The non-cycling conjecture for 4-free Fibonacci sequences

A 4-free Fibonacci sequence is a Fibonacci-type sequence defined by the paper's 4-free divisibility rule. Non-cycling conjecture. With probability $1$, a 4-free Fibonacci sequence does not cycle. The paper's probabilistic model is shown to grow with probability $1$, and this motivates the claim that 4-free sequences do not all become periodic.