In my recent work, I’ve explored transforming Boolean satisfiability (SAT) problems into spectral signals using Fourier and Walsh-Hadamard transforms. By applying UMAP on spectral features like entropy, energy, and variance, I've observed that satisfiable and unsatisfiable instances tend to separate in low-dimensional space — suggesting a geometric structure behind solvability.

Could this imply that complexity classes (P, NP, etc.) have a manifold-like topology that can be studied visually?

I’m curious whether others have tried embedding logic or computation into continuous topological or spectral frameworks — and what tools or ideas might help formalize such a space.