Complete Computation of All Three-Loop Five-Point Massless Planar Integrals.

We calculate all three-loop, five-point, massless planar Feynman integral families in the dimensional regularization scheme. This is a new milestone in Feynman integral computations. The analysis covers four distinct families of Feynman integrals for this configuration, for all of which we derive the canonical differential equations. Our results also confirm a prediction on the three-loop five-point alphabet. The boundary values are analytically determined. These differential equations offer a promising route toward efficient high-precision evaluation of the integrals. Our work establishes the foundation for next-to-next-to-next-to-leading-order calculations of the production of three massless final states, as well as corresponding bootstrap studies in gauge theories.