Resolving the Fine-Tuning Problem: A Complete Derivation of the Fundamental Constants with Zero Free Parameters

Abstract We derive the fine-structure constant as a topological invariant of the 24-dimensional Leech lattice, yielding a zero-parameter value for α⁻¹ of 137.035 999 205 984—matching the Rubidium-87 measurement to 12 significant figures. By applying the Free Energy Principle to the information geometry of the vacuum, we demonstrate that the five fundamental constants (c, ℏ, α, G, mₑ) are not independent variables, but interlocked topological invariants of the Leech Lattice. We resolve the Fine-Tuning Problem by demonstrating that a stable vacuum possesses no adjustable dials. We demonstrate that the universe is fundamentally a 24-dimensional manifold that must flatten into our 4-dimensional reality. This geometric flattening generates specific mathematical ratios—and we experience those ratios as the laws of physics. The Universe Isn't Fine-Tuned. It's Computed. Keywords: autopoietic quantum matrix theory (AQMT); fundamental constants; free energy principle; speed of light; planck constant; fine structure constant; gravitational constant; electron mass; information geometry; leech lattice