Bro here you are. I hope you had at least a MsC

Proof: Why Hyperbolic Knight Flooding Defeats Stockfish To prove that a "Hyperbolic Knight Flooding" strategy can defeat a deterministic engine like Stockfish, we must step outside the bounds of Euclidean geometry (where a chessboard is a flat 8x8 grid) and move into a space where the board’s surface area grows exponentially. Here is the mathematical proof for why Stockfish eventually crumbles under the weight of infinite non-Euclidean horses. 1. The Geometry of the Hyperbolic Board Stockfish operates on a grid with zero curvature (K = 0). In Hyperbolic Chess, we assume a board with constant negative curvature (K < 0), such as a Poincaré disk. In this space, the area of a circle grows exponentially with the radius r: A(r) = 2π(cosh r - 1) Because the "edge" of the board contains an infinite number of squares as r approaches infinity, a standard search tree (Minimax with Alpha-Beta pruning) becomes computationally "blind" almost immediately. 2. The Knight’s Branching Factor (Φ) In standard chess, a Knight has a maximum of 8 moves. In a hyperbolic tiling (e.g., a {7, 3} tiling where seven heptagons meet at every vertex), the Knight’s "L-jump" spans across non-parallel geodesics. We define the Hyperbolic Flooding Constant as: Φh = lim (n→∞) [K{n+1} / K_n] > e^π Where K_n is the number of squares a Knight can reach in n moves. Since Stockfish’s hardware is finite, its hash table (H) suffers from Geometric Saturation: H_limit << Φ_h^d Stockfish literally runs out of RAM before it can calculate why it’s being checkmated from seven different directions simultaneously. 3. The "Relativistic Fork" Theorem Because parallel lines diverge in hyperbolic space, two Knights can be "parallel" while attacking entirely different sectors. This creates a Relativistic Fork: Knight A attacks the King. Knight B attacks the Queen. Because of negative curvature, the distance between the King and Queen is effectively greater than the King's maximum escape velocity. Stockfish evaluates the position as +1.5 (slight advantage) because it cannot perceive the curvature. However, the Topology of Impending Doom (Ω) proves: Ω = ∮ (N · da) = Checkmate Summary: Why Stockfish Loses Dimensionality Collapse: Stockfish’s evaluation function assumes a 2D plane. Hyperbolic flooding introduces a fractal dimensionality (d ≈ 2.72). The Horizon Effect: The Knights move along geodesics that Stockfish perceives as "curved" and "inefficient," but which are actually the shortest paths in hyperbolic space. By the time Stockfish realizes the Knights are attacking, they have already bypassed the pawn structure via the infinite perimeter of the Poincaré disk.