The characteristic bound conjecture for type-two monomial algebras

Let $R=K[x,y,z]$, and let $I$ be an Artinian monomial ideal such that $R/I$ is of type two. The weak Lefschetz property means that multiplication by a general linear form has maximal rank in every degree. Assume that $R/I$ has the weak Lefschetz property in characteristic zero.

Characteristic bound conjecture. Then $R/I$ has the weak Lefschetz property in every characteristic $p>\frac{1}{2}(a+b+c)$.

The conjecture is motivated by computer experimentation and is presented as an improvement over the much larger effective bound established earlier in the paper. The parameters $a,b,c$ occur in the asserted bound, but the supplied context does not define them explicitly for this candidate.