Scale-Dependent Clustering Suppression from Late-Time Dark Matter Pressure: A CLASS Boltzmann Code Implementation and Validation Protocol

This technical report presents a complete CLASS Boltzmann code implementation of a pressure-bearing dark matter model derived from the BigSnap scalar field framework. 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, where r = λ_Λ/λ_m is a coupling ratio and γ ∈ [1, 2] parameterizes unknown scalar field microphysics.The c_s²(a) ∝ a³γ time dependence produces a late-time, scale-dependent Jeans suppression: σ₈-scale modes enter pressure support at z ~ 1–2 while CMB primary anisotropy scales remain unaffected throughout.Version 2 adds first numerical results. For r = 4×10⁻⁴ and γ = 1.5, the implementation produces σ₈ = 0.780 compared to the ΛCDM reference σ₈ = 0.822 — a 5.1% suppression. Three validation checks passed: the result is numerically stable across resolution levels Nloga = 3000, 6000, and 12000; suppression builds correctly from 0.0% at z=2 to 5.1% at z=0; and the CMB TT spectrum deviates from ΛCDM by at most 0.007%, well within the 1% threshold. A gauge-invariant verification via CLASS's dark fluid sector was attempted but failed due to numerical singularity in the NDF15 solver for negative time-varying w(a). This is a toolchain limitation, not a model falsification. A custom solver is required for full gauge-invariant confirmation, deferred to future work.The viable window for S₈ resolution (4–7% suppression) corresponds to r ≈ 3–6 × 10⁻⁴ at γ = 1.5. This does not constitute a claimed resolution of the S₈ tension. The correct statement is: the mechanism produces suppression consistent with the observed S₈ discrepancy for this parameter range.This deposit records the pre-committed predictions, validation protocol, implementation code changes, and first results. The mode-entry prediction (Figure 1), unit test suite, and parameter scan grid were all specified before the first CLASS run.