Function new 

pub fn new<F, Inner>(
    pad_eq_prefixes: Vec<F>,
    eval_point: Vec<F>,
    inner: Inner,
) -> ZeroPadMleCheckProver<F, Inner>
where
    F: Field,
    Inner: MleCheckProver<F>,

Creates the prover for one padded fractional-addition layer.

Arguments

• pad_eq_prefixes - Equality weights of the claim point’s padding segment: entry i is $\prod_{c < i} \textsf{eq}(0, \rho_{\text{pa}, c})$. Its length fixes the padding segment at one less, so a single-entry table leaves the inner reduction uncorrected. Every layer of a batch shares one point, so one table of prefix products serves them all.
• eval_point - The padded layer’s claim point, [padding | real].
• inner - The unpadded layer’s MLE-check, seeded at the real segment of the claim point with the claims unpad_claims returns.

Preconditions

• pad_eq_prefixes is non-empty and its last entry — the padding segment’s equality weight — is non-zero
• eval_point.len() + 1 >= pad_eq_prefixes.len()
• inner.n_vars() == eval_point.len() + 1 - pad_eq_prefixes.len()