We present a formal and testable framework for a polar color-weight web architecture intended as a candidate substrate for structured internal cognition in artificial general intelligence (AGI). The proposal synthesizes ideas from four conceptual sources: Xi-Theory(distinction, structuring, integrity), Innernet (network dynamics, return to baseline), Absolibrium (spectral selection, attentional emphasis), and TurboQuant (polar encoding, angular preservation). The architecture is defined as a discrete-time dynamical system over a state space of polar variables: radial weight (integrity), angular coordinate (color), and spectral channel, with interactions governed by a directional kernel that favors angular affinity and weight-based dominance. Self-centers are defined as persistent, high-weight, recurrently dominant configurations. The paper provides explicit assumptions, candidate stability heuristics, a staged implementation pathway, a falsifiable experimental program, and a clear separation between formal results, hypotheses, and open questions. The framework does not claim to solve the philosophical hard problem of consciousness, but offers a mathematically precise and empirically testable architecture for investigating self-organizing internal coherence.