Chern-Simons potentials of higher-dimensional Pontryagin densities

We develop a novel and systematic approach to computing the Chern-Simons potentials given the Pontryagin densities in arbitrary even dimensions $ D\geq4 $. Throughout we work with a generic affine connection, that results in a non-vanishing torsion in general and allows for non-metricity, which accommodates the existence of non-trivial Pontryagin densities in $ D=4n-2 \, (n \geq 2) $ dimensions. We outline an algorithm, with its implementation as a code, which lets one to determine the Chern-Simons potential of the Pontryagin density given an arbitrary even dimension.