The Ξ-Constant: A Universal Theory of Emergence

This work introduces the universal, dimensionless Xi Constant, a quantitative measure of stability and emergence for systems of any kind. Xi is defined using the fundamental axioms of information capacity I_k, dynamic decay rate D_m, and normalized extreme-value pressure DeltaE in [0,1]. The constant is given by:

Xi(S) = t_P * DeltaE(S) * min(I_k(S)/D_m(S), 1/t_P)

where t_P is the Planck time.

Xi quantifies the efficient occupation of a system's stability space and reaches a universal fixed point Xi_* = 1 at maximal emergent order. The theory links microscopic dynamics to macroscopic structure, provides a scale-invariant perspective on emergence, and is fully consistent with known physical constants and fundamental informational limits.

Applications are discussed across physical, biological, social, and cosmological systems. Limitations regarding operationalization are outlined, and directions for simulations, empirical measurements, and interdisciplinary research are proposed.

The Xi constant provides a robust, universal framework that allows stability and emergence to be quantitatively compared without replacing domain-specific mechanisms.