Entropy–Area Relations in the Quantum Entanglement Spacetime Theory (QuEST)

This paper gives a self-contained, constructive proof of an entropy–area relation inside the Quantum Entanglement Spacetime Theory (QuEST). Regions are modeled as parts of a labeled hypergraph. The main result shows that the entropy associated with a region’s boundary is always bounded by the smallest cut that lies entirely inside that region. The bound includes an exactly computable, non-negative “gap” that measures any excess interior capacity; the gap disappears precisely when the interior cut’s capacity matches the boundary. All quantities are defined from QuEST’s own primitives, and the result is checkable with a single weighted min-cut computation, requiring no statistical, thermodynamic, or geometric assumptions. The paper also states properties such as monotonicity and refinement invariance, and it documents compliance with the QuEST Execution Protocol for full symbolic transparency.