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

We show that G_eff(ρ) = G_N e−ρ/ρc is the unique function maximizing the Shannon entropy functional S[G] = −∫p(ρ)ln p(ρ) d(ρ/ρc), where p(ρ) = G_eff(ρ)/G_N, 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 S_max = 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.