The w = −1 Prediction from TTOE: Dark Energy as the Vacuum of the E8 Sector — A Theorem from Lorentz Invariance, Confrontation with DESI DR2, and Falsifiability by Euclid

In the TTOE framework, dark energy is identified with the vacuum energy of the E8 Yang–Mills sector, in the sense of Sakharov's induced gravity. Under the single premise that this vacuum is a Lorentz-invariant condensate with no rolling scalar field, Lorentz invariance forces T_μν = −ρ_vac g_μν, hence w0 = −1 and wa = 0 exactly — with zero free parameters and without using the value of the infrared scale Λ_E8. This is a prediction by exclusion: the theory structurally forbids dynamical dark energy unless a scalar sector absent from its field content is added (ledger ID PRED-086). The prediction is confronted with DESI DR2 (14M galaxies and quasars, percent-level BAO over 0 ≤ z ≤ 2.5): (i) the robust geometric probes (BAO alone, constant w) are fully consistent with w = −1; (ii) the 4.2σ frequentist tension with DES-SN5YR traced back to supernova calibration errors, since corrected (DES-Dovekie); (iii) an independent Bayesian reanalysis with corrected calibration (Ong, Yallup & Handley 2026) modestly prefers ΛCDM over dynamical dark energy (ln B = −0.01), and the paper also discusses Efstathiou's 0.04-mag offset, Cortês & Liddle's parametrisation critique, and Turyshev's systematics analysis. The paper separates the falsifiable prediction (Claim A: w = −1, derived) from the numerical postdiction of ρ_vac (Claim B: conditional, blocked by the mass-gap problem), and states the decisive forthcoming tests: DESI DR3/DR4 (expected 2026–2028) and Euclid (FoM > 400). If the preference for wa < 0 consolidates at high significance with systematics under control, the premise is falsified.