A First-Principles Paired Signature of the Dark-Sector Attractor: Phantom Dip and Growth Suppression in DESI DR2

This work derives a testable observational signature of the Regime-Limited Dynamical Systems (RLDS) framework applied to interacting dark-sector cosmology.The model predicts a paired signal consisting of a transient phantom dip in the expansion history and a corresponding suppression in the growth sector. The prediction arises directly from the RLDS dynamical structure and remains largely independent of the unknown interaction strength at leading order.Using observational constraints from DESI DR2 and Markov Chain Monte Carlo analysis, we show that current data provide partial support for the predicted behavior in the expansion sector. However, the decisive falsification test of the RLDS framework lies in the growth sector, where the model predicts a characteristic suppression amplitude.This work therefore provides a concrete observational test of the RLDS scenario and outlines the roadmap for future verification using upcoming large-scale structure measurements.