  We study the spectral representation of finite temperature, out of time
ordered (OTO) correlators on the multi-time-fold generalised Schwinger-Keldysh
contour. We write the contour-ordered correlators as a sum over time-order
permutations acting on a funda- mental array of Wightman correlators. We
decompose this Wightman array in a basis of column vectors, which provide a
natural generalisation of the familiar retarded-advanced basis in the finite
temperature Schwinger-Keldysh formalism. The coefficients of this de-
composition take the form of generalised spectral functions, which are Fourier
transforms of nested and double commutators. Our construction extends a variety
of classical results on spectral functions in the SK formalism at finite
temperature to the OTO case.
