Exceptional Spectral Geometry of Sedenion Zero Divisors: Clifford Transverse Slices, Sharp Jackson-Riesz Concentration, and Parameter-Free Prime Reconstruction on G₂/SO(3)

We establish the spectral geometry of the zero-divisor variety of the real sedenions. The normal bundle of ZD (S) ≅ V₂ (ℝ⁷) ≅ G₂/SO (3) acts on the annihilator kernel as an irreducible Cl (3) -Clifford module with metric diag (2, 2, 1), yielding the exact transverse slice law E = 4q sin² (t), global Morse–Bott bounds on all of S¹⁴, and normal injectivity radius exactly π/4. For Jackson–Riesz spectral multipliers built from the Riemann zeros we prove the sharp concentration law C (ΛN w) ⁻³ inside the prime-free window δ₀ < log 2 of the Weil explicit formula, and a parameter-free Prime Reconstruction Theorem: the tube kernel recovers the von Mangoldt function to 1. 2×10⁻³ and the Chebyshev function ψ (16) to 0. 025%. Applications to sub-quadratic transformer attention and post-quantum algebraic primitives are included.