Regressions are bad and they should be avoided. Still, software engineering is a complex thing and regressions happened long time before coding agents were a thing. Unless one can pinpoint regression to changes that were more sloppy than the human-written rsync commits were I don't think coding agents are to blame.
I believe your point is not that it has never failed for anyone in the last few years after upgrade? Then, if the claim is that breakage is considerably worse than it used to be before using coding agents: it is possible, but I think it requires more evidence than a few anecdotes.
No need to imagine, it's enough to look into non-Euclidean geometry (obtained by excluding Euclid's fifth axiom), non-standard models of geometry, or reverse mathematics (studying which axioms are necessary for a specific theorem to be provable).
These are not possible, as x can be 7 only if y is 7, and likewise for 8. Semantics isn't based on sets, but on non-deterministic assignments to variables: y is either 7 or 8 and x is either y or 2.
It's a social construct in the the same sense anything not directly verifiable using senses is. Is there an Eiffel tower in Paris? Most people haven't seen it, so they can only accept the social consensus that it is there.
If one can afford it, they can travel to Paris and check themselves. The same with mathematical truth: if one has means (time, intelligence, access to training), they can check the proof themselves. Otherwise they need to trust the consensus.
So again, is the truth in mathematics just a social construct? In some sense, I guess, but probably not the one some people might assume hearing such a statement.