lens reference

canonical specification for polynomial commitment — five lenses for five algebras.

the trait

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

three operations. commit is O(N). open produces a proof. verify checks the proof. all transparent (no trusted setup), all post-quantum. see trait for the full specification.

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

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)
bbg (state commitment via Lens.commit)

arithmetics (lens depends on — one per algebra)

consumers