The state already funds science. So the answer is 'nothing'.
I just keep hoping for a breakthrough in this discussion with you.
"The state" does not exist in nature, it is a creation of humans. I'd even acknowledge it is a necessity for humans living in close quarters, say more than one little band inside a few hundred square miles even. It is necessary because we prefer laws over continual warfare, or battles to the death over our place on earth. So we formally agree to respect some rights we can agree on, and support some kind of government that can serve as a guarantor of those rights and an arbiter of conflicts. It saves us a lot of trouble.
But historically, we have had problems with governments that go wrong. The honcho with the army decides he can do what he wants. March our boys off to his own wars, and enlarge upon his own realm in the manner of a tyrant.
There was one surprising development in history you seem to have missed, at least so far as recognizing the value it introduced into the scheme of things. The American Revolution was undertaken by some classically-educated elites on a relatively isolated continent, who chaffed at not being respected as British subjects with the same rights folks in England had fought for, the Magna Carta. When they rebelled against the greatest armed power on the face of the planet, they were able to articulate their grievances in a manner that many ordinary folks understood, and were willing to support and fight for, and they succeeded, then negotiated amongst themselves to agree upon a fundamentally limited type of government that was designed to restrict the various possible ways governments have gone wrong throughout history.
fun stuff, this Magna Carta so valued by British subjects was a negotiated settlement to armed conflict almost a thousand years ago. It created a certain set of "rights" for people, and a certain set of limits on the Monarchy.
There has been, however, a certain tension between folks who see a government as a tool suitable to their ideals of things, ever since the concept of human rights achieved any recognition in the Western world. Throughout history, when any government has existed, there have been "Statists", the people who believe the government is wonderful or authoritative, or superior to individuals. It is an inconvenience to these folks to make certain allowances for human rights. Most do, in some way or another, but there is continual chaffing at the inconvenience. Even the most absolute of tyrants will try to put out a good line of propaganda, in hopes of calming the masses of ordinary folks. Some will even offer bread and milk, free. Or whatever else it may seem to take to keep the people in line.
So I do this little bit about contrasting the objectives of statists with the things I would like to see as recognized human rights, like the right to ask questions and look for solutions to problems, for both collective groups of humans and individuals.
Science was not state supported when it emerged from the "dark ages" of medieval Europe, neither was it state-supported when it thrived in the Middle East during those European dark ages. It was not state-supported in Greece or Rome, either. I guess maybe I don't know everything, after all, but it seems to me that probably no great civilization of the past ever had a state-supported system of enquiry that sought to independently, objectively, develop a body of demonstrable verifiable technology or science. Probably, the small number of folks who had such a thirst for knowledge had the sense not to agitate for social change. . . . .
But seriously Siro, let's discuss what science is, or should be, and how an authoritative clergy or established professional authority can sometimes put a drag on enquiry. . . . .