We formalize the notion of "countable formation" in systems with internal organizational structure. By integrating Hausdorff geometry, Jensen-Shannon information metrics, and thermodynamic free-energy costs, we demonstrate that the emergence of discrete, countable entities is not merely combinatorial but a consequence of non-equilibrium phase transitions. We validate this framework using a unit disk graph realization, showing that the order parameter N exhibits power-law scaling near the critical formation strength sc 0. 39.
Jeong Min Yeon (Sat,) studied this question.