Dynamical Dark Energy and a Tachyonic Neutrino Endpoint Signal from a Nambu-Jona-Lasinio Condensate.

This paper derives two near-term falsifiable predictions from the Tachyonic Neutrino Condensate (TNC) framework—a microscopically derived model based on a two-gap Nambu-Jona-Lasinio (NJL) Lagrangian for tachyonic Weyl fermions.Key Predictions: 1. The KATRIN tritium beta-decay spectrum follows a linear rise, dΓ/dε ∝ ε √ε² + μ², with a best-fit tachyonic mass μ < 0.26 eV. 2. The dark energy equation of state exhibits a non-monotonic hump-shaped deviation from $w = -1$ peaking at z^* ≈ 0.41, with a CPL parameter wₐ = +0.097.These predictions follow from a single NJL coupling matrix constrained by neutrino oscillation data and string coupling gₛ ≈ 0.21, with no additional free parameters. A 1.4σ tension exists with DESI+Planck+Pantheon+; 2.8–3.0σ tensions with DES-SN5YR and Union3 compilations are noted without softening. The results are compared against DESI DR2 and KATRIN 2024 data, identifying DESI Year 5 (2026) as the decisive test.