Bit Density Evolution

Bit Density Evolution is the growth of bit density over time as an exponential doubling law multiplied by a recursive amplification factor for architectural breakthroughs. The book treats exponential scaling as more than a doubling law: each technological breakthrough amplifies the base trajectory, so paradigm shifts become part of the quantitative history of computation. The amplification is the Recursive Amplification Factor R(t) = ∏ᵢ₌₁ⁿ (1 + αᵢ × exp((t − tᵢ)/τᵢ)), a product over breakthroughs with strengths α₁ = 10.2 ± 1.5 for GUI emergence, α₂ = 98 ± 15 for network recursion, α₃ = N⦿² for parallel processing and α₄ = 2^(N⊡⊹) for quantum systems. Bit density is one factor of computational capacity in the Bit Curve predictions. The formal statement is ρ▣(t) = ρ₀ × 2^((t − t₀)/T⇈) × R(t), where ρ▣(t) is the bit density at time t, ρ₀ the initial bit density (10³ bits·cm⁻², circa 1971), t₀ the reference time, T⇈ the historical doubling period (1.8 ± 0.3 years) and R(t) the recursive amplification factor. Dimensions: ρ▣(t) and ρ₀ [𝕃⁻²], t, t₀, T⇈ [𝕋], R(t) [∅]; the book's check is valid and verified. It connects to the Recursive Amplification Factor, Bit Curve, GUI Computational Enhancement, Network Computational Enhancement and Computational Capacity.