Is there a reversible transform that reduces the number of distinct values? The idea is to take a sequence like $\langle 1,2,3,4 \rangle$ and reduce it to something like $\langle 1,2,2,3 \rangle$, or something similar. The key point is that there are fewer distinct values $\{1,2,3\}$ vs $\{1,2,3,4\}$. In the case that the number of distinct values cannot be reduced, i.e. $\langle 0,0,0,0 \rangle$, it would output the same value $\langle 0,0,0,0 \rangle$. An algorithm that doesn't always decrease the number of distinct values is ok, as long as it doesn't increase the number of distinct values, or as long as it does so only rarely. The output sequence length can be less than or equal to the input sequence length, and the input sequence is bounded by $[0,255]$, but the output sequence need not be, though they should be integers in the range $(-\infty,+\infty)$. Another restriction on the input, if it helps at all, is that it's a restricted growth string. A property of restricted growth strings that might be useful is that the first $0$ in the sequence always comes before the first $1$, the first $1$ before the first $2$, and so on. So a valid sequence might look something like $\langle 0,0,1,0,2,1,1,0,2 \rangle$.

As an example, consider this simple algorithm. First, construct a "dictionary" from the input sequence consisting of all distinct values in the input. So, for the input sequence $\langle 1,2,2,3 \rangle$, the dictionary would be $\langle 1,2,3 \rangle$. It then iterates over the input, doing two things: replacing the input value with its position in the dictionary, and rotating the dictionary left by one. For most inputs, this will do little to reduce the number of distinct values, but for the input sequence $\langle 1,2,3,4 \rangle$, it will output $\langle 0,0,0,0 \rangle$. This can be inverted by applying a similar algorithm. Starting with the same dictionary, iterate over the output, successively replacing the values in the output with the value in the dictionary at that output value's index (that is, if $D$ is our dictionary and $i$ is a value in our output sequence, replace that value with $D_i$) and then rotate the dictionary to the left by one.
There are many reversible transformations that take a list of (let's say) non-negative integers and output a single integer. Here are two examples:
$$
2^{a_1} \cdot 3^{a_2} \cdot 5^{a_3} \cdot 7^{a_4} \cdot 11^{a_5} \cdots \\
\langle a_1, \langle a_2, \langle a_3, \ldots, \langle a_{n-1}, a_n \rangle \cdots \rangle, \quad \langle a,b \rangle = \binom{a+b+1}{2} + a.
$$