Yang–Mills Existence and Mass Gap as a Pre-Formally Void Problem: A Constructibility-Criterion and Gauge-Bundle Dissolution

Ungrounded companion note to the QGD / MPDT Problem Register. Not assigned a portfolio (P-series) number. The Yang–Mills existence and mass gap problem asks for a rigorous quantum Yang–Mills theory on ℝ⁴, satisfying the Wightman axioms for a compact simple gauge group, with a spectral mass gap Δ > 0. This note argues that both halves of the problem are pre-formally void under Quantum-Geometry Dynamics' Constructibility Criterion (P40). The existence question fails on two independent grounds, neither reducible to the other: the Wightman axioms quantify over continuum objects (Minkowski space, an infinite-dimensional Hilbert space, Schwartz-space test functions) that fail FC1, and — separately — the gauge-bundle structure specific to this theory is a second, independent continuum import, since gauge symmetry is a derived encoding of preonic momentum conservation rather than a foundational structure requiring its own continuous fiber (P30). The mass gap question requires no separate dissolution: it is a spectral predicate asserted of the same Hilbert-space object already shown void, and inherits that voidness exactly as the companion Navier–Stokes note's blow-up predicate inherited FC1 failure from ℝ³. Both results are explicitly Level 1, conditional on QGD's axioms, and say nothing about the problem's status under ZFC. A specific caution is stated and defended: QGD's own confinement mechanism (P25) and discrete momentum law (P11) are real, independently established physics that answer QGD-native questions, and must not be presented as solving, or as a mechanism for, the Wightman-spectral mass gap — doing so would be a category error, supplying a positive mechanism for a predicate on a nonexistent object. Companion to: QGD / MPDT Problem Register; structurally parallel to the Navier–Stokes companion note (same series).