Kontsevich–Zagier-type conjecture for multiple harmonic values

Consider the domains and summands described in the source: domains are formed from finite disjoint unions and finite products of sets defined by chains of equalities and inequalities among positive integers; summands are generated by powers, binomial coefficients of affine functions, and factorials; and the resulting sums are viewed in $\mathbb{Q}_p$. Kontsevich–Zagier-type conjecture for multiple harmonic values. Every equation expressing the vanishing of a $p$-adically and weight-adically convergent sum of $\mathbb{Q}$-linear combinations of multiple harmonic values can be obtained using these domains and summands, together with equalities of summation domains, equations for summands, changes of variables, and operations from the complete topological-field structure of $\mathbb{Q}_p$. This proposes an elementary-generation principle for all such relations.