  A central aim of theoretical physics is to account for the structure of
matter at the most elementary level as underlying the Standard Model of
particle physics, and ideally also as a basis for a substantial dark sector, as
distributed in 4-dimensional spacetime. A broad class of theories augment the
global 4-dimensional spacetime arena itself to a higher-dimensional spacetime
structure, with the properties of matter then deriving from the properties of
the extra spatial dimensions. We motivate an alternative approach in which we
begin with the local structure of 4-dimensional spacetime and augment the local
form for a proper time interval. The symmetries and properties of the residual
components, over the local 4-dimensional spacetime form, are found to exhibit
appropriate features to account for the visible Standard Model sector while in
parallel direct connections can also be identified with dark sector models.
