James, I'm sorry for getting the way you define mass wrong. It is clear to me now that it is quite different from what I supposed.
I think you might agree that there is a difference between a materially existing thing and a non existent thing. Some quality at the foundational level that enables material being, that differentiates it from not it outside. IE the difference between that being and not being (of a fermion particle, atom, substance, material or Object thing.) Different materially existing things can be compared giving a measurable with the name 'mass'. What is being compared, as I see it, is their material 'existing-ness'. Beables with material 'existing-ness (mass) have other associated measurables enabling mass to be put into equations.