Recursive Amplification Factor

The Recursive Amplification Factor is the dimensionless multiplier by which recursion enhances a baseline quantity, compounding the exponential contributions of successive breakthroughs in the computational case and modifying the critical density in the cosmological case. In the computational reading, each technological breakthrough i adds its own exponential enhancement to computational capacity after its onset time, and the factor is the product of all of them. In the cosmological reading the book gives, a recursive amplification factor Fℜ is embedded in cosmic expansion and multiplies the standard critical density, ρ⨶ = (3H₀²)/(8πG) × Fℜ. The book reads this as showing that cosmological parameters such as the Hubble constant and critical density are not arbitrary values tuned by chance but signatures of recursive amplification, the balance between expansion rate and density encoding the same negotiation between computation and geometry. R(t) = ∏ᵢ (1 + αᵢ × exp((t − tᵢ)/τᵢ)) in the computational form, and Fℜ [∅] in the Critical Density Relation, where ρ⨶ is [𝕄·𝕃⁻³], H₀ is the Hubble constant [𝕋⁻¹] and G is the gravitational constant [𝕄⁻¹·𝕃³·𝕋⁻²]. It connects to the Critical Density Relation, Recursive Amplification Parameters, Recursive Amplification, Hubble Constant Connection and Historical Computational Progression.