A no-phantom obstruction for late-time dark energy in IKKT/Yang emergent gravity: a falsifiable w≥−1 prediction and an honest negative result.

This work investigates whether a late-time dark-energy sector built on emergent gravity from the IKKT matrix model and Yang's symplectic framework can reproduce the equation-of-state behaviour currently favoured by DESI DR2. The model is a holographic "frozen-horizon" condensate: a cooling (Gibbons–Hawking) phase transition crystallises the vacuum at a redshift z† and freezes the holographic IR cutoff, producing a de Sitter–like component. The mechanism yields two sharp predictions — a transition at z† ≈ 0.4–0.65 and a present-day equation of state w₀ = −7/9 ≈ −0.778 — together with a structural ceiling: the dark-energy equation of state cannot cross w = −1 (no phantom). We test this against a fully calibrated compressed CMB likelihood (R, ℓ_A, ω_b; Planck 2018 distance priors) combined with the full-covariance DESI DR2 BAO data. Under the complete CMB the data prefer a phantom crossing at ~2.45σ, in a region the model is structurally forbidden to reach. We then examine whether the one available escape — a w < −1 contribution from the higher-spin/torsion modes neglected in Steinacker's C_μλ derivation, or an apparent w < −1 from the IKKT "mirage-matter" modified-Friedmann sector — can be derived. We find it cannot: a fundamental w < −1 is blocked by an IKKT no-ghost theorem, the neglected modes are dark-matter-like (wrong direction), and the mirage sector supplies no apparent phantom either. We therefore report this as a clean, falsifiable result rather than a model claim: this class of emergent-gravity dark energy predicts w(z) ≥ −1 for all z, with w₀ = −7/9 and a transition near z† ≈ 0.4–0.65. A genuine, model-independent phantom crossing established at z ≳ 2 (by Subaru PFS, DESI DR3, Rubin, Euclid, or Roman over 2026–2028) would rule the class out; a confirmation of w ≥ −1 would leave it viable. A full honesty table of what is derived versus assumed or borrowed is included. The record contains the LaTeX source and compiled PDF, the calibrated CMB+BAO likelihood code, the phantom-escape and mirage-matter analyses, and the complete session log. Analysis was assisted by Claude (Anthropic).