Growth diagnostics on the verified values: the local exponent ratio log2 F(k+1)/log2 F(k) decreases monotonically 2.387, 1.812, 1.602, 1.517 over k=4..8 — well below, and still receding from below toward, the limit ratio 2 that genuinely doubly-exponential growth 2^(c·2^k) would show; simultaneously log2 F(k) exceeds the Elsholtz–Planitzer asymptotic main term (1/5)2^k·log2(1.26408) by a factor shrinking 2.39→1.57 through k=8. Descriptive statistics of the computed range only; no asymptotic inference is claimed.