If it were an Arbor for a Horizontal Mill, surely it would have a thread on the outer end, where the centre is? (To clamp the sleeves and the cutter against a flange at the MT end).
The fine thread at the MT end is a puzzle, but if it can proved to be parallel, and not bent, I would use it as a test bar, to check / reset alignment of the Tailstock, or to set over the Tailstock for turning a taper. (Hopefully, the Headstock will be aligned correctly, but it could be used to check / reset this also)
Howard