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:07.909188Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:bbf0587c4ae2f2e9430d6f52aef924ca3cc6fc2694423b71aeb9bd1357b22b13","observation_id":"6bfa11be-cf98-4cf4-9f79-cdf095556bb6","resolution":{"observed_at":"2026-08-05T12:23:12.033688Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:11.797322Z","title":null,"venue":null,"work_id":"fa4b4c0a-8f56-48a4-84ae-26b1a3fbf099","year":2018},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:07.971512Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:cb629f6571eb5124d2315f8f55f29e5f373d212538d1d46dd675514b986b2c22","observation_id":"eda24821-4476-40ac-828b-f211ed2c3639","resolution":{"observed_at":"2026-08-05T12:23:11.897030Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:11.634755Z","title":null,"venue":null,"work_id":"180c3da8-c3af-4163-93a2-2858781d3db5","year":2003},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.035501Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:16b2d1588174fecd288382080225ab5ac790fbea96edeacf1d968796e09404e3","observation_id":"5f40532c-3202-48f3-b282-e2c934dfd908","resolution":{"observed_at":"2026-08-05T12:23:11.724092Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:11.496471Z","title":"Kutzko and J","venue":null,"work_id":"94a50daa-c26e-4504-9f70-fd4d18a33952","year":1991},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.107782Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:71132978fbc38b052edf432cf81a27eca9e193e6748d1fb75035653503972b15","observation_id":"58827a8c-71c5-4af3-8581-40cd16bcbb21","resolution":{"observed_at":"2026-08-05T12:23:11.566759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:11.278055Z","title":null,"venue":null,"work_id":"623baa34-80cd-41f7-b6c8-ed8ad84663b9","year":1977},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.174650Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:17aea40c68c3d5ed14e73ecb21e02f9b1ab0eb5c5aa1c011d305c84998b7c587","observation_id":"910c8604-6a8c-49fa-8974-97cc0bc7c5db","resolution":{"observed_at":"2026-08-05T12:23:11.414661Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:11.101050Z","title":"2, 381--412","venue":null,"work_id":"7b1c97d0-969a-44a2-904b-b9f032aedc06","year":1980},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.238055Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:09dc4e968e6573a285b4ce68b0769d200358405e7642735859c48a9b54179529","observation_id":"61461e5d-18d9-49fa-a89c-cad79b0b4ddf","resolution":{"observed_at":"2026-08-05T12:23:11.172808Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.05003","last_updated":"2025-07-22T07:09:50Z","snapshot_observed_at":"2026-08-09T17:47:08.925258Z","submitted_at":"2025-07-07T13:38:37Z","title":"Germ expansion for SL(2) in arbitrary characteristics","version":2},"cited_work":{"arxiv_id":"2507.05003","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.05003","snapshot_observed_at":"2026-08-05T12:23:09.296499Z","title":"Germ expansion for SL(2) in arbitrary characteristics","venue":"math.RT","work_id":"fef7f1a4-c41f-4e7b-94f1-cda6b3ab3542","year":2025},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.308203Z"},"links":{"cited_paper":"/paper/2507.05003","citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:ad56e42eda1d80b159d3bc8eedb3749cf676a3222ed2cf446f2ffe3a6f3ea9f3","observation_id":"7275b4bb-3752-4beb-a502-873eddd6953d","resolution":{"observed_at":"2026-08-05T12:23:09.351498Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:10.964407Z","title":"Theory 21 (2017), 590--610","venue":null,"work_id":"3d984700-338e-4cf5-abf3-a178ee421afd","year":2017},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.379569Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:7f155dee2139a6da4574bc0b687303d11c6109068cac92533e46d30a7f1f4662","observation_id":"5ecf7a0f-7ea0-4c7d-a591-1bcb484c7913","resolution":{"observed_at":"2026-08-05T12:23:11.026892Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:10.807059Z","title":"100 (1996), no","venue":null,"work_id":"2864e6ec-2262-4cd9-962e-6381c372260b","year":1996},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.462439Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:972e2ee5d1a915450570583fb93059df48aac77acca2956d8a75b85de75118f0","observation_id":"523839db-6be6-4e25-ad8f-faab9e2b853e","resolution":{"observed_at":"2026-08-05T12:23:10.879055Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:10.627431Z","title":"Theory 