The f-conjecture for union-closed families

Let $f(n,a)$ denote the optimization quantity defined in the paper for union-closed families on $n$ ground-set elements with maximum element frequency at most $a$. $f$-conjecture. For fixed $a\in\mathbb{N}^+$, one has

$$f(n,a)=f(n+1,a)$$

for every $n\in\mathbb{N}^+$ satisfying $n\geq\lceil\log_2 a\rceil+1$. The conjecture asserts stabilization of this quantity as the ground-set size increases; the paper gives computational evidence, but no general proof is supplied.