Symplectic Monodromy and Horizontal Sato--Tate for Reciprocal Qudit Wigner Functions

For odd primes p, reciprocal-phase qudit states lead, away from one exceptional phase-space row, to the two-parameter exponential sums: Tₚ(A,B) = ∑t ≠ ± 1 eₚ(A t/t²-1 + B t) A companion paper established the exact Wigner dictionary, generic cohomological rank four, an exact fourth-moment factorization, and a conditional USp(4) interpretation. In this sequel we prove the missing monodromy and equidistribution theorems. The involution t ↦ -t gives an alternating self-duality, so the geometric monodromy lies in Sp₄. The previously obtained fourth-moment factorization has exactly four top-dimensional geometric components, which yields the geometric moment M2,2=3 over finite extensions. A Fourier–Deligne specialization at $B=0$ has rank drop 4 → 3 and forces a symplectic transvection, hence infinite monodromy. Larsen's alternative, in the form recorded by Katz–Tiep, then gives: Ggeom = Sp₄ After a geometrically constant weight normalization, the arithmetic and geometric monodromy groups coincide. Uniform complexity bounds from quantitative sheaf theory imply horizontal equidistribution of Frobenius conjugacy classes in USp(4) as p → ∞. Consequently, the normalized Wigner values converge to the standard USp(4) trace law. Since the normalized traces are uniformly bounded, the mana asymptotic becomes unconditional: M(Rc) = 1/2 log p + log(4096/525 π²) + o(1) The monodromy proof uses the earlier fourth-moment factorization but is independent of the $K3$ and CM-modularity results of the companion paper.