Uncertainty Stacks and Entropic Binding in Networks of Overlapping Horizons

This work introduces the uncertainty-stack mechanism within a broader horizon-bounded emergent spacetime framework. In horizon-bounded descriptions of physics, each observer subsystem possesses access only to a finite causal region. The boundary of this region behaves as a causal horizon carrying entropy, which implies that every observer subsystem carries intrinsic thermodynamic uncertainty. When many observers coexist, their causal diamonds overlap and generate shared information regions. These overlaps produce correlations that constrain the uncertainties of neighboring observers. The present work proposes that classical spacetime domains arise when correlation binding across overlap networks becomes strong enough to overcome the intrinsic uncertainty carried by the observers themselves. The framework introduces uncertainty stacks, entropic binding functionals, and a coherence functional that acts as an order parameter for spacetime phases. Classical spacetime is interpreted as a stable thermodynamic phase emerging from overlap networks of horizon-bounded observers. The record includes two files: 1. The main paper introducing the uncertainty-stack mechanism and its thermodynamic interpretation. 2. A supporting toy model demonstrating how coherence thresholds emerge on overlap networks. This work forms part of a broader research program exploring emergent spacetime from observer-bounded thermodynamic systems. Related contributions in the program include work on thermodynamic admissibility constraints (“Iron Laws”), perturbative stability conditions for coherent spacetime domains, and the inevitability of observers in irreversible universes.