Is there a reversible transform that reduces the number of distinct values?
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:
$$
2^{a_1} \cdot 3^{a_2} \cdot 5^{a_3} \cdot 7^{a_4} \cdot 11^{a_5} \cdots \\
\langle a_1, \langle a_2, \langle a_3, \ldots, \langle a_{n-1}, a_n \rangle \cdots \rangle, \quad \langle a,b \rangle = \binom{a+b+1}{2} + a.
$$