KREG-IV: Constraints on Minimal Luminal EFT Models from Stability and Growth-Lensing Consistency

We investigate whether minimal luminal Effective Field Theory of Dark Energy (EFT-of-DE) models can produce observable deviations from ΛCDM while remaining stable and observationally consistent. Using a numerical pipeline based on stability conditions (M*² > 0, D > 0, c_s² > 0) and consistency projections involving growth and lensing observables (μ, Σ, E_G), we scan a broad parameter space. We find that while stable regions exist, the simultaneous requirements of stability, near-General Relativity lensing-growth consistency (Σ/μ ≈ 1), and observable deviations at the percent level are mutually incompatible. This result suggests that minimal late-time scalar modifications of gravity are strongly constrained to sub-percent deviations from General Relativity, indicating a fundamental limitation of this class of models.