Radical Compression in Maximal Prime Gaps: Asymptotics and the Transient Stability Illusion

We prove that the radical compression ratio q = log(∏Cᵢ)/log(rad(∏Cᵢ)) of a prime gap of length g near X satisfies q = 1 + log(g)/log(X) + O(1/log X), using Legendre's formula and Mertens' estimates. In the Cramér regime g ~ c·log²X, this yields q = 1 + 2·log(log X)/log(X) + O(1/log X) → 1 as X → ∞. The apparent "stabilization" of q near 1.30 observed for X ≤ 10^7 is therefore a transient artifact of the notoriously slow decay of log(log X)/log(X) — a cautionary example of how the iterated logarithm can create illusory numerical plateaux in computational number theory. Verified against all 21 maximal prime gaps (g ≥ 20) up to 10^8, with the asymptotic formula matching observed values to within 3.5%. Source code and data: https://github.com/Ruqing1963/radical-compression-prime-gaps This is Paper XI of the Titan Project.