Quantum-resistant proofs are very expensive. Buterin stated that running quantum-resistant proofs on the chain is extremely expensive and that "the solution is again protocol-layer recursive signature and proof merging." Instead of verifying each signature and proof individually on the chain, a single master proof or "validation frame" would verify thousands of them simultaneously, keeping costs close to zero. Buterin explained, "In this way, a block can 'contain' a thousand validation frames, each containing a 3kB signature or even a 256kB proof."