The Breathing Universe: 807_A Minimal Simulation Framework for the Breathing Universe Model

This paper presents a minimal, explicit simulation framework demonstrating that the Breathing Universe Model (BUM) is computationally realizable under its own ontological and structural constraints. The objective is not physical realism, numerical accuracy, or empirical prediction. Instead, the framework establishes that the full emergence hierarchy claimed by the BUM can be executed within a finite, rule-based system without presupposing spacetime, physical time, particles, forces, or geometry. The simulation is constructed around a single conserved scalar substrate defined over an abstract index set with no topology or metric. Pre-structural asymmetry is introduced without localization, followed by continuous redistribution rules that preserve global conservation. Discreteness arises exclusively through formally defined instability thresholds that trigger snapping events. Operator constraints act strictly as non-generative admissibility filters, selecting persistable configurations without creating structure. Coherence is defined as bounded recurrence of configuration signatures under admissible evolution, and a time-like index is introduced only after coherence exists, defined solely as a recurrence counter rather than a fundamental temporal variable. All simulation steps represent logical ordering rather than physical duration, and all simulation elements are structural placeholders rather than physical entities. The framework explicitly defines internal observables, failure modes, and stress tests to ensure constraint integrity and robustness of the emergence sequence. This work functions as a demonstrability artifact. It does not derive operator algebra, map internal observables to empirical data, or claim physical correspondence. Its role is to establish internal consistency and computational realizability, thereby enabling formal operator analysis and falsification protocols developed elsewhere in the Breathing Universe research program.