That's what's covered by the "assuming you have formalized the statement correctly" parenthetical.
Given a formal statement of what you want, Lean can validate that the steps in a (tedious) machine-readable purported proof are valid and imply the result from accepted axioms. This is not AI, but a tiny, well reviewed kernel that only accepts correct formal logic arguments.
So, if you have a formal statement that you've verified to represent what you are interested in by some other means, Lean can tell you whether the proof created by genAI is correct. Basically, there is a nigh infallible checker that won't accept incorrect hallucinations.
It depends on whether you are doing something security critical with the result.
Maybe you have a trusted table hash but only a user-supplied version of the table. Before you use that data for security sensitive queries, you should verify it hasn't been modified.
Basically, if you ever have to contend with a malicious adversary, things are more interesting as usual. If not, addition is likely fine (though 2^k copies of a row now leave the k lowest bits unchanged).
XOR is not a great choice here. Consider that 2 copies of a row give the same result as 0 (or 4, 6, etc). And even without multiple copies of rows, you can force any hash you'd like by observing what happens when you insert more random rows
and finding a subcollection that flips exactly the bits you want.
What you probably want to look at is homomorphic hashing. This is usually implemented by hashing each row to an element of an appropriate abelian group and then using the group operation to combine them.
With suitable choice of group, this hash can have cryptographic strength. Some interesting choices here are lattices (LtHash), elliptic curves (ECMH), multiplicative groups (MuHash).
Sometimes these are officially sanctioned and even required! Most notably, including logos/other embellishments are a form of "trap street" where the idea is to have something to point to that trivially proves someone is using your mask design if it comes to it.
> For decades, Intel’s cleanrooms have been lit like darkrooms, bathed in a deep, low yellow. “That’s an anachronism,” says Mark Bohr, a small, serious man who has spent his entire 38-year career making chips, and who’s now Intel’s top manufacturing scientist. “Nobody’s had the courage to change it.”
My understanding is that was the original purpose, but probably unnecessary given that all the relevant process steps are encased in tools that are not exposed to the general clean room environment in operation (they have to maintain a higher grade of clean room internally).
However, I suspect it's probably going to continue being propagated forward due to Copy Exactly which has historically meant that Intel documents and copies the smallest details in all their fabs just in case they are necessary. In the end, if it ain't broke...
Given a formal statement of what you want, Lean can validate that the steps in a (tedious) machine-readable purported proof are valid and imply the result from accepted axioms. This is not AI, but a tiny, well reviewed kernel that only accepts correct formal logic arguments.
So, if you have a formal statement that you've verified to represent what you are interested in by some other means, Lean can tell you whether the proof created by genAI is correct. Basically, there is a nigh infallible checker that won't accept incorrect hallucinations.