Scale-Dependent Clustering Suppression from Late-Time Dark Matter Pressure: CLASS Implementation, Validation Protocol, and First Results

This technical report presents a CLASS Boltzmann code implementation of a pressure-bearing dark matter model derived from the BigSnap scalar field framework, together with a pre-committed validation protocol and first numerical results.The model is characterized by a time-dependent dark matter equation of state w_dm(a) = −r·a³/(4Ω_R0) and an effective perturbation sound speed c_s²(a) = |w_dm(a)|^γ. The scaling c_s²(a) ∝ a³γ produces a late-time, scale-dependent Jeans suppression of structure growth while leaving CMB scales unaffected.First numerical results: For r = 4×10⁻⁴ and γ = 1.5, the implementation yields σ₈ = 0.780 compared to the ΛCDM reference σ₈ = 0.822 (5.1% suppression). A full (r, γ) parameter scan identifies a continuous viable region for S₈-level suppression near γ ≈ 1.5, r ≈ 3–5×10⁻⁴.Validation checks passed: Resolution stability across Nloga = 3000/6000/12000. Redshift evolution consistent with late-time activation (0.0% at z=2, 5.1% at z=0). CMB TT deviation 0.007% (threshold 1%). fσ₈ deviation 0.9% at z=0.5, within current ~2–4% measurement precision. BAO peak shift 0.009%, an order of magnitude below current survey sensitivity. Background evolution implemented analytically as a function of scale factor and is gauge-independent at the background level. Sub-horizon analysis shows gauge corrections < 0.0002% at the σ₈-dominant scale.Scope: The model passes all implemented internal validation checks and is consistent with current observational precision for key summary observables. This does not constitute a claimed resolution of the S₈ tension, nor does it replace a full likelihood analysis against combined datasets. The correct interpretation is that the mechanism produces suppression consistent with the observed S₈ discrepancy for r ≈ 3–5×10⁻⁴ at γ ≈ 1.5, with no detected conflicts at current precision. This deposit records the pre-committed predictions, validation protocol, and first results prior to any likelihood analysis.