Persistence Filtering of the Multiverse

String theory predicts an immense landscape of possible vacuum states — on the order of 10^500 or more — each representing a mathematically distinct universe. This so-called “string landscape” presents a challenge: which of these vacua are physically viable, and why did our universe emerge among them?We propose a solution grounded in Persistence Theory, integrated with Terence Tao’s structural mathematics. By applying a thermodynamic-informational filter to the landscape, we derive a selection mechanism based on reversibility efficiency (η) and entropy cost, yielding a finite subset of persistent, viable universes. This approach reframes multiverse selection as a function of informational coherence and entropy management — not anthropic reasoning.