AI Capability Driven by Access Structure, Not Just Scale.

The prevailing belief, the Platonic Representation Hypothesis, suggests that as AI models scale, their internal representations converge towards a shared understanding of reality. This paper introduces a new perspective, the Capability Convergence Hypothesis, which posits that under a fixed per-token inference budget, representational convergence does not automatically lead to capability convergence. Instead, capability converges towards a specific class of "access-complete hybrid" architectures. These hybrid architectures combine a compressive O(1)-state channel with a scalable verbatim-index channel, allowing them to overcome fundamental resource limitations (Shannon, horizon, and circuit walls) that hinder purely scaled models. The research anchors this principle on a "Newton's-apple problem" witness task and provides information-theoretic lower bounds and pre-registered experimental results. These tests demonstrate a significant "scissors gap" where hybrid models dramatically outperform attention-only models for exact retrieval, confirming that access structure is a critical determinant of capability.