Mastering Chess with Zero Parameters and Zero Gradient Descent: The Topological Fold as an Exact Evaluation Field

We present the theoretical formulation and empirical validation of a chess engine containing exactly zero tunable parameters and zero trained weights that achieves master-adjacent playing strength through direct topological evaluation of the board's geometry. Rather than utilizing hand-crafted heuristic evaluation functions (such as in classical Stockfish) or deep neural networks trained via reinforcement learning self-play (such as in AlphaZero), the engine evaluates positions by computing the exact rational share of the board's commanded spatial coordinates. In refereed, pinned-binary matches, the engine defeated Stockfish's Elo-1900 setting with a score of 6W-3D-3L (62.5%) and contested Stockfish's Elo-2100 setting, achieving a draw rate of 50% in half its games (1W-6D-5L, 33.3%). Furthermore, we demonstrate that the solved value fields of chess endgames are dyadically smooth: when projected into the Walsh-Hadamard basis, a compact set of only 32 coefficients carries 81.1% to 86.7% of the signed value field energy and reconstructs 92.7% to 95.3% of all exact positions. This provides the first empirical proof that master-level chess play can be derived from first-principles geometry rather than statistical approximation.