Unbounded torsion-prime conjecture for syzygies of Veronese embeddings

Let $r\geq 7$. For each $d$, consider the $d$-uple embedding of $\mathbb P^r$ and its Betti table. Unbounded torsion-prime conjecture. As $d\to\infty$, the number of primes $\ell$ such that the Betti table of $\mathbb P^r$ under the $d$-uple embedding has $\ell$-torsion is unbounded. This strengthens the characteristic-dependence prediction by asking for torsion in arbitrarily many prime characteristics as the embedding becomes more ample; the source presents it as a conjectural heuristic motivated by random flag complexes.