Structure-Entropy Synchronization at K = 1 in π-Driven Systems

The circular constant π appears ubiquitously in mathematics, physics, and information sys- tems. In this paper, we investigate whether π also acts as a structural equilibrium point in dynamic systems governed by structure–entropy interactions. We propose that K = 1, defined as the ratio between the logarithmic growth rates of entropy and structure, emerges naturally as an attractor in π-based systems. We build upon the framework of the Exponential Law of Structural Conservation (SCI), where K = 1 is defended as a conserved, structural–information ratio under exponential growth processes [1].