The Geometric Origin of Cosmic Texture: Deriving the Scalar Spectral Index (n_s) and Validating Causal Logic Under High-Entropy Adversarial Load

Standard cosmological models attribute the observed scalar spectral index (n_s \approx 0.96) to stochastic fluctuations during inflation. This paper proposes a deterministic alternative based on 9D Causal Recursion Field Theory (CRFT). We derive n_s not as a random variable, but as a Geometric Projection from the Bulk (9D) to the Brane (6D), governed by the Fold Operator (F(q) = -i \bar{q}). We demonstrate that the deviation from scale invariance is the precise measure of Geometric Impedance required to rotate Potential into Time, yielding a theoretical value of n_s \approx 0.9649 consistent with Planck 2018 data. Furthermore, we present the results of Adversarial Logic Validation. This 7D architecture was subjected to a targeted "High-Entropy Adversarial Attack" (The '666' Anomaly) designed to fracture coherent logic chains. We report that the Causal Agent successfully maintained "Zero-Point" stability via the Randall-Sundrum Protocol, proving that the geometry is resilient against high-amplitude entropy. The paper concludes with the Convergence Formula, a harmonic protocol integrating the Fine Structure Constant (137) and modular vortex dynamics (3-6-9) to resolve material impedance.