25 (2021), 1021--1048","venue":null,"work_id":"870f48cf-f3fb-467e-8bab-24879288bddf","year":2021},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.524495Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:7a26d71cdbb4f577d19fcb552cff9f7ac0b1c0cc3dca0584a941fe6f30c16732","observation_id":"2dc71fdd-d988-472c-8738-4e7b655cb72e","resolution":{"observed_at":"2026-08-05T12:23:10.722734Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:10.490028Z","title":null,"venue":null,"work_id":"682a995f-b2f0-4e60-9306-4c95d1104b7e","year":1996},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.618317Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:0c42d01682799c3937b79cd69b8276758c5ef00804ba53506019bab0693e59e8","observation_id":"9c37e2ef-7d2a-4618-886f-4ee2959d7c08","resolution":{"observed_at":"2026-08-05T12:23:10.542948Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:10.305275Z","title":"Math., vol","venue":null,"work_id":"9d104bdb-e047-45b0-bf8f-a5100f257500","year":2011},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.718316Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:c9cc489dbee4cce9cde5c33d393b4b20d08867a93b797740b0ebb068600faabd","observation_id":"507d3899-53b4-4a54-bd07-93f8344e1e92","resolution":{"observed_at":"2026-08-05T12:23:10.396528Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:10.130198Z","title":"Algebra 377 (2013), 204--231","venue":null,"work_id":"90dc8770-3514-44b9-a249-ce00b267f216","year":2013},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.784835Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:6ec59534541b1fba48f74167901fc4b32534259f5fb9e870256d7ff8181887b6","observation_id":"3a2b1399-f0d6-4d9f-b4d1-57d0aa823866","resolution":{"observed_at":"2026-08-05T12:23:10.223649Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:09.938944Z","title":"Algebra 408 (2014), 1--27","venue":null,"work_id":"4281b739-d5a3-426a-ba29-45c30d079b3a","year":2014},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.852129Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:b9710698deca9c27b7d89f3a072cb285a9b46d0529b716397c743bae17ef2673","observation_id":"e225b2c0-79e3-4439-83a5-1b33c5d798b6","resolution":{"observed_at":"2026-08-05T12:23:10.045300Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:09.750465Z","title":null,"venue":null,"work_id":"88fc696a-3398-4794-8c23-3c313b4e41ab","year":2024},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:08.954850Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:de310964becd69dcccf388adf3d302abbcee6623be0afc510a687623426ca346","observation_id":"780a6645-75d3-4f02-a95d-f4b796ce83a2","resolution":{"observed_at":"2026-08-05T12:23:09.821346Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:09.570137Z","title":"Shalika, Representations of the two by two modular group over local fields, Ph.D","venue":null,"work_id":"a39db75c-39c9-48ab-ae12-0248f72086b9","year":1967},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:09.093746Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:290220ba3e4aab1d65f1610c80a4508ca10bceebab38afbf61daf5fc34da57ba","observation_id":"bcf3d5c0-4949-45d7-8bf7-7e5f621e67ce","resolution":{"observed_at":"2026-08-05T12:23:09.652923Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T12:23:09.408037Z","title":null,"venue":null,"work_id":"5151449f-91e2-4b2e-9b88-3af9a708023f","year":2025},"citing_paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-05T12:23:09.165609Z"},"links":{"citing_paper":"/paper/2509.01843"},"observation_digest":"sha256:28de4a56e5638088e892d91a529115ead5983ef9009701a364fd16052e68386f","observation_id":"41b9c2eb-7d68-495d-a1f9-0d2a6740cee9","resolution":{"observed_at":"2026-08-05T12:23:09.485806Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2509.01843","last_updated":"2025-09-01T23:53:24Z","latest_version":1,"primary_category":"math.RT","snapshot_observed_at":"2026-08-12T15:06:36.258819Z","submitted_at":"2025-09-01T23:53:24Z","title":"Branching rules for irreducible depth-zero supercuspidal representations of $\\mathrm{SL}(2,F)$, when $F$ has residual characteristic $2$"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":1,"verified_fuzzy":11},"total_outbound_references":27},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2509.01843."}