The Order Variation Theory of Euler's Constant γ and Its 14FT Origin: Continuous Limit Residual of Intrinsic Order Loss (V17)

Abstract

Euler’s constant  is a fundamental mathematical constant derived from the convergent difference between the harmonic series and the natural logarithm, which is widely applied in mathematical analysis, number theory, and quantum statistical physics. However, its underlying geometric origin and physical implication have long remained unsolved. Based on the Order Variation Theory (OVT) and the 14-Order Unified Field Theory (14FT), this paper proposes a novel interpretation: γ is the convergent integral value of the global projection residual generated by the intrinsic order loss  of tetrakaidecahedron fundamental units during the transition from discrete three-dimensional infinite tiling to continuous field. It originates from the intrinsic information dissipation between discrete grids and continuous fields formed by the 36-edge channel network of fundamental units in spatial tiling. This paper derives constrained analytical formulas for γ based on the inherent geometric parameters of 14FT. The research realizes a paradigm shift of Euler’s constant from a pure mathematical definition to a geometric characterization of cosmic intrinsic order loss, and improves the unified interpretation system of fundamental mathematical constants.