The Yang-Mills Mass Gap as Topological Crystallisation: Mechanism, Value, and Falsification from the Bootstrap Framework

The Yang-Mills mass gap problem asks whether pure SU(N) gauge theory has a strictly positive lowest excitation energy. Seventy years of perturbative methods have failed to resolve this because the mass gap is a non-perturbative, topological phenomenon inaccessible to Feynman diagram expansion. We provide the mechanism, the value, and six falsifiable predictions from the Bootstrap Universe framework. The strong coupling constant is derived by two independent routes. Route 1 (geometric cavity): αs = 1/(3π − 1) = 0.11870, from the cavity factor of three-phase Eisenstein closure. Route 2 (spectral complement): αs = H_colour / (8 − λ₁) = 0.11882, where H_colour is the harmonic weight of the six colour primes and λ₁ = 5 − √5 is the colour-mode eigenvalue of the icosahedral Laplacian. The normalisation 8 − λ₁ = 2φ² = 3 + √5 is the spectral complement — the phase space available for colour-mode coupling within the 8-gluon structure — identified as the spectral back-EMF of the colour modes against the driving field. Both routes match the PDG world average αs(MZ) = 0.1180 ± 0.0009 and agree with each other to 0.1%. No free parameters. The mass gap is identified as the crystallisation energy Δ = 12 × EG = 292.62 MeV — the energy released when the Delta(1232) locks into the proton ground state through phason condensation. Confinement is the impossibility of defining a fractional topological charge on S³/2I. Six falsifiable predictions are provided, each capable of destroying the entire framework.