The aim of this paper is to show the existence of a canonical distance \(\mathsf d'\) defined on a locally Minkowski metric measure space \((\textsf{X},\mathsf d,\mathfrak m)\) such that: i) \(\mathsf d'\) is equivalent to \(\mathsf d\) ,
ii) \((\textsf{X}, \mathsf d', \mathfrak m)\) is infinitesimally Hilbertian.
This new regularity assumption on \((\textsf{X}, \mathsf d,\mathfrak m)\) essentially forces the structure to be locally similar to a Minkowski space and defines a class of metric measure structures which includes all the reversible Finsler manifolds and it is actually strictly larger. The required distance \(\mathsf d'\) will be the intrinsic distance \(\mathsf d_\textsf{KS}\) associated to the so-called Korevaar-Schoen energy, which is proven to be a quadratic form. In particular, we show that the Cheeger energy associated to the metric measure space \((\textsf{X}, \mathsf d_\textsf{KS}, \mathfrak m)\) is in fact the Korevaar-Schoen energy.
