A high-precision result for a full-color three-loop three-point form factor in $\mathcal{N}=4$ SYM

We perform a high-precision computation of the three-loop three-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM. Both the leading-color and non-leading-color form factors are expanded in terms of simple integrals. We compute the complete set of integrals at a special kinematic point with very high precision using $\mathtt{A}\mathtt{M}\mathtt{F}\mathtt{l}\mathtt{o}\mathtt{w}$. The high-precision leading-color result enables us to obtain the analytic form of a numerical constant in the three-loop BDS ansatz, which is previously known only numerically. The high-precision values of the non-leading-color finite remainder as well as all integrals are also presented, which can be valuable for future use.