The companion paper on glueball masses established the universal formula mdressed N = (2N−1)ΛQCD for N-body pure-gauge Fock states on the TCH gauge web, with confirmed predictions for the 0++ scalar (1660 MeV) and 2++ tensor (2324 MeV) glueballs. The substrate-level Feshbach decay width, however, exhibits a 1/ϵregulator dependence indicat- ing that the discrete 208-state Q-spectrum is a step-function approximation to a smooth con- tinuum. Direct diagonalisation of the local Q-matrix reveals four exactly-degenerate eigen- states sitting rigidly at 1ΛQCD (corresponding to the four vertices of a single C4 plaquette, each hosting a single-parity-violation transition). Combined with strong-coupling thresh- old pinning of the dressed pole, this yields the Threshold Bound State Theorem: restricted to the local Hilbert space of a single TCH unit cell, the substrate-level glueball tree-level decay width is identically zero. The empirically observed scalar-glueball width∼100–300 MeV must therefore arise entirely from non-local macroscopic spatial routing: virtual q¯ q ¯ pairs propagating across multiple TCH cells before hadronising into asymptotic ππ/ηη/K K continua. The physical decay is intrinsically non-local in spacetime, not merely strongly- mixed in Hilbert space. We formalise the macroscopic routing programme as Brillouin- zone integration of the momentum-dependent walk operator WQQ(k) over the simple-cubic gauge web, derive phenomenological consequences (scalar-tensor width hierarchy via D-wave angular-momentum suppression, structural explanation of f0-manifold mixing), and identify two falsifiable signatures distinguishing the framework from standard local-vertex glueball treatments: anomalous lattice-volume scaling of glueball widths, and production-decay cor- relations in J/ψ→γG→γππ.
David Elliman (Mon,) studied this question.