Mass Without Mass from a Berry--Shifted SU(3) Holonomy Rotor

Abstract: We identify a local, gauge-invariant mechanism that generates a finite spectral scale in pure SU(3) Yang--Mills theory on a punctured three-ball. Fixing a $\mathbb{Z}_3$ center sector isolates a single gauge-invariant holonomy angle whose Berry shift produces a quantum rotor with strictly nonzero level spacing. Gauss law is enforced by a covariant Dirichlet Helmholtz projector built from the Dirichlet inverse of the covariant scalar Laplacian with relative boundary conditions. The slow holonomy mode is chosen variationally as the minimizer of transverse electric energy under the holonomy constraint, yielding an inertia \emph{independent of the gauge representative} with linear domain-size scaling and a controlled commutator-dominated regime. We prove projector stability and derive an adiabatic variational upper bound on the first positive Yang--Mills eigenvalue, with error controlled by the transverse vector gap of the covariant Laplacian on divergence-free one-forms. A femtometer-scale benchmark at realistic coupling gives an upper bound at a hadronic ($\sim 1\,$GeV) scale. In Wilczek's sense this realizes ``mass without mass'': no explicit mass term or Higgs field is introduced, and the nonzero level spacing is fixed by gauge invariance, topology, and the chosen center sector. The present results are derived on a finite domain; interpreting the length $R$ in Minkowski space requires an additional physical input (e.g.\ as a local confinement length), which we make explicit.