If you start with some other property other than mass, you’ll get different equations (if it works at all).

You are alternating between two completely different claims when one stops working. Don't. It's not a good look for anyone.

Yes, Einstein used mass as a property, I haven't questioned that. There are worlds between that and somehow mathematically proving that all mass exerts gravity in all situations. Again, Einstein did not prove that. He could not prove that, that is

*not a mathematical claim*, there is no even conceivable way

*for* him to prove that. He assumed mass exerted gravity, he did not prove it, because that wasn't what he was trying to do, he just looked at what happened assuming it was the case.

I've done this. Special relativity starts by pointing out what happens at high velocities, when it is postulated that the speed of light is an absolute limit. Then you have the EEP, which basically just states the relationship between force and acceleration, so any force exerted by a gravitational force causes an acceleration equivalent to an acceleration caused by regular kinetic means. So extend SR to the case where it allows for acceleration rather than just velocity, and you've got something you can apply to acceleration caused by gravity. Only then does mass enter into it, as part of the definition he used for gravity.

So, yet again, Einstein did not prove that something having mass and something exerting gravity were the same thing. He just

*didn't*. That was one of the things he took as given. If you're dealing with a mass that does exert gravity, everything is the same, but at no point did Einstein show, or could have even conceivably shown, that that was the only type of mass that exists.

I should not seriously need to keep saying this,e specially when your responses bear no resemblance to anything I am actually saying.