Your comment seems to imply that the conjecture’s “99%” is about circuits C for which P(C) is false. Otherwise, it would be impossible for a V to miss 100% of random reversible circuits without missing the circuits C for which P(C) is true. In the conjecture, should “random reversible circuits C” be read as “random reversible circuits C for which P(C) is false”? It does not change much indeed, but I might have to correct my presentation of the conjecture here.
The statements are equivalent if only a tiny fraction (tending to 0) of random reversible circuits satisfy P(C). We think this is very likely to be true, since it is a very weak consequence of the conjecture that random (depth-~O(n)) reversible circuits are pseudorandom permutations. If it turned out to not be true, it would no longer make sense to think of P(C) as an “outrageous coincidence” and so I think we would have to abandon the conjecture. So in short we are happy to consider either version (though I agree that “for which P(C) is false” is a bit more natural).
Your comment seems to imply that the conjecture’s “99%” is about circuits C for which P(C) is false. Otherwise, it would be impossible for a V to miss 100% of random reversible circuits without missing the circuits C for which P(C) is true. In the conjecture, should “random reversible circuits C” be read as “random reversible circuits C for which P(C) is false”? It does not change much indeed, but I might have to correct my presentation of the conjecture here.
The statements are equivalent if only a tiny fraction (tending to 0) of random reversible circuits satisfy P(C). We think this is very likely to be true, since it is a very weak consequence of the conjecture that random (depth-~O(n)) reversible circuits are pseudorandom permutations. If it turned out to not be true, it would no longer make sense to think of P(C) as an “outrageous coincidence” and so I think we would have to abandon the conjecture. So in short we are happy to consider either version (though I agree that “for which P(C) is false” is a bit more natural).