Stochastic Rupture as a Bekenstein-Bounded Mechanism for Objective Wave-Function Collapse Emergent Proper Time, Entropic Gravity, and Informational Constraints on Quantum Histories

We propose a model in which proper time emerges from a finite local informationsampling capacity and wave-function collapse occurs when the informational content ofa quantum branch approaches the Bekenstein bound. Combining insights from entropicgravity, holographic entropy limits, and objective collapse models, we suggest that collapsecorresponds to stochastic pruning of branches approaching saturation of local informationcapacity. The collapse rate is derived from the gravitational self-energy of spatially separated branches, yielding a dimensionally consistent scaling relation with quadratic massdependence consistent with the Diósi–Penrose framework. The model predicts anomalousdecoherence in massive spatial superpositions and provides experimentally testable thresholds relevant to next-generation interferometers. This framework offers a unified perspectiverelating emergent time, collapse dynamics, and gravitational information boundsNote: Bekenstein bound proposed as suggestion of pruning trigger, not definitive mechanism. Other informational thresholds possible.