Non-almost-realizability conjecture for the partition numbers

For $n\geq1$, let $p(n)$ be the number of partitions of $n$, meaning unordered sums of positive integers.

Partition-number conjecture. The sequence

$$(p(n))_{n=1}^\infty=(1,2,3,5,7,11,15,\ldots)$$

of partition numbers is not almost realizable.

This conjecture concerns the realizability framework developed for combinatorial sequences. The source motivates it by computational evidence, while its status remains unresolved.