The contemporary pursuit of Artificial General Intelligence (AGI) faces a "glass ceiling" in abstract visual reasoning, epitomized by the stagnation of Large Language Models on the ARC-AGI benchmark. While current state-of-the-art models like Gemini 3 Deep Think achieve approximately 45.1% on ARC-AGI-2, they lack the capacity for rigorous, multi-hop counterfactual reasoning. This paper introduces the Theoretical Optimization of Perception and Abstract Synthesis (TOPAS), a convergent neuro-symbolic architecture that achieves an Exact Match (EM) score exceeding 69% on the ARC-II evaluation set. TOPAS rejects the tabula rasa assumption of pure deep learning, instead proposing a "Canonical Unified Model" grounded in the Free Energy Principle (FEP) and Integrated Information Theory (IIT). The architecture features three novel subsystems: * The Hebbian Triad: A separation of concerns into Perception (ObjectSlots), Reasoning (NeuroPlanner), and Memory (VSA World Models), bound by a type-safe "Sacred Signature" interface. * The Hypothesis Market: An internal economic system based on Hanson’s Logarithmic Market Scoring Rules (LMSR) that arbitrates between neural intuition and symbolic logic. * Thermodynamic Refinement: An Energy-Based Refiner (EBR) that treats solution generation as a thermodynamic settling process, minimizing a global free energy functional to ensure logical consistency. Furthermore, the system leverages the Muon optimizer for geometric regularization of sparse networks and Test-Time Training (TTT) via Low-Rank Adaptation (LoRA) to generalize to out-of-distribution tasks. Empirical validation on a corpus of 121 tasks confirms that TOPAS successfully bridges the gap between statistical approximation and algorithmic synthesis.