Can't be solved, it's always possible but we can minimize the risk through audits, eyes on code, and being cautious with upgrades to that part of the protocol.
A lot more info here:
https://sethforprivacy.com/posts/dispelling-monero-fud/#you-cant-audit-the-monero-supply
Great resource, thank you!
No need to reply to this, I just want to summarize for my own learning: it seems like monero’s supply can be algorithmically verified - you just need to trust the algorithm. This is different from bitcoin which *could* be manually verified. Now nobody or nearly nobody does that for bitcoin because it would take too long. Instead they write algorithms to add everything up automatically. The main difference then is that the bitcoin supply verification tests can be run on real blocks and manually checked, while monero blocks can never be run on real blocks and manually checked. Just on test blocks generated for quality control purposes. The two paradigms are closer than most give credit.
I think you can verify the whole supply. So if someone by any chance found a way to inflate the supply, it would be announced. But you could not tell which address did it. Also, Fluffypony mentioned the source code responsible for a double spend is pretty tiny, so chances are pretty low.
