Struct ProverMultipointEvaled 

pub struct ProverMultipointEvaled<'a, Zt: ZincTypes<D, FD>, U: Uair, C: BaseFieldConfig, const D: usize, const FD: usize> { /* private fields */ }

After step 6 (multipoint eval).

Implementations

impl<'a, Zt, U, C, const D: usize, const FD: usize> ProverMultipointEvaled<'a, Zt, U, C, D, FD>

where Zt: ZincTypes<D, FD>, Zt::Int: ProjectableToField<C>, Zt::CombR: MulByScalar<Zt::Chal>, <Zt::ArbitraryZt as ZipTypes>::Eval: ProjectableToField<C>, U: Uair<Prime = Zt::Fmod> + 'static, C: BaseFieldConfig<Integer = Zt::Fmod> + ProjectPrimitiveIntegersWithConfig + ProjectElementWithConfig<Zt::Int> + ProjectElementWithConfig<Zt::CombR> + ProjectElementWithConfig<Zt::Chal> + 'static, C::Integer: ConstTranscribable,

pub fn step7_lift_and_project( self, ) -> Result<ProverLifted<'a, Zt, U, C, D, FD>, ProtocolError<C::Element>>

Step 7: Lift-and-project.

1. Sample $q’‘$. A fresh PCS-only prime, decoupled from the constraint primes $q_0, q_1, \dots, q_n$. Sampled here (start of step 7) — before any lifted evals are produced, so that the $q’‘$-family lift can be computed and sent in this step. This is post-commitments and post-$r_0$, so soundness is preserved (the prover cannot influence $q’’$).
2. Compute per-family lifted MLE evaluations at $r_0$:
   • Q-family ($q_0$): all columns (public + witness) interleaved by UAIR column layout, stored locally; only witness columns make it into the proof.
   • Per declared prime $q_i$ (i ≥ 1): witness-only lifted evals under that family’s field cfg. The $\phi_{q_i}$-projected coefficient trace was already built in step 2 (fq_staging) and threaded through projected_trace_fq; this step runs compute_lifted_evals on it at $r_0$ lifted into family $i$’s field.
   • $q’‘$-family: witness-only lifted evals under $q’‘$. Same pattern as fq families; the $r_0$ lifted into $F_{q’‘}$ gives $r^\star = r_0 \bmod q’’$ which doubles as the PCS evaluation point in step 8.
3. Absorb each family’s coefficients into the FS transcript in a deterministic order: Q-family first, then each declared prime in primes() order, then $q’’$.

Soundness: with $r_0$ shared across all constraint families (a consequence of the lockstep sumcheck), the per-family MP-eval consistency check in step6_lifted_evals (verifier) binds each $\bar u_j^{(i)}$ to the prover’s actual $q_i$-projected trace at $r_0$. The $q’’$-family lift is independently bound to the trace by the PCS open at $r^\star$ in step 8.

Trait Implementations

impl<'a, Zt: Clone + ZincTypes<D, FD>, U: Clone + Uair, C: Clone + BaseFieldConfig, const D: usize, const FD: usize> Clone for ProverMultipointEvaled<'a, Zt, U, C, D, FD>

where C::Element: Clone,

fn clone(&self) -> ProverMultipointEvaled<'a, Zt, U, C, D, FD>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<'a, Zt: Debug + ZincTypes<D, FD>, U: Debug + Uair, C: Debug + BaseFieldConfig, const D: usize, const FD: usize> Debug for ProverMultipointEvaled<'a, Zt, U, C, D, FD>

where C::Element: Debug,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.