Research-Stack/2-Search-Space/README.md

2-Search-Space

Purpose: Quaternion, braid, and manifold primitives for high-dimensional search space navigation.

Depends on: 0-Core-Formalism

Components

Component	Status	Description
PIST	In core/, scratch/	Perfectly Imperfect Square Theory
SVQF	In core/	Spherical Quaternion Vector Field
FAMM	In core/, scratch/	Frustration-Aware Manifold Mesh
Braid Theory	Planned	Topological constraints via braid brackets

Key Optimizations

1. Quaternion Sieve — Counter-rotation as band-pass filter
2. Non-linear Gearbox — φ-based fractional steps
3. Calabi-Yau Compactification — Discarded space folded into compactified dimensions
4. Ricci Flow — Self-smoothing via ∂g_ij/∂t = -2R_ij

Hardware Range

Framework uses fixed-point arithmetic (Q16_16) — runnable on NES (1983) to modern FPGA.