If we want to live in the least convenient possible world assume that in second 1 it constructs the smooth structures; it takes three seconds to prove that there are no more for n>5, three seconds to prove no more for n=1,2, and three more seconds to prove there are no more for n=3 and runs out of time. These results are obtained incidentally from inequalities that arise when pursuing a proof for n=4, which is the central value of some equation at the core of the proofs. (so the proofs really say “if another smooth structure exists, it exists for n<5, 2<n<5, 3<n<5.”)
If it really can’t prove any theorems that directly include the translation of “the number of smooth structures for n=4 is,” it simply won’t ever update that.
If we want to live in the least convenient possible world assume that in second 1 it constructs the smooth structures; it takes three seconds to prove that there are no more for n>5, three seconds to prove no more for n=1,2, and three more seconds to prove there are no more for n=3 and runs out of time. These results are obtained incidentally from inequalities that arise when pursuing a proof for n=4, which is the central value of some equation at the core of the proofs. (so the proofs really say “if another smooth structure exists, it exists for n<5, 2<n<5, 3<n<5.”)
If it really can’t prove any theorems that directly include the translation of “the number of smooth structures for n=4 is,” it simply won’t ever update that.
Well it can prove “the number of structures for n=4 is at least 1.”