Collapse Memory Threshold Failure: Fluidization of Structural Systems Through Recursive Field Collapse

This paper introduces the Dimensional Convergence Theorem (DCT), which formalizes how recursive field systems stabilize into discrete dimensional identities. Within the Stick Theory framework, fractal and fractional structures are reinterpreted as transitional residues of unresolved recursion. The collapse intensity scalar \Sigma = \mu \cdot \nu / \tau is used to define convergence thresholds where recursive geometry resolves into whole-number dimensionality. The DCT provides a field-based alternative to compactified string models and offers a deterministic origin for dimension rooted in structural recursion.