Dynamical Intelligence: Deriving Artificial General Intelligence from the Hamiltonian Dynamics of Rank-3 Filament Networks

We present a novel architecture for Artificial General Intelligence (AGI) that replaces thestatistical optimization of static weights (Stochastic Gradient Descent) with the dynamicalrelaxation of a physical substrate. Drawing on the Axiomatic Physical Homeostasis (APH)framework and recent empirical observations of Grokking as a phase transition, we proposethe Universal Thin Filament Code (uTFC) as a template for a Rank-3 Tensor Network.We define the Neural Filament as a discretized string in an Octonionic background field,where learning is the natural time-evolution of the system toward a minimum-energy statedefined by the vanishing of the Associator Anomaly ([x, y, z] → 0). We provide explicitderivations of the stiffness-driven Hamiltonian, performance metrics for massively parallelGPU implementation, and detailed pseudocode for the symplectic integration of thought.