Layer 2 chains that post a proof with each batch, so Ethereum checks correctness itself.
The idea: The rollup executes transactions offchain and posts a proof that the new state follows from the old one by the rules. Ethereum checks the proof, which takes about the same small effort however many transactions the batch contained, so the batch is final as soon as the proof is accepted, with no waiting for challenges.
Why it matters: Their safety rests on the proof system having no flaws.
On the map: validity proofs checked on L1
Rollups that post a validity proof with each batch, so Ethereum checks correctness directly instead of waiting for challenges.
Some verify STARK proofs directly. Many wrap their proof in a Groth16 or PLONK proof on BN254 to keep gas low, which brings in pairing assumptions and a trusted setup. Proof-system bugs are the most practical risk today[1], which is why many rollups keep security councils or multiple provers[2].
If any of these breaks, this breaks too.
If this breaks, these break with it.
Nothing on the map depends on it: it is an end point, something people use directly.