The sharp bounds conjecture for the exceptional-set exponent

Let $T(a,s)$ denote the exponent governing the exceptional-set estimate, and let the lower bounds for $T(a,s)$ be those established in Propositions 1 and 2. Sharp bounds conjecture. Those lower bounds are in fact upper bounds for $T(a,s)$; equivalently, the bounds from Propositions 1 and 2 give the exact values of the corresponding exceptional-set exponents. The conjecture asserts sharpness of the examples in Propositions 1 and 2, including the Szemerédi–Trotter-type and integer-type lower bounds. The source does not state a resolution, so this conjecture remains open.