A Deterministic Solution to Catastrophic Forgetting in Artificial Intelligence: Continuous Learning via the Anti-Collision Identity (ACI) and Spectral Gating

This paper presents a formal resolution to the problem of catastrophic forgetting and the stability-plasticity dilemma in neural architectures. Grounded in the Unified Field Theory-F (UFT-F) framework, we demonstrate that knowledge degradation in Large Language Models (LLMs) is a consequence of non-isospectral weight updates that violate the $L^1$-Integrability Condition (LIC). We introduce the Anti-Collision Identity (ACI) as a universal regulator that enforces spectral stability, ensuring that neural manifolds remain self-adjoint and stable during continuous learning cycles. Empirical validation via the Project Lacia architecture confirms that minimizing internal spectral dissonance ($\kappa_x$) allows for the retention of prior knowledge while simultaneously achieving a 50-53% reduction in computational redundancy. Patent and Intellectual Property Notice: This work provides the empirical implementation of the Sovereign Training and Hallucination-Free Inference claims within Patent Application: 63/954,620 (filed January 2026). The methods described herein—including the Synthetic Spectral Neuron, inverse spectral reconstruction via the GLM transform, and the $O(1)$ Modular Fingerprinting process over $\mathbb{Z}/24\mathbb{Z}$—are the intellectual property of the author.