Semantic Concurrency Limits in Large Language Models

Abstract

High-dimensional embedding spaces can host many semantic directions with small mutual overlap. But small overlaps are not zero: when many directions are jointly active, their residual interference accumulates and limits what a finite readout channel can recover. We formulate this as a distinction between \emph{kinetic capacity} -- what the geometry can host -- and \emph{epistemic accessibility} -- what readout can recover. The two sides are summarized by N < exp(c d_{eff} ε^2) for coexistence and σ_{int} \sim \sqrt{k/d_{eff}} for simultaneous readout. Thus dimension acts not merely as storage capacity but as semantic concurrency bandwidth. On this geometric foundation we propose a separate hypothesis: some polysemous tokens may be organized around stable token-associated hinge directions, with sense information carried by low-dimensional subspaces in the hinge-perpendicular carrier. The capacity/accessibility distinction is the main claim; the hinge hypothesis is a stronger, separately falsifiable empirical proposal.