  The combination of integrability and crossing symmetry has proven to give
tight non-perturbative bounds on some planar structure constants in
$\mathcal{N}$=4 SYM, particularly in the setup of defect observables built on a
Wilson-Maldacena line. Whereas the precision is good for the low lying states,
higher in the spectrum it drops due to the degeneracies at weak coupling when
considering a single correlator. As this could be a clear obstacle in restoring
higher point functions, we studied the problem of bounding directly a 4-point
function at generic cross ratio, showing how to adapt for this purpose the
numerical bootstrap algorithms based on semidefinite programming. Another tool
we are using to further narrow the bounds is a parity symmetry descending from
the $\mathcal{N}$=4 SYM theory, which allowed us to reduce the number of
parameters. We also give an interpretation for the parity in terms of the
Quantum Spectral Curve at weak coupling. Our numerical bounds give an accurate
determination of the 4-point function for physical values of the cross ratio,
with at worst 5-6 digits precision at weak coupling and reaching more than 11
digits for 't Hooft coupling $\frac{\sqrt{\lambda}}{4 \pi} \sim 4$.
