When I was an undergraduate I tried to develop a coordinate system for mass, where the center of mass of the universe was the origin, and the axes where the three fundamental forces. Then I found out from a professor that John Wheeler, who was very much alive at that time, had attempted it and I kinda gave up after that.
Later, in graduate school I learned about Wheelers geometrodynamics ("mass without mass"). Talk about paradoxes. I don't know how you resolve all of those paradoxes. I'm guessing that is why he gave up.
If negative mass were confirmed it would be a seismic shift in physics. I'm getting old, and don't keep up anymore. Let me know if it was confirmed, or what other research has been done to substantiate the idea.