Access Structure, Not Scale, Drives Model Capability – New Hybrid Sequence Bounds
The paper proposes the Capability Convergence Hypothesis, claiming that under a fixed per‑token inference budget, a model’s capability is determined by having both a compressive O(1) state channel and a scalable verbatim‑index channel. Pre‑registered experiments confirm the predicted performance gap, demonstrating that only hybrid sequence models can breach the three proved resource walls.