Pseudocontinuity, the Principle of Least Action, and the YangMills Mass Gap from the MigdalWitten Character Expansion

We show that the brane gauge eld of the One-Octonion Framework is fundamentally a discrete hopping amplitude on the G2-symmetric Fano lattice with cell size ℓP , and only appears continuous at macroscopic scales a pseudocontinuous regime arising from the exponential suppression of non-trivial G2 representations in the MigdalWitten character expansion (Migdal 1975; Witten 1991). We prove that the principle of least action is not a postulate but an emergent consequence of this suppression: the trivial at connection dominates the partition function ZK at A ≫ℓ2 P , and its saddle-point condition is precisely δS = 0. The action quantum h = ℓP mP c is the Boltzmann unit of the character expansion; without the discrete lattice, the path integral is undened and the principle of least action cannot function. Applying the MigdalWitten exact partition function on the Klein quartic (G = G2, g = 3, χ = −4) we derive the YangMills mass gap: ∆= 1 2 e2ℓ2 P C2(G2, adj) = 2 e2ℓ2 P > 0, where C2(G2, adj) = 4 is the quadratic Casimir of the adjoint representation, derived si- multaneously from four independent directions: the UV loop regulator (Paper CXXXI), the Migdal Boltzmann suppression rate, the dual Coxeter number h∨(G2), and the Seifert form eigenvalue ratio (Paper CXXVI). Zero free parameters. We identify this as a resolution of the Clay Millennium YangMills mass gap problem within the framework. Contents Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.