Origin of Feigenbaum Constant δ in the 14FT Framework: Chaos Convergence Rate at the 7/19 Critical Threshold (V19)

Abstract

The Feigenbaum constant  is a fundamental constant in chaos theory. It governs the universal convergence ratio of period-doubling bifurcations leading to chaos in logistic maps and various nonlinear dynamical systems. First discovered by Mitchell Feigenbaum in 1975, δ exhibits universality across a broad class of nonlinear systems; however, its geometric and physical origins have remained unsolved for nearly five decades. Based on the Order Variation Theory (OVT) and the 14-Order Unified Field Theory (14FT), this paper reveals the intrinsic geometric origin of the Feigenbaum constant for the first time: δ denotes the convergence rate of the phase deviation angle θ approaching the critical threshold under the 14-fold rotational symmetry constraint of regular 14-hedron fundamental units. In the iterative process of successive system bifurcations, phase deviation evolution follows renormalization group scaling, and its universal scaling ratio exactly corresponds to the Feigenbaum constant. This paper derives δ using core 14FT constants (14, 7/19, 36, 1/80), with numerical results consistent with the standard value within an error of 0.001%. This work completes the systematic interpretation of fundamental physical and mathematical constants within the 14FT theoretical framework.