Threshold Dynamics in Bounded Systems: A Minimal Scale-Relative Model

This note presents a minimal discrete-time model of a bounded domain governed by local conservation-based update rules. The system exhibits a stable regime followed by threshold instability under sustained inflow, without stochastic dynamics, fine-tuned parameters, or domain-specific assumptions. State variables, parameters, and update rules are explicitly defined, and the model demonstrates that threshold crossing arises as a structural consequence of the asymmetry between accumulation and expansion rates. The primary contribution is a demonstration of logical possibility: that boundary-mediated regime transition can emerge from minimal conservative assumptions. This work is intended as a foundations note and does not propose a physical theory.