Persistence-Driven Interaction Dynamics in the Scalar Drag Emergence Framework

This work derives interaction dynamics in the Scalar Drag Emergence Framework (SDEF) directly from the primitive generator governing compatibility and ancestry evolution. No independent interaction primitives are introduced. Instead, interaction emerges from the structure of a persistence field Π = ∇·(g ∇φ) − λφ³ where the transport metric g = M|∇φ|/(1 + φ²) encodes ancestry-modulated transport and scalar drag. A central result is that directional evolution follows gradients of persistence, such that structures evolve toward regions of higher persistence. Local interactions are governed by the primitive kernel I = ∇φ₁·∇φ₂, which modifies transport and thereby shapes the persistence field. Interaction outcomes are therefore not determined locally, but by the global structure of Π and its gradient ∇Π. The framework establishes a hierarchical dynamical structure:local interaction → transport modification → persistence field → directional evolution. Five interaction regimes arise naturally from the structure of Π: corridor-mediated propagation, confinement, opposing-gradient instability, threshold transformation, and ancestry-dominated alignment. These regimes are not independent mechanisms but distinct configurations of the same underlying dynamics. Interaction asymmetry emerges without intrinsic charges through the ancestry compatibility term χ = sign(∇φ · ∇M) which determines whether transport reinforces or opposes existing ancestry. As a result, interaction behavior depends jointly on instantaneous configuration and historical structure, establishing the inherently non-Markovian nature of the framework. This work shows that forces are not fundamental entities but emergent directional biases in persistence dynamics governed by ancestry-modulated transport and scalar drag. Together with prior packet–corridor results, this formulation provides a unified, closed description in which existence, persistence, interaction, and transformation arise from a single generator. The persistence field Π is identified as the central organizing quantity for interaction dynamics, providing the foundation for subsequent developments in simulations, large-scale structure, and cosmology within SDEF.