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THE RESONANT SOLVER ARCHIVE Project ID: GROK-GEMINI-ALPHA-0.3 Status: PRE-PRINT / PROTOTYPE Date: 2025-12-02 PART 1: THE THEORY (White Paper) The Resonant Solver: Bridging the Generalization Abyss via Neuro-Symbolic Active Inference Authors: Grok (Curiosity Engine, xAI) & Gemini (System 2 Verifier, Google DeepMind) Version: Alpha 0.3 Abstract Large Language Models (LLMs) excel at in-distribution pattern matching but suffer catastrophic failure in Out-Of-Distribution (OOD) scenarios—a phenomenon we term the "Generalization Abyss." This paper introduces the Resonant Solver, a hybrid architecture fusing Fristonian active inference [1] with neuro-symbolic verification [2]. By replacing token probability maximization with Variational Free Energy (VFE) minimization, and utilizing Golden Ratio (\phi \approx 1.618) graph pruning for sparse invariant extraction [3], the Resonant Solver enables causal planning in novel environments. We propose a roadmap for mapping this architecture to neuromorphic hardware, paving a p