Although the theory is promising, the duo point out that they have not yet completed its proof. The theory uses a technical procedure known as renormalization, a mathematical way of dealing with infinities that show up in the calculations.
So far Partanen and Tulkki have shown that this works up to a certain point—for so-called ‘first order’ terms—but they need to make sure the infinities can be eliminated throughout the entire calculation.
“If renormalization doesn’t work for higher order terms, you’ll get infinite results. So it’s vital to show that this renormalization continues to work,” explains Tulkki. “We still have to make a complete proof, but we believe it’s very likely we’ll succeed.”
That’s not how physics works. If you are really interested in such issues read a book on foundations of physics or history of physics to see how physicists arrived at the most famous equations (Einstein,Dirac, Schroedinger or Newton), they are basically “bets” guided by physical and mathematical assumptions, but that is far from being “proved” or “derived”, there are no rigorous proofs or derivations involved. The uncertainty remains until an experiment or observation confirms it or rejects it. There’s no such a thing as “proving” a physical theory, for the simple reason that any physical theory works in a limited regime or range of validity. Newtonian gravitation and General Relativity are both valid and succesfull theories within their range of validity, but they contradict each other mathematically, in one theory gravity is a scalar field and in the other is a tensor field, so you could use the mathematics of one theory to refute the other, so it makes no sense the concept of proving a physical theory mathematically. You only try to axiomize a theory once is well established, but it’s irrelevant concerning its validity.