Not math: optimistic rollups assume someone honest is watching and will challenge a false claim in time.
Why it matters: If nobody challenges, a false claim goes through.
On the map: disputes a bad claim within the window (not cryptographic)
Optimistic rollups post state claims to Ethereum without proving them. During a challenge window, usually about a week, anyone can dispute a false claim with a fault proof[1].
The security assumption is that at least one honest party is watching, able to submit a challenge in time and can't be censored long enough. It isn't cryptographic: if nobody challenges, a false claim is accepted.
If any of these breaks, this breaks too.
If this breaks, these break with it.