Introduction

The goal of the SP1 Hypercube Protocol is to prove the correctness of a program in the RISC V (RV64IM) instruction set. The protocol is based on an Interactive Oracle Proof (IOP) that relies on the following key sub-protocols, with which we assume basic familiarity.

• Zerocheck Protocol, see Chapter 4 of https://people.cs.georgetown.edu/jthaler/ProofsArgsAndZK.pdf
• Jagged PCS https://eprint.iacr.org/2025/917
• LogUp GKR https://eprint.iacr.org/2023/1284
• Basefold https://eprint.iacr.org/2024/1571
• Multiset Hash https://docs.succinct.xyz/assets/files/SP1_Turbo_Memory_Argument-b042ba18b58c4add20a8370f4802f077.pdf

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SP1 Hypercube takes a piecemeal approach. This means that the computation is divided into "shards", consisting of roughly $2^{22}$ RISC V instructions each. We then:

• Prove that each shard executed correctly.
• Prove memory consistency across the different shards (i.e., if a shard changed memory location $i$ to value $v$, then this will be the value of the memory the next time that it is read).

The shard proofs are then aggregated and compressed via a recursion mechanism into a single succinct proof.