Resolve the Cho–Ham–Lee cone exponent conjecture

Determine whether the piecewise formulas for s_n(α) and β(α,Γ^n) proposed by Cho, Ham, and Lee give the sharp exponents in the ranges of α not already proved or disproved, namely whether s_n(α) equals the stated three-piece formula and β(α,Γ^n) equals its equivalent three-piece formula for n≥4.

Background

The cited conjecture proposes explicit formulas for the optimal fractal restriction exponent s_n(α) and the equivalent cone Fourier-decay exponent β(α,Γ^n) when q=2 and n≥4.

The paper verifies only a special case for n=4 and 19/5≤α<4, while showing that the formulas are false in a range when n≥6. Outside the ranges known to be true or false, determining the sharp exponents remains unresolved.