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We compute the two-loop helicity amplitudes for the scattering of fivegluons, including all contributions beyond the leading-color approximation. Theanalytic expressions are represented as linear combinations of transcendentalfunctions with rational coefficients, which we reconstruct from finite-fieldsamples obtained with the numerical unitarity method. Guided by the requirementof removing unphysical singularities, we find a remarkably compact generatingset of rational coefficients, which we are able to display entirely in themanuscript. We implement our results in a public code, which provides efficientand reliable numerical evaluations for phenomenological applications.

Double-Virtual NNLO QCD Corrections for Five-Parton Scattering: The Gluon Channel