DESI BAO 2024 measures the sound horizon at the drag epoch at r_d ≈ 147 ± 1 Mpc, while Planck CMB inference within ΛCDM gives r_d ≈ 150 ± 0.4 Mpc (DESI 2024; Aghamousa 2016). A 2.3σ mismatch in what is supposed to be a single universal standard ruler. The disagreement persists across DESI tracer types and survey-systematic checks.
The standard model treats the BAO scale as set by the pre-recombination sound speed c_s² = 1 / [3(1 + R)] with R = (3/4)(ρ_b/ρ_γ), where the baryon-loading term sits in the denominator (baryon inertia decreases sound propagation). With ΛCDM's assumed plasma composition, this fixes r_d at one specific value and demands every BAO measurement agree.
SCT replaces the hot-dense-center with a superluminal collision and the thermalized debris field. From this single change, the cascade-thermalized plasma evolved with baryons that share bulk motion within their parent comoving frame (P08, P10), and their acoustic contributions add coherently rather than load incoherently. The CAR formula in paper 4216 captures this structural inversion: c_s² = (1 + R_b) / 3 with R_b in the numerator as a coherent-amplification term, replacing ΛCDM's denominator-form baryon-inertia loading (P45).
R_b = 0.2545 ± 0.032 is derived first-principles in paper 4217 from cascade geometry: SO(3) cascade modes plus QCD boundary correction plus photon-heating correction, with no BBN or CMB input. Plugging this into the CAR formula gives c_s² = 0.4182 c², substantially higher than the ΛCDM denominator value. Running this through the modified-CAMB Boltzmann solver yields r_d = 149.1 ± 0.3 Mpc, sitting between DESI's ~147 and Planck's ~150 inferences and reducing the inter-dataset tension from 2.3σ to about 1.1σ (P29, P30 guarantee post-thermalization evolution is origin-agnostic, while the input c_s differs).
PROVISIONAL. Paper 4216 section 2.3 acknowledges a 28 Mpc gap between the simple analytic c_s integral (~178 Mpc) and the modified-CAMB output (149.1 Mpc), most likely because the CAMB patch modifies c_s² in the perturbation equations but not fully in the background-evolution routines. r_d = 149.1 Mpc and H₀ = 70.4 km/s/Mpc remain provisional pending independent third-party verification of the modified CAMB code.
DESI Year 5 measuring r_d > 150.5 Mpc or < 145.0 Mpc at greater than 3σ would refute the CAR prediction directly. Independent re-derivation of CAMB-CAR by a third party producing r_d outside 146 to 152 Mpc would refute the modified-Boltzmann implementation regardless of the analytic CAR formula.