The Kochenov Matrix A Geometric Framework for Physical Constants

This work presents a complete geometric framework in which the fundamental physical constants — the gravitational constant G, the speed of light c, Wien's displacement constant b, the fine-structure constant α, and the Planck scale — are shown to be projections of a single discrete geometric matrix. The matrix is built from the following anchors: 31 — spatial anchor (Mersenne prime, 25−125−1) 144 — Fibonacci node (F12F12, the only square in the Fibonacci sequence) 720 — synchronization operator (6!, spinor cycle) ϕ — golden ratio 5 — golden radical Δ — residual vacuum tension (≈−1.33956×10−8≈−1.33956×10−8) CORE RELATIONS phi^12 / sqrt(5) = 144 + 1/720 + Delta G c^2 ≈ 31^3 * 90 * sqrt(5) G_Koch = (31^2 / (144 + 1/720 + Delta)) * 10^(-11) c^2 ≈ 2790 * phi^12 * 10^11 b_geom = (90 / 31) * 10^(-3) alpha_geom^(-1) = 137 + 31/1000 + 5/1000 KOCHENOV LENGTH AND MASS (NATURAL UNITS) L_Koch = 31 / sqrt(144 + 1/720 + Delta) ≈ 2.5833 M_Koch = 1 / L_Koch ≈ 0.3871 ELECTRON MASS (NUMERICAL APPROXIMATION) m_e ≈ m_p * (1/720) * (1/2.531) * (1 - alpha) where: 2.531 = 5/2 + 31/1000 UNIFIED OPERATOR O = 90/31 = 720/(8 * 31) = 6! / (2^3 * 31) MIRROR PAIR Theta^2 = G c^2 / (31^4 * sqrt(5)) ≈ 90/31 lambda_0 = 31/90 Theta^2 * lambda_0 = 1 All decimal scaling factors (10^-11, 10^11, 10^-8, 10^-35) are shown to be anthropic artifacts arising from Earth-based unit definitions (meter from the meridian, kilogram from water, second from the solar day). The framework replaces continuous spacetime with a discrete lattice bounded by L_Koch and M_Koch, offering a possible route toward avoiding singularities in gravitational models.