Conditional Inflation from Quantum Entanglement Spacetime Theory

This work establishes geometric (exponential) growth within the Quantum Entanglement Spacetime Theory (QuEST), following the QuEST Execution Protocol (QEP). The result is derived using only two postulates: (1) a bounded-valence quantum hypergraph substrate, and (2) unitary local Pachner 2→3 dynamics. A two-sided face-density condition is introduced, requiring that every reachable triangulation contains a sufficient number of internal triangular faces shared by exactly two tetrahedra. From these ingredients, a constructive recurrence is obtained that guarantees multiplicative growth of the tetrahedron count across dynamical steps. This implies a lower bound corresponding to exponential growth of the QuEST-native scale factor. The analysis is self-contained, employs no external gravitational equations or hidden assumptions, and does not rely on Postulates 3 or 4.