With regards to subsidizing: all the subsidizer needs to do in order to incentivize work on P is sell shares of P. If they are short P when P is proven, they lose money—this money in effect goes to the people who worked to prove it.
To be more concrete: Suppose P is trading at 0.50. I think I can prove P with one hour of work. Then an action available to me is to buy 100 shares of P, prove it, and then sell them back for $50 of profit. But my going fee is $55/hour, so I don’t do it. Then a grantmaker comes along and offers to sell some shares at $0.40. Now the price is right for me, so I buy and prove and make $60/hr.
With regards to subsidizing: all the subsidizer needs to do in order to incentivize work on P is sell shares of P. If they are short P when P is proven, they lose money—this money in effect goes to the people who worked to prove it.
To be more concrete:
Suppose P is trading at 0.50. I think I can prove P with one hour of work. Then an action available to me is to buy 100 shares of P, prove it, and then sell them back for $50 of profit.
But my going fee is $55/hour, so I don’t do it.
Then a grantmaker comes along and offers to sell some shares at $0.40. Now the price is right for me, so I buy and prove and make $60/hr.