Glossary

Predicate. A statement in first-order logic about a proposed state transition. On Modulus, the predicate is the contract.

Witness. The inputs that make a predicate true for a given transition, such as signatures and amounts. A proof can establish that a witness exists without revealing it.

Proof. A cryptographic object establishing, at the stated security level, that the named predicates are satisfied over the stated transition.

State transition. A proposed change to chain state: state consumed, state produced, and the transaction presenting them. Admitted only with a proof.

Validator slot. The position in a chain's design where transactions are checked for admission. On Modulus, zkFOL proofs occupy the validator slot; on execution chains, a virtual machine does.

Prover envelope. The three quantities this project claims and measures: proving time, proving memory, and the hardware proving runs on.

Arithmetisation. Translating the validity of a logical assertion into a checkable property of a polynomial.

Polynomial semantics. The translation route of eprint 2024/954: logical connectives map directly to polynomial operations, with no abstract machine in the middle.

Soundness. The property that an accepted proof implies the proved statement holds, at the stated security level.

Safety failure and liveness failure. A safety failure admits something wrong; a liveness failure refuses something right. Modulus converts a class of the former into the latter: a transition that cannot be proved does not occur.

Static in units. The fee property Modulus claims: a given transaction costs the same over time in units of the native asset. Predictability in external value is a separate, open question.

Naming

Modulus is the chain. Modulus zkFOL is the full name, used on first reference only. zkFOL is the language and compiler; Modulus is the chain that consumes it.

Correct: "zkFOL proofs in the validator slot", "a predicate on Modulus". Incorrect: "the zkFOL chain", "the zkFOL blockchain", "zkModulus".