Function unpad_leaf_claim 

pub fn unpad_leaf_claim<F: Field>(
    eval: F,
    point: &[F],
    n_pad_vars: usize,
) -> MultilinearEvalClaim<F>

Reduces a leaf claim on a one-padded witness to the claim on the witness itself.

A batched product check over trees of unequal depths lifts each shallow tree to the batch’s depth by filling n_pad_vars extra leaf positions with ones, which leaves its product unchanged. binius_ip::prodcheck::verify is oblivious to that, so the claim it outputs for such a tree is a claim on the padded witness

$$ M’(X_\text{pad}, X_\text{real}) = 1 + \bigl( M(X_\text{real}) - 1 \bigr) \cdot \text{eq}(0^\nu; X_\text{pad}), $$

whose padding variables are the lowest ones. This divides out their equality weight and drops them from the point, leaving the claim on $M$.

Arguments

• eval - The claimed evaluation of the padded witness.
• point - The reduced evaluation point, with the batch’s selector coordinates already stripped.
• n_pad_vars - How much depth this tree was padded by: the batch’s layer count less the tree’s own.

Preconditions

• point.len() >= n_pad_vars

Panics

Panics if the padding coordinates’ equality weight is zero, which requires one of them to equal one. They are the verifier’s own challenges, so no prover can induce this; it happens with probability at most $\nu / |K|$.