Operational Modeling of Membrane Rupture: Application of the Trace-Indexing Framework to Soap Bubble Dynamics

This paper applies the trace-indexing framework (established in Paper A) to the stability and collapse of soap bubbles. We model the soap film as a finite trace carrier that continuously records molecular rearrangements. Rupture is reclassified from a stochastic external event to a deterministic operational failure: collapse occurs when the cumulative magnitude of internal "slip" (\mathcal{S}_n) exceeds a constraint-dependent tolerance (\mathcal{K}). The framework provides a non-temporal, deterministic model for the lifetime of dynamic equilibrium systems.