Stratified Universes as Local Shtuka Diamonds in the v-Topology: from GLₙ (Lubin–Tate) to Reductive G

We develop a diamond-theoretic geometric avatar of a ``stratified universe'' tower by organizing local Shimura and local shtukamoduli as honest v-stacks on PerfDiam. For G=GLₙ and the basic class bₙ of slope 1/n, with minuscule = (1, 0, , 0), the height-n stratum is identified with the standard local shtuka diamondₙ \;\; Sht₆₋䂸, ₁䂸, ,. e. \ the Lubin--Tate/Rapoport--Zink space in the Fargues--Scholze formalism. For general reductive G/Qₚ and minuscule we define the admissible ``stratified-universe'' stack\ U^adm₆, \;: =\;₁ ₁ (₆, ) Sht₆, ₁, , with a natural forgetful morphism U^adm₆, BunG, whose image is the union of Newton strata indexed by B (G, ). We record the relevant stabilizers Jb (Qₚ) and the Hecke/Grassmannian diagrams governing bounded modifications. On the semantic side, working in the -topos X=Shvᵥ (PerfDiam, S) we show that the ``transfinite jump'' construction built from ¹ of an inverse tower is internal and functorial. We then isolate two natural geometric towers T suitable for this mechanism: (A) congruence-level refinements Uₙ (m) and (B) -adic jet truncations of theB₃ₑ^+-Grassmannian, and prove a commuting level--jet compatibility square. The remaining conjectural step is a realization theorem identifying a specific syntactic UF/HoTT universe tower with the canonical geometric tower in X.