  In this work we initiate a positive semi-definite numerical bootstrap program
for multi-point correlators. Considering six-point functions of operators on a
line we reformulate the crossing symmetry equation for a pair of comb-channel
expansions as a semi-definite programming problem. We provide two alternative
formulations of this problem. At least one of them turns out to be amenable to
numerical implementation. Through a combination of analytical and numerical
techniques we obtain rigorous bounds on CFT data in the triple-twist channel
for several examples.
