\section{The wall, stated precisely}\label{ms:sec:wall}
Everything proved in Part~II --- the bounded smooth part, the variance identity and its constants, the exact intra-orbit fourth moment, the decoupling of the conductor-$1$ orbit, the prime-arrival invariance of the cross term, and (modulo Conjecture~\ref{ms:conj:r4}) the full Gaussian fourth moment --- concerns averages over $x$ with the truncation $D$ fixed. The Riemann hypothesis \eqref{ms:eq:rh} is a different kind of statement: a \emph{pointwise} bound along the moving diagonal $D=x$, one value of $\widetilde\Phi$ per window, with no average left to take.

It is worth spelling out what a full Gaussian theorem would and would not give. If the tails of Section~\ref{ms:sec:gauss} were a theorem uniform in $D$ --- $P\bigl(|\widetilde\Phi_D|>\lambda\cdot0.166\sqrt D\bigr)\le Ce^{-\lambda^2/2}$ --- then $\lambda=\sqrt{2(1+\varepsilon)\log x}$ and a union over windows would give
\[
|\Phi(x)|\le0.24\sqrt{x\log x}\qquad\text{outside a sparse exceptional set},
\]
the Gaussian-heuristic version of RH, with a logarithmic loss and almost everywhere. Two gaps separate this from RH, and they are the whole distance. \emph{Uniformity}: our moments average at fixed $D$; the diagonal couples the argument to the truncation. \emph{The exceptional set}: no mean-value control excludes isolated large values, and a zero off the critical line is precisely a measure-zero phenomenon in this metric --- it would show in $\Phi$ as a coherent oscillation of size $x^{\beta}$ visible only at the right scales, costing nothing in any fixed moment. Part~I proves a no-go theorem (Section~\ref{ce:sec:limits}) on the other side of the same coin: weights indistinguishable from the primes' up to $q^{\delta-1/2}$ satisfy every such average statement and still carry an off-line zero, so no argument built from size estimates and fixed-order moments alone can close \eqref{ms:eq:rh}; the exact identities --- \eqref{ms:eq:anchor} here, $\Lambda=\mu*\log$ there --- must enter beyond their first moments. What Part~II adds to that program is the exact second-moment structure \eqref{ms:eq:diag}, the identification of all the observed constants, and one new finite problem, Conjecture~\ref{ms:conj:r4}, that can be attacked without meeting the wall.