Curvature-Guided Wavefront Execution for GPU-Accelerated Constraint Satisfaction on the Davis Manifold

Overview This deposit contains the full paper, source code, CUDA GPU solver, benchmark data, and visualizations for curvature-guided wavefront execution — a geometry-aware GPU parallelism strategy for finite-domain constraint satisfaction problems (CSPs) derived from the Riemannian structure of the Davis manifold. Classical GPU approaches to CSPs treat the constraint graph as topologically uniform: checkerboarding assigns equal resources to every vertex, and jackknife branching allocates one execution unit per speculative branch regardless of its likelihood of success. Curvature-guided wavefront execution breaks this uniformity. The local curvature field $K_{\text{loc}}(v)$, defined by the Davis Field Equations, quantifies the constraint density at each point of the discrete Riemannian manifold. The information value functional $V(v)$ identifies which variable resolutions propagate the most information globally. These geometric quantities provide a scheduling signal that directs GPU threads toward high-curvature regions where they have the greatest marginal impact. Method The solver implements a three-phase GPU pipeline: Phase I — Wavefront Constraint Propagation. Bitmask-based arc consistency and hidden-single detection, parallelized across warps. Converges in a single ballot pass per iteration. Phase II — Continuous Manifold Relaxation. Softmax-parameterized probability distributions over variable domains, minimized via curvature-adaptive gradient descent ($\eta_v = \eta_0 / (1 + K_{\text{loc}}(v))$) on the Davis energy functional. Fully data-parallel. Phase III — Curvature-Directed Speculative Branching. Iterative-deepening DFS with branch point selection by $V(v)$, value ordering by curvature gradient, and holonomy-based dead-branch pruning. The trichotomy parameter $\Gamma = m\tau / (\hat{K}_{\max} \cdot \log|S|)$ gates instances into the optimal phase combination: $\Gamma > 1.0$: Phase I alone suffices (constraint propagation resolves the instance) $0.35 < \Gamma \leq 1.0$: Phase I → II → III (manifold relaxation reduces search space) $\Gamma \leq 0.35$: Phase I → III (bypass relaxation; direct curvature-guided DFS) The paper proves that classical heuristics (MRV, degree heuristic, checkerboarding) emerge as degenerate cases of the curvature-guided ordering when specific curvature weight components are set to zero. Results Evaluated on 15-clue extreme Sudoku (66 empty cells, $\Gamma \approx 0.19$) on a consumer laptop GPU: Metric Value Batch throughput 260,042 puzzles/sec Per-instance time (batch) 3.85 µs Single-instance GPU time 20.4 ms (including host overhead) Batch size 65,536 Solve rate 65,536 / 65,536 (100%) Single-instance CPU→GPU speedup 1,226× Batch CPU→GPU throughput ratio > 6 × 10⁶ Head-to-Head Comparison (single 15-clue instance) Solver Solve Time Davis GPU (CUDA) 20.4 ms DLX (Dancing Links) 77.8 ms CP (Constraint Programming) 3,066 ms DFS (Backtracking) 4,195 ms Davis CPU (Python) 25,012 ms Hardware Component Specification GPU NVIDIA GeForce RTX 5070 Laptop GPU Architecture Blackwell (compute capability 12.0) Streaming Multiprocessors 36 CUDA Cores 4,608 Memory 8 GB GDDR7 CUDA Toolkit 13.1 (V13.1.80) Repository Contents: https://github.com/nurdymuny/sudoky-energy curvature_guided_wavefront.pdf — Full 19-page paper with mathematical framework, proofs, worked example, and empirical evaluation curvature_guided_wavefront.tex — LaTeX source davis_solver_blackwell.cu — CUDA GPU solver kernel (~1,500 lines C++/CUDA) davis_solver_gpu.py — Python ctypes wrapper for the GPU solver Makefile — Cross-platform build system (sm_80, sm_90, sm_100, sm_120 targets) davis_solver.py — Davis manifold CPU solver (Python reference implementation) solvers — Five additional CPU solvers (DFS, DLX, CP, Simulated Annealing, MCTS) for comparison visualizations — 9 publication-quality figures + Dr. Blackwell portrait scripts — Benchmark, visualization generation, and utility scripts tests — Unit test suite (30/30 passing) results — Benchmark output data (JSON + Markdown summaries) Key Equations Local curvature (three independent scalar invariants of the constraint fiber bundle): $$K_{\text{loc}}(v) = w_s \cdot \sigma(v) + w_r \cdot \rho(v) + w_c \cdot \kappa(v)$$ where $\sigma$ = saturation (boundary curvature), $\rho$ = scarcity (fiber dimension), $\kappa$ = coupling norm (connection rigidity). Information value (curvature-weighted variable ordering): $$V(v) = \frac{1}{|D(v)|} \left( K_{\text{loc}}(v) + \sum_{u \in N(v)} K_{\text{loc}}(u) \right)$$ Davis energy functional (path through configuration space): $$E[\gamma] = \lambda_1 \int_\gamma ds + \lambda_2 \int_\gamma K_{\text{loc}}(s), ds + \lambda_3 \int_\gamma |\text{Hol}_\gamma(s) - I|, ds$$ Applicability The framework is domain-agnostic. Any CSP expressible as a set of variables with finite domains and pairwise constraints admits a Davis manifold whose curvature field guides GPU scheduling. The paper discusses applicability to: Boolean Satisfiability (SAT) Graph Coloring Scheduling and Timetabling Register Allocation Combinatorial Optimization Related Work Davis, B. R. (2026). The Field Equations of Semantic Coherence: A Geometric Theory of Meaning, Curvature, and Reasoning in Transformer Architectures. Zenodo. https://doi.org/10.5281/zenodo.18511306 Davis, B. R. (2025). The Davis Manifold: Geometry-First Detection with Compositional Error Budgets. Zenodo. https://doi.org/10.5281/zenodo.17642038 B. R. Davis, "The Geometry of Sameness," 2025. #1 New Release in Vector Analysis Mathematics, Amazon. https://a.co/d/02ZjdNaW Patent Notice The curvature-guided wavefront execution method, three-phase GPU pipeline with trichotomy gating, information value functional for variable ordering, and holonomy-based branch pruning described in this deposit are the subject of U.S. Provisional Patent Application "System and Method for Curvature-Guided Wavefront Execution for GPU-Accelerated Constraint Satisfaction on a Discrete Riemannian Manifold," filed February 2026 by Bee Rosa Davis. This deposit is published for purposes of scientific communication and priority establishment. It does not constitute a grant of license, express or implied, to any intellectual property rights held by the author. License Code: MIT License Paper: © 2026 Bee Rosa Davis. All rights reserved. Keywords constraint satisfaction, GPU computing, CUDA, Riemannian geometry, discrete manifold, curvature, wavefront execution, Sudoku, combinatorial optimization, parallel algorithms, Blackwell architecture, Davis manifold, field equations