  We combine supersymmetric localization with the numerical conformal bootstrap
to bound the scaling dimension and OPE coefficient of the lowest-dimension
operator in $\mathcal{N} = 4$ $\text{SU}(N)$ super-Yang-Mills theory for a wide
range of $N$ and Yang-Mills couplings $g_\text{YM}$. We find that our bounds
are approximately saturated by weak coupling results at small $g_\text{YM}$.
Furthermore, at large $N$ our bounds interpolate between integrability results
for the Konishi operator at small $g_\text{YM}$ and strong-coupling results,
including the first few stringy corrections, for the lowest-dimension
double-trace operator at large $g_\text{YM}$. In particular, our scaling
dimension bounds describe the level splitting between the single- and
double-trace operators at intermediate coupling.
