The Prime Structure of Electromagnetic Constants

We systematically rewrite eighteen electromagnetic quantities—from the Bohr radius to the quantum Hall conductance—in a canonical form built from the Riemann zeta value ζ(−3) = 1/120 and the primes {2, 3, 5}. Starting from the ζ-Wyler identity α = 3²ζ(−3)^{1/4}/(2⁴π^{11/4}), every quantity Q with mass dimension d decomposes as Q = mₑᵈ × f(2, 3, 5, π, ζ(−3)), requiring only one experimental input (the electron mass) plus pure mathematics. Three structural results emerge: a Rationality Theorem (α⁴π¹¹/ζ(−3) = 3⁸/2¹⁶), a Mirror Theorem linking quantum-vacuum α to thermal-vacuum ζ(4) via the functional equation, and an mₑ-Separation Principle. All eighteen theoretical values match CODATA 2018 to within 0.30–3.05 ppm, governed by a single offset Δα/α = 6.1 × 10⁻⁷. This is the companion paper to "The Arithmetic of Light" [doi:10.6084/m9.figshare.31744981].