Conjecture on sharp bounds for diagonal equations with restricted solution sets

Let $d_1,\dots,d_s$ be the exponents of a diagonal equation, and suppose there is a bound for the number of its solutions with restricted coordinates, explicitly expressed in terms of $d_1,\dots,d_s$. The paper's preceding Problem asks for such a bound in terms of $d_1,\dots,d_s$ and $q$, and for the conditions under which it is attained. Conjecture on extremal diagonal equations. If such a bound exists, then the diagonal equations attaining it are precisely those satisfying the conditions of Theorem~3.03. This conjecture concerns the unresolved problem of determining sharp bounds and their equality cases for diagonal equations with restricted solution sets.