  We propose a novel Kaluza-Klein scheme which assumes the internal space to be
maximally non-Riemannian, meaning that no Riemannian metric can be defined for
any subspace. Its description is only possible through Double Field Theory but
not within supergravity. We spell out the corresponding Scherk-Schwarz
twistable Kaluza--Klein ansatz, and point out that the internal space prevents
rigidly any graviscalar moduli. Plugging the same ansatz into
higher-dimensional pure Double Field Theory and also to a known
doubled-yet-gauged string action, we recover heterotic supergravity as well as
heterotic worldsheet action. In this way, we show that 1) supergravity and
Yang-Mills theory can be unified into higher-dimensional pure Double Field
Theory, free of moduli, and 2) heterotic string theory may have a
higher-dimensional non-Riemannian origin.
