Function commit_base 

pub fn commit_base<F, Dft, MT, Challenger>(
    order: VariableOrder,
    dft: &Dft,
    mmcs: &MT,
    challenger: &mut Challenger,
    poly: &Poly<F>,
    folding: usize,
    starting_log_inv_rate: usize,
) -> (MT::Commitment, MT::ProverData<DenseMatrix<F>>)
where
    F: TwoAdicField,
    Dft: TwoAdicSubgroupDft<F>,
    MT: Mmcs<F>,
    Challenger: CanObserve<MT::Commitment>,

Encodes and commits the initial base-field polynomial.

This is the first WHIR commitment. It lays out the polynomial according to the residual variable order, applies the Reed-Solomon expansion with dft, commits the resulting codeword matrix with mmcs, and observes the Merkle root in the transcript.

Prefix order transposes the local folding block before padding so the first folded variables become columns. Suffix order keeps the folding block as the row width and only zero-pads the row count.