Novikoff et al.'s bounded-increment conjecture for flashcard games

Let $T_i(n)$ denote the first time card $i$ is seen for the $n$th time. Novikoff et al.'s bounded-increment conjecture. We have

$$T_i(n+1)-T_i(n)\leq 2n$$

for all $i$ and $n$. The paper states that this conjecture remains quite open; the preceding results establish quadratic growth but do not improve bounds on these differences.