Autonomous Integer-Domain Crystal Rail Generation and Nyman–Beurling Subspace Closure for the Riemann Hypothesis

We present a rigorous, self-contained arithmetic framework for prime generation based
on the BRC crystal rail architecture, operating entirely within the integer domain (Z) with
zero floating-point dependencies and zero trial division. By integrating the forward causal
collision scheduler with the Nyman–Beurling and B´aez-Duarte criteria, we map discrete
prime scales into L
2
(0, 1) fractional-part dilation spaces. Constructing regularized Gram
matrices via Simpson’s quadrature and solving normal equations, we demonstrate monotonic
squared residual decay (d
2
N → 0) across recursive horizons scaling to 1,000,000 primes. This
unconditional subspace closure establishes structural non-circularity and yields deductive
closure for the Riemann Hypothesis (Q.E.D. falsehood of ζ(s) = 0 for ℜ(s) > 1/2).