Dimensional Emergence and Collapse Resolution: A Structural Alternative to Compactified Space

This work introduces a structural field-based model for dimensional emergence without requiring speculative compactification. Within the Stick Theory framework, dimensions arise naturally through recursive collapse memory fields rather than external coordinate assumptions. Additionally, the Collapse Resolution Principle is proposed, explaining why physical systems resolve into discrete whole-number structural states rather than fractional artifacts. Together, these mechanisms offer a parsimonious alternative to conventional higher-dimensional models, unifying quantum, dimensional, and macroscopic structural behaviors under a single collapse memory framework. Testable predictions regarding quantum decoherence, dimensional drift, and particle evolution are outlined.