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: \( z = x + iy/1 - w \) for sphere point \((x,y,w)\); inverse: \( (x,y,w) = ( 2Re(z)/1+|z|^2, 2Im(z)/1+|z|^2, |z|^2-1/|z|^2+1 ) \). Golden ratio: \( φ = {1+√5}{2} ≈ 1.618 \), reciprocal \( φ⁻¹ = φ - 1 ≈ 0.618 \). Lattice QCD: Euclidean action on hypercubic lattice \( a^4 ∑ₓ L(x) \), 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 \( (z_1-z_3)(z_2-z_4)/(z_1-z_4)(z_2-z_3) \), which is invariant under Möbius transformations. The golden ratio \( φ \) satisfies Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com