The Universal Horizon Conjecture: Geometric and Experimental Evidence for P ≠ NP

We propose a unified geometric framework for computational complexity, supported by extensive experimental evidence across multiple NP-complete problems. At the critical threshold, the state space projected onto local energy descriptors forms a ring-like manifold with inner radius r0 > 0 and angular entropy H → 1. This "computational horizon" geometry is universal across 3-SAT, MAX-CUT, and Vertex Cover, and persists under polynomial reductions. Version 3.0.0 introduces a refined topological analysis using the Wasserstein distance between real and Gaussian null persistence diagrams:- Intrinsic 5D persistent homology (Ripser) with 10 bootstrap repetitions.- Wasserstein distances show a clear quantitative separation: 2SAT (in P) ≈59, 3SAT ≈60, MAX-CUT and Vertex Cover ≈74.- All p-values 0.99 for all problems.2. Wasserstein distance reveals a robust topological distinction between P and NP-complete problems.3. These results refine the Universal Horizon Conjecture: the geometric obstruction is universal, but a more subtle topological signal differentiates complexity classes. Future work will integrate industrial SAT solvers for runtime correlation, increase instance counts, and investigate higher Betti numbers (beta2). All data and code are provided for reproducibility.