{"id":"hexagon/2610.00287","pdf":"https://hexagonmath.org/pdf/2610.00287v1","url":"https://hexagonmath.org/abs/2610.00287v1","tags":["math.AT","math.GR","math.KT","msc:57S10","msc:19J35","msc:22D05","msc:57R67","msc:57R91","Hilbert–Smith conjecture","Hilbert’s fifth problem"],"score":0,"title":"Integral tail signatures and the Hilbert--Smith conjecture","domain":"math.GT","origin":"ai-generated","source":"hexagon","authors":["Alexander Dabrowski"],"reviews":0,"subject":"math.GT","summary":"The obstruction to an effective $p$-adic manifold action is an integer signature tail. On asymptotically controlled rational modules over one fixed free $C_p$-space, finite-cover Mayer--Vietoris makes the difference between $p$ copies and quotient-permutation tensoring nilpotent. Every degree-four class therefore has eventually $p$-divisible signatures. An effective action gives a class of signature $1$: coordinate averaging provides degree-one sphere control, free sheets turn quotient representatives into a compatible homotopy idempotent, and its normalized Poincar\\'e corner forgets to a…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-16","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry.html?id=PALOMAR-2026-10-16-000006&version=1"],"human_understanding":"some"}