The Topological Axion: Algorithmic Relaxation of Chiral Stress via Peccei-Quinn Phase Updates in QGEFT

The current Paper 85 benchmark does not claim that the physical axion of continuum QCD, its mass, or its couplings have been derived from first principles. It does show that the verified QGEFT repository now resolves, in one self-contained Monte-Carlo experiment, the algorithmic core of the Peccei–Quinn mechanism. A heavy particle emitting the Paper-10 chiral flux `F_CP = 0.541` at node 885 of a `41x41` vacuum triggers a spontaneous phase relaxation that locks the source onto `+0.541` (settled values `0.5255 / 0.5410 / 0.5430` for seeds `{7,11,13}`, worst-case deviation `0.0155`; residual local penalty `2.50e-03 / 1.72e-08 / 4.08e-05`). The correction is radiated as a photon–axion wave that crosses all `40/40` shells in `23–32` sweeps at `1.25–1.74` shells/sweep, visible as a sharp diagonal in the space-time plot. The null control (`F_CP = 0`) develops no persistent phase (source tail `0.0095`), establishing that the mechanism is flux-driven. The calibration exposes a deep structural requirement: the axion must carry a *global mass* — a weak Peccei–Quinn potential on every vacuum node (`alpha_vac = 0.4`) — because, without it, the massless phase field cannot propagate a clean correction wave through the network (soft-mode noise and Metropolis barriers block the front). The axion is the pattern of phase updates by which an optimizing vacuum automatically repairs its own CP-violating stress, building directly on the spontaneous CP-violation result of Paper 10, the emergence program of Paper 82, and the Metropolis-acceptance framework of Paper 83.