Struct OnePadMleCheckProver 

pub struct OnePadMleCheckProver<F: Field, Inner> { /* private fields */ }

MLE-check prover for one layer of a product check over a one-padded witness.

The tree’s product is a scalar, so the layer’s claim point is node coordinates only, split into two segments with the padding ones lowest:

    [ padding (nu) | real (m) ]

The padded layer is the unpadded one wrapped in the one-padding $\textsf{sel}(\textsf{eq}(0^\nu, Z’), \cdot)$ over the padding variables. MLE-check binds variables from the highest index down, so the real rounds come first and the padding rounds last:

• Real rounds. Delegate to inner, the ordinary MLE-check over the unpadded layer, and correct each round polynomial by the affine map $R’(X) = 1 + q \cdot (R(X) - 1)$, where $q$ is the equality weight $\textsf{eq}(0^\nu, \rho_\text{pa})$ of the claim point’s padding segment. Off the all-zeros padding slab both children are one, which is where the residual weight $1 - q$ comes from.
• Padding rounds. No multilinear is touched. Every real variable is bound by now, so inner‘s two child evaluations $g_0, g_1$ are scalars and the round polynomial is the closed form $R’(X) = (1 - e) + e \cdot \textsf{sel}(E(X), g_0) \cdot \textsf{sel}(E(X), g_1)$, where $e$ is the equality weight of the padding coordinates still unbound and $E(X)$ that of the ones already bound.

Finishing returns the padded layer’s child evaluations $\textsf{sel}(e^*, g_b)$, which is what the batch’s selector rounds consume.

Trait Implementations

impl<F: Field, Inner: MleCheckProver<F>> MleCheckProver<F> for OnePadMleCheckProver<F, Inner>

fn n_vars(&self) -> usize

The number of variables still free.

fn execute(&mut self) -> Vec<RoundCoeffs<F>>

Computes this round’s message, one univariate polynomial per claim.

fn fold(&mut self, challenge: F)

Binds this round’s variable to the verifier challenge.

fn finish(self) -> Vec<F>

Consumes the prover and returns every multilinear’s evaluation at the challenge point.

fn eval_point(&self) -> &[F]

The still-unbound part of the evaluation point, one coordinate per free variable.