So nothing? Ok

Yes, looks like the actual advantage (or disadvantage , depending on who you are) is ensuring that you don’t send a false location to a third party.

You then execute that SNARK on your local device with your current exact GPS coordinates

No, that’s what I’m suggesting. The proposed method in the paper makes no use of GPS, instead it’s some peer-to-peer network.

You mean the hexagon? What prevents you from mapping your GPS output to a hexagon?

We just re-elected a fascist tyrant who wants to close as many avenues of education and free speech which can be used to educate, organize, and publish against him as he possibly can

Can you point me to instances of Trump closing avenues to education and free speech during his first 4 years? Can’t find any, but I’m curious.

How is this better than just mapping GPS data to a hexagon and sending that to the third-party?

Don’t see the point of this standard which runs over an inferior type of networking

Inferior how? Matter is not comparable to Z-Wave. Z-Wave is a mesh network, Matter is just a standard which would allow Alexa, Siri, Google, etc. to control the same devices. To allow Z-Wave like functionality, Matter is able to work on top of Thread, which is in fact superior to Z-Wave.

is brought to us by the companies that created the interoperability problem in the first place

Of course. You don’t want to be the company known for refusing to participate in an open standard, even if you secretly don’t want it to succeed. Anyways, there’s no reason for companies to not want an open standard for controlling smart devices, since it literally helps everyone support more devices for basically no effort once you add support for Matter.