The Reason Riemann's Hypothesis is True: ℜ(∆) = d/2

The nontrivial zeros of the Riemann zeta function lie on the line ℜ(s) = 1/2. The reason is two lines long: the zeros are conformal dimensions of massless states, and the conformal dimensions of massless states lie on the principal series. 1. The zeros are conformal dimensions. In Tate's theory the variable s is the weight of a dilation character: it is the conformal dimension Δ at d = 1, so s = Δ. The functional equation ξ(s) = ξ(1 − s) is the celestial shadow involution Δ ↦ d − Δ at d = 1, and its principal series fixed-line is ℜ(s) = 1/2. The explicit formula reads the same object as a spectrum: the prime counting function decomposes into one mode per zero, each zero ρ entering as a mode weighed by x^ρ, with ℜ(ρ) the scaling weight of the mode and Im(ρ) its frequency. The prime sum on the other side of the formula is the two-point function of this one-dimensional theory. 2. The conformal dimension of a massless state lies on the principal series. A massless primary state is a state of the theory only where its norm converges. For the Klein-Gordon inner product the radial integral converges exactly at ℜ(Δ) = d/2 and nowhere else: normalizability admits the principal series Δ = d/2 + iλ, λ real, and excludes every other weight. Therefore every zero, being the conformal dimension of a massless state of the arithmetic theory, has ℜ(ρ) = 1/2. That is the Riemann Hypothesis.