lens trait

the universal cryptographic primitive. commit to a polynomial, prove evaluations, verify without seeing the polynomial. one primitive serves proof commitment, state authentication, noun identity, and data availability.

a lens is how an algebra presents its work for verification. each algebra computes in its own structure — scalars, binary, rings, isogenies. the lens makes that computation verifiable. different structures need different optics.

the interface

trait Lens<F: Field> {
    fn commit(poly: &MultilinearPoly<F>) -> Commitment;     // 32 bytes
    fn open(poly: &MultilinearPoly<F>, point: &[F], transcript: &mut Transcript) -> Opening;
    fn verify(commitment: &Commitment, point: &[F], value: F, proof: &Opening, transcript: &mut Transcript) -> bool;
    fn batch_open(poly: &MultilinearPoly<F>, points: &[(Vec<F>, F)], transcript: &mut Transcript) -> Opening;
    fn batch_verify(commitment: &Commitment, points: &[(Vec<F>, F)], proof: &Opening, transcript: &mut Transcript) -> bool;
}

five operations. commit is O(N). open produces a proof. verify checks the proof. batch_open amortizes m openings into one. all transparent (no trusted setup), all post-quantum.

see commitment for the complete specification including types, security properties, and crate structure.

naming convention

every algebra has five names at different layers:

lens files are named domain-algebra.md (full name). construction names are inside files. impl repos are dependencies.

five lenses

four constructions implement Lens<F> directly. Assayer is a wrapper protocol that delegates commitment to Brakedown over F_p — see tropical-semiring.

three roles

proof commitment — commit nox execution trace for zheng verification state commitment — commit bbg polynomial state (BBG_poly, A(x), N(x)) noun identity — commit nox noun polynomial for content addressing

one trait. five lenses. three roles.

dependency

hemera (hash — commitment binding, Fiat-Shamir)
  ↓
lens (polynomial commitment — this repo)
  ↓
nox (noun identity via Lens.commit)
zheng (proof commitment via Lens.commit/open/verify)
bbg (state commitment via Lens.commit)

arithmetics (lens depends on — one per algebra)

consumers