Capability from Access Structure, Not Scale: Lower Bounds and Pre-Registered Tests for Hybrid Sequence Models

Abstract

arXiv:2607.14144v1 Announce Type: new Abstract: The Platonic Representation Hypothesis (PRH) holds that as models scale, representations of heterogeneous networks converge toward a shared model of reality. We propose its sequel and boundary, the Capability Convergence Hypothesis (CCH): under a fixed per-token inference budget, representational convergence does not entail capability convergence. Capability instead converges toward a class, the access-complete hybrid: any architecture holding both