The non-finite axiomatizability conjecture for inequality over the Weihrauch lattice

Let $\mathfrak{W}$ be the Weihrauch lattice equipped with meet $\sqcap$, product $\times$, and unit $1$, and consider the partial axiomatization of inequalities over $(\mathfrak{W},\sqcap,\times,1)$ given in the paper. Non-finite axiomatizability conjecture. There is no way of extending this axiomatization with finitely many inequalities to obtain a complete system. This conjecture asserts that the valid inequalities of the Weihrauch lattice with meet and multiplication cannot be captured by any finite extension of the proposed axioms; the paper provides no resolution.