G2bar and the E8 Mass Gap: Casimir Scaling, Z2 Correction and Cosmological Implications

We adopt Ḡ₂ = 1.9758 as a conditional working value for the E8 Yang–Mills coupling parameter, obtained from Casimir scaling (QCD analogy) with a Z2/Immirzi-type correction, g² = (4π/h∨)(1 − ln 2/h∨) = 0.4092, and propagate it to all downstream observables. This single conditional value unlocks: the vacuum energy density ρ_vac = 6.79 Λ_E8⁴ (+3.55% vs. observation), the Hubble constant H₀ = 68.6 km/s/Mpc (postdiction, +1.76%), the asymptotic expansion rate H∞ = 56.8 km/s/Mpc (prediction), and the E8 mass gap Δ = 2.64 meV via Frasca's infrared mapping (whose Clay-level existence proof remains open, as stated). The de Sitter quantities (T_dS = 1.93×10⁻³⁴ eV, S_dS = 3.2×10¹²², horizon radius 1.63×10²⁶ m) follow. The program's own dual-cone conjecture (Δ/Λ = 2.122, requiring Ḡ₂ ≥ 3.39) is honestly refuted for this value, and Frasca's ratio c = 1.886 is adopted. The cosmological-constant hierarchy 10⁻¹²¹ is exhibited as the cascade ratio to the fourth power, C_vac·(Λ_E8/M_Pl)⁴, reducing six ΛCDM inputs to two external inputs (Λ_E8, Λ_UV) plus one conditional parameter (Ḡ₂). Every quantity is classified by epistemic status; five falsifiable entries (PRED-077 to PRED-081). The single decisive arbiter is a lattice E8/G2 computation: Ḡ₂ ≥ 3.39 would reopen the cone, and any lattice value of the coupling directly tests the whole chain.