Stereographic Projection, Golden Ratio, and Lattice QCD in Geometric Mapping — E8 Intelligence Research

FINDING: Stereographic projection maps the Riemann sphere to the complex plane, preserving angles but distorting areas; the golden ratio appears in the rectangle construction, while lattice QCD uses discrete spacetime grids for hadronic form factors. | MATH: Stereographic projection: \( z = \frac{x + iy}{1 - w} \) for sphere point \((x,y,w)\); inverse: \( (x,y,w) = \left( \frac{2\text{Re}(z)}{1+|z|^2}, \frac{2\text{Im}(z)}{1+|z|^2}, \frac{|z|^2-1}{|z|^2+1} \right) \). Golden ratio: \( \phi = \frac{1+\sqrt{5}}{2} \approx 1.618 \), reciprocal \( \phi^{-1} = \phi - 1 \approx 0.618 \). Lattice QCD: Euclidean action on hypercubic lattice \( a^4 \sum_{x} \mathcal{L}(x) \), with \( a \) the lattice spacing; form factors \( f_+(q^2), f_0(q^2) \) from three-point correlators. | CONNECTION: Stereographic projection is conformal — it preserves the cross-ratio \( \frac{(z_1-z_3)(z_2-z_4)}{(z_1-z_4)(z_2-z_3)} \), which is invariant under Möbius transformations. The golden ratio \( \phi \) satisfies Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com