The Retentive Fixed Point at Gamma ≈ 0.64: Structural Saturation, Flux Inversion, and the Late-Time Cosmological Regime

This work demonstrates that the observed growth index γ ≈ 0.64 is a retentive infrared fixed point emerging from structural saturation in the Λψ–Ξ sector. Starting from a minimal retentive Lagrangian, we derive a scale-independent modification of the matter growth equation, establish the attractor behaviour of the fixed point, and show that the late-time universe transitions into a regime of flux inversion and stationary Δψ dynamics. The framework yields explicit, falsifiable predictions for Euclid DR1, providing a structural alternative to ΛCDM and modified gravity.