This work presents a scientific statement and minimal proof of a structural principle governing the finite closure of structural evolution in systems with limited distinguishability. The framework proposes that in systems with finite informational capacity, the generation of novel distinguishable configurations necessarily decreases over time and ultimately vanishes, leading to the collapse of admissible dynamical directions. As a result, structural evolution terminates in finite time even in the presence of sustained driving forces. A formal structure is provided, including assumptions, lemmas, and a finite-time closure theorem, together with a minimal mathematical proof. The work further outlines a distinction between standard dynamical models, in which growth asymptotically slows but does not cease, and the present framework, which predicts a strict termination of evolution. Potential cosmological relevance is indicated through qualitative consistency with observed suppression of structure growth and plateau-like behavior in large-scale observables.
Logacheva Yulia (Sun,) studied this question.