The baryon-to-photon ratio η ≈ 6 × 10⁻¹⁰ is one of the most precisely measured cosmological parameters, jointly constrained by BBN light-element abundances and CMB acoustic-peak structure (Steigman 2010; Cyburt 2016). ΛCDM takes it as an observational input. There is no first-principles derivation of why it has this particular value, and the model offers no mechanism that would predict it.
The standard model treats η as a free initial condition of the hot-dense-origin scenario. Once the universe is assumed to begin in a singular hot-dense state, the baryon-photon ratio is whatever the unknown high-energy physics happened to leave behind. The model has no internal mechanism to fix the value, so the question of why it equals 6 × 10⁻¹⁰ is unanswerable from within the framework.
SCT replaces the hot-dense-center with a superluminal collision and the thermalized debris field that became our visible universe. From this single change, the baryon-photon ratio is no longer a free initial condition. It emerges from the geometry of the multi-stage cascade thermalization itself. Paper 4217 derives R_b = 0.2545 ± 0.032 from first principles using three ingredients: SO(3) cascade-mode topology (3 cascade modes), QCD-boundary energy-loss factor (roughly 14% deduction), and photon-heating correction across the QCD transition (factor of 1.57 from the relativistic-degree-of-freedom shift).
The derivation uses no BBN abundances and no CMB acoustic peaks as input. It runs entirely from cascade geometry plus standard Standard Model thermodynamics across the QCD transition. The output R_b = 0.2545 ± 0.032 sits at the 0.17σ agreement level with the observed R_b ≈ 0.260 ± 0.002 from combined BBN + CMB constraints. That agreement is a test passed, not a fit performed. The accompanying derivation produces N_eff = 2.514 ± 0.050 as a companion prediction, which CMB-S4 will test at 17.7σ forecast separation from the Standard Model value 3.046.
The Sakharov conditions for baryogenesis are satisfied through P41 geometric CP violation: the angular momentum vector J = μ(b × v_rel) of the original collision provides a geometric CP-violating term of magnitude roughly 10⁻² to 10⁻³, compared to the CKM value 10⁻²⁰. That is geometric amplification of standard-model CP violation by nearly eighteen orders of magnitude, sufficient to produce η_B ≈ 6 × 10⁻¹⁰ without invoking any beyond-Standard-Model physics. Both the value of η and the mechanism that delivers it follow from removing the hot-dense-center assumption.
A measured R_b outside the 3σ SCT prediction window of [0.158, 0.350] would refute the cascade-geometry derivation. The companion N_eff = 2.514 prediction is the cleaner near-term test: CMB-S4 measuring N_eff = 3.046 ± 0.030 would falsify the cascade-mode topology at 17.7σ.