Prussian Visor Cap for Reserve Officer - Mystery

I am most puzzled by this officer cap.... To begin it is in outstanding condition, with only a very slight hint of a moth track on the top. The visor cap has a fine black visor and the State kokarde for a Prussian reserve officer and a Reich kokarde. The side band is black. There are three trim piping bands. Two are red and there is one that is white. It is this white piping that puzzles me. Can any one help with this mystery?

Inside the leather sweatband is complete but shows normal use. The silk liner shows signs of perspiration and hair oil. A fine presentation if we can unravel the mystery.

This is a consignment item.