  We present non-linear uplift ansaetze for all the bosonic degrees of freedom
and dual fields in the 7-sphere reduction of D=11 supergravity to maximal SO(8)
gauged supergravity and test them for the SO$(7)^{\pm}$ invariant solutions. In
particular, we complete the known ansaetze for the internal components of the
metric and 4-form flux by constructing a non-linear ansatz for the internal
components of the dual 7-form flux. Furthermore, we provide ansaetze for the
complete set of 56 vector fields, which are given by more general structures
than those available from standard Kaluza-Klein theory. The novel features
encountered here have no conventional geometric interpretation and provide a
new perspective on Kaluza-Klein theory. We study the recently found set of
generalised vielbein postulates and, for the 7-sphere compactification, we show
that they reduce to the E7(7) Cartan equation of maximal SO(8) gauged
supergravity in four dimensions. The significance of this framework for a
higher-dimensional understanding of the embedding tensor and other gauged
maximal supergravities is briefly discussed.
