> Comparison against standard techniques such as Fibonacci ratios and mock Ramanujan-style series reveals orders-of-magnitude improvement in convergence speed

Given that computing The n-th term involved computing the factorial of 60 times n, I don’t see that as being interesting. If I define

  FF(n) = F(n!) ÷ F(n! - 1)

With F(n) the nth Fibonacci number, that converges way faster than F(n), too.

Also, given that AIs can hallucinate: does this provably converge to √5?