The Critical Angle of Projection: A Geometric Answer to Hilbert's Eighth Question

Hlbert's eighth problem (1900) is commonly misremembered as simply "prove the Riemann Hypothesis.'" His actual question was deeper: What rigorous principle guarantees that the discrete primes obey a stable infinite law compatible with continuous analysis? We provide a geometric answer within the Kosmoplex axiomatic framework. From seven axioms, the five Peano axioms augmented by two Hilbertian axioms (Triadic Closure and Total Function), emerges a forced incidence structure: the Fano plane superimposed on Pascal's triangle. We identify a critical angle $\theta_c = 360^\circ(1/7 + 1/137) = 54.0563^\circ$ at which the projection from 8-dimensional octonionic space to 4-dimensional spacetime achieves simultaneous coverage of all four division algebra basins while maintaining spectral emergence. This critical angle is \textit{unique}: the basin window collapses as $O(1/N)$ under scaling, pinching to a single point in the limit. As $N \to \infty$, the asymptotic critical angle converges to $360^\circ(144-\gamma)/959 = 53.84^\circ$, where $\gamma$ is the Euler--Mascheroni constant encoding the discrete-to-continuous matching cost. We conjecture that this critical angle is the geometric manifestation of the Riemann critical line $\Re(s) = 1/2$, the principle that forces stable transition from discrete to continuous. We do not claim a proof of RH; we identify the structural necessity that any such proof must satisfy.