PsiQRH Riemann Sphere — Mathematical Framework & Benchmarks

Complete mathematical framework for the PsiQRH Riemann Sphere language model. Hidden states h in R^d are mapped to S^2 via stereographic projection z = (x+iy)/(1+z_w), rotated by Mobius transformation w = (az+b)/(cz+d) with (a,b,c,d) in SL(2,C) — the double cover of the Lorentz group SO(3,1) — and projected back to R^d. 96 trainable parameters (0.0003% of 32.1M total) implement 12 RiemannSphere modules (2 per layer x 6 layers). Attention remains softmax(Q*K^T)*V O(n^2); the sphere acts as a geometric regularizer. Benchmarks across 5 domains (code, poetry, math, dialogue, science) plus GSM8K reasoning, against GPT-2 (124M) and random baseline. GPU: RTX 5060 Ti.