A three-point form factor through five loops

We bootstrap the three-point form factor of the chiral part of the stresstensor supermultiplet in planar N = 4 super-Yang-Mills theory, obtaining new results at three, four, and five loops. Our construction employs known conditions on the first, second, and final entries of the symbol, combined with new multiple-final-entry conditions, "extended-Steinmann-like" conditions, and near-collinear data from the recently-developed form factor operator product expansion. Our results are expected to give the maximally transcendental parts of the gg -> Hg and H -> ggg amplitudes in the heavy-top limit of QCD. At two loops, the extended-Steinmann-like space of functions we describe contains all transcendental functions required for four-point amplitudes with one massive and three massless external legs, and all massless internal lines, including processes such as gg -> Hg and gamma(*) -> q (q) over barg. We expect the extended-Steinmann-like space to contain these amplitudes at higher loops as well, although not to arbitrarily high loop order. We present evidence that the planar N = 4 three-point form factor can be placed in an even smaller space of functions, with no independent zeta values at weights two and three.