P72: The Maximum Entropy Derivation of CCEGA — Geff (ρ) = GN e^−ρ/ρc is the Unique Maximum-Entropy Gravitational Coupling

We show that Gₑff (ρ) = GN e^−ρ/ρc is the unique function maximizing the Shannon entropy functional SG = −∫p (ρ) ln p (ρ) d (ρ/ρc), where p (ρ) = Gₑff (ρ) /GN, subject to normalization and the single constraint ⟨ρ/ρc⟩ = 1. By the Jaynes maximum entropy theorem, the exponential distribution is the unique distribution consistent with knowing only the mean of ρ/ρc. The maximum entropy is exactly Sₘax = 1 nat = ln e, directly explaining all appearances of Euler's number in CCEGA information theory (P69–P71). The exponential form is not a model choice — it is the maximally ignorant coupling consistent with knowing only ρc. P43 (geometric derivation) and P72 (entropic derivation) are independent and complementary.