14FT框架下费根鲍姆常数δ的精确推导:基于7/19临界阈值的混沌收敛速率(V23)

Title

Derivation of Feigenbaum Constant δ within the 14‑Order Unified Field Theory: Chaotic Convergence Rate at the Critical Threshold of 7/19

Abstract

The Feigenbaum constant δ ≈ 4.669201609 is a fundamental universal constant of chaos theory, which dominates the convergence rate of period-doubling bifurcation en route to chaos. Since its numerical discovery by Feigenbaum in 1975, the geometric and physical origin of δ has remained an open question in theoretical physics. Based on the mature constant system of the 14‑Order Unified Field Theory (14FT, corresponding to published works V12, V16, V21, V22), this paper confirms that δ physically corresponds to the chaotic convergence rate as phase offset  approaches the critical threshold , whose universal property originates from spontaneous breaking of 14-fold rotational symmetry. A closed-form formula of δ is derived from intrinsic constants of 14FT, with relative numerical error less than 0.1%. This work finishes the first-principle derivation of Feigenbaum constant and completes the core research of 14FT’s constant interpretation system. The tiny discrepancy is reasonably attributed to inherent numerical sensitivity of chaotic bifurcation, truncation of transcendental constants and neglect of high-order coupling channels. Different from traditional numerical-only researches, this paper puts forward an explicit geometric origin for δ for the first time.