Geometric Derivation of the Yang–Mills Mass Gap from the Static 12³ Tessellation in Geometric Topology 14D (TG): Resolution of the Clay Problem, Proton Radius Puzzle and Multiple ΛCDM Tensions

We derive the Yang–Mills mass gap geometrically from the static 12×12×12 tessellation of the General Theory (TG): Δ_QCD = (P_s P_d / 12) m₂ ≃ 1.478 GeV (0.3σ agreement with experimental glueball data). The same discrete systolic architecture (so(12) ⊕ so(7) ⊕ so(7) → so(26)) resolves the proton radius puzzle (r_p = 0.8769 fm), shows that the Clay Mathematics Institute formulation is incomplete for a discrete substrate, and dissolves multiple ΛCDM tensions (Hubble, S₈, early massive galaxies, lithium, dark-energy dynamics, Axis of Evil) without exotic particles or forces. Redshift is a metric effect of the future evolution of P_s; nucleosynthesis is exclusively stellar; the true age of the cosmos is ∼8.75×10¹⁸ yr. The framework predicts a natural cutoff at 13.7 TeV (L5s monopole) and anisotropy of the speed of light (experimental data forthcoming). All parameters are fixed by the fine-structure constant and a documented thermometric correction to the absolute temperature scale.