Bootstrapping the Four-Point NMHV Stress-Tensor Form Factor

We bootstrap the two-loop four-point next-to-maximally helicity-violating (NMHV) ratio function for the chiral stress-tensor form factor in planar maximally supersymmetric Yang-Mills theory (sYM) at the symbol level. Starting from an ansatz built from NMHV leading singularities and the known two-loop five-point one-mass integral function space, we impose finiteness, dihedral symmetry, parity and Galois symmetry, spurious-pole cancellation, collinear limits, and finally triple-collinear consistency, which together fix the result uniquely. We then subject the answer to independent soft and double-soft checks. The resulting symbol contains 78 letters, all drawn from the 88-letter alphabet previously identified for the four-point MHV form factor through four loops. This provides the first multi-loop result for a non-MHV form factor, and direct evidence that the 88-letter alphabet extends beyond the MHV sector, which may provide the natural universal alphabet for four-point form factors. Our result supplies new data for the study of physics and mathematics of multi-loop form factors including the antipodal duality, as well as their relations to Higgs-parton amplitudes in QCD.