Yang–Mills Existence and Mass Gap from Configured Observation Planes

For each N ≥ 2, we construct quantum SU(N) Yang–Mills theory on four-dimensional Euclidean space and prove a strictly positive mass gap on the physical (gauge- and charge-conjugation-invariant) sector. The construction uses Configured Observation Planes (COP) of Spencer (2026a, 2026f): the projective blow-up of the probability simplex, with its tower of exceptional divisors and seam consistency condition, applied to lattice gauge theory via the Weyl-chamber identification of the COP simplex with the gauge group's maximal-torus quotient and charge conjugation as the chart transition. The technical centerpiece is a level-uniform spectral gap for the resulting tower of refined lattice gauge theories, derived from the Π⁰₂-classification of the seam consistency condition. Reflection positivity, Euclidean covariance, and the cluster property follow standard arguments adapted to the tower limit; Osterwalder–Schrader reconstruction produces the Wightman theory with the stated properties.

Note on publication status. This work depends on results from Spencer 2026a, 2026f, and 2026n, currently in peer review or being prepared for journal submission. Submission to a refereed journal is deferred until those foundations are published. The present manuscript is timestamped on Zenodo to establish priority and to make the construction publicly available in the interim.