Jet calculus beyond leading order for the gluon sector

We report results for the order-${C_A}^2{{\alpha }_s}^2$ jet-calculus three-, two-, and one-gluon distributions of the pure gluon singlet channel. Included is an independent calculation of the ${C_A}^2$ part of the gluon→gluon inclusive distribution which has been a subject of controversy for several years. We confirm the results of Furmanski and Petronzio for scheme-independent observables.