{"id":"openai-math/Global-Arthur-Enhancements-of-Cuspidal-Excursion-Parameters","pdf":"https://github.com/openai/math/blob/main/preprints/Global-Arthur-Enhancements-of-Cuspidal-Excursion-Parameters-October-5-2026/manuscript.pdf","url":"https://github.com/openai/math/tree/main/preprints/Global-Arthur-Enhancements-of-Cuspidal-Excursion-Parameters-October-5-2026","tags":["langlands-program","automorphic-forms","function-fields","representation-theory"],"score":0,"title":"Global Arthur Enhancements of Cuspidal Excursion Parameters","domain":"Number theory","family":"014","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"Under the finite-level Ramanujan–Arthur decomposition stated in Theorem 1.1, we construct a global Arthur enhancement for every occurring cuspidal excursion parameter at a specified full finite level for a split connected semisimple group over a global function field. A single algebraic SL 2 and a commuting Weil centralizer map recover the given parameter by diagonal specialization on the entire Weil group, including inertia. The result does not assert ellipticity, Arthur-packet classification, or a multiplicity formula.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Restricted geometric Langlands, global Arthur enhancements, and generic Ramanujan"}