GPU-accelerated constraint satisfaction guided by intrinsic Riemannian curvature. A geometry-aware solver that crushes the world's hardest Sudoku at 1,226× speedup over Python CPU — demonstrating that constraint satisfaction is fundamentally a geometry problem.
Computational resources should flow toward regions of highest curvature — where they have the greatest marginal impact on constraint resolution. Classical GPU approaches treat every vertex equally. The Davis manifold tells you where the hard work is, before the work begins.
The solver implements a three-phase CUDA pipeline derived from the Davis Field Equations. A trichotomy parameter Γ automatically classifies each instance by its geometric complexity and routes it to the optimal phase combination — no manual algorithm selection required.
Classical heuristics — MRV, degree heuristic, checkerboarding — all emerge as degenerate cases of the curvature-guided ordering when specific curvature weight components are set to zero.
The constraint graph induces a discrete Riemannian manifold in the sense of Regge calculus — not a metaphor, but a genuine geometric structure with a metric tensor, connection, and holonomy group. The local curvature field measures three independent scalar invariants of the constraint fiber bundle.
The trichotomy parameter $\Gamma = \dfrac{m \cdot \tau}{\hat{K}_{\max} \cdot \log |S|}$ classifies instances by the ratio of assigned structure to geometric complexity, automatically gating them into the optimal phase combination.
Evaluated on 15-clue extreme Sudoku (66 empty cells, Γ ≈ 0.19) — the hardest class of well-posed puzzles. All 11 hardest-known instances solved in under 9ms on a consumer laptop GPU (NVIDIA RTX 5070, Blackwell architecture).
Sudoku is just one demonstration. The Davis Manifold framework applies to any finite-domain constraint satisfaction problem.
See the full framework →