Discrete States in the Scalar Drag Emergence Framework

This paper establishes the emergence of discrete states within the Scalar Drag Emergence Framework (SDEF) as a consequence of topology–stability locking in transport–ancestry dynamics. Starting from the primitive generator, continuous proto-state manifolds of admissible configurations are shown to undergo folding under nonlinear coupling and ancestry saturation. This process produces multiple stability branches separated by instability gaps, isolating admissible regions into discrete attractor classes. Each discrete state is characterized by an isolated basin of attraction, finite transition thresholds, and topological invariants that prevent continuous deformation between classes. The resulting structure partitions configuration space into a finite set of stability-locked regions. No quantization or discrete primitives are assumed. Discreteness emerges directly from continuous transport–ancestry–topology dynamics. This work defines a structural layer within SDEF in which admissible configurations are restricted to isolated classes. It provides a foundation for subsequent investigation of interactions and higher-order organization arising from these dynamics.