Function batch_reduced_aux_values 

pub fn batch_reduced_aux_values<EF>(
    constraint_dag: AceDag<EF>,
    config: &ReducedAuxBatchConfig,
) -> AceDag<EF>
where
    EF: ExtensionField<Felt>,

Extend an existing constraint DAG with auxiliary trace boundary checks.

Takes the constraint DAG and appends the running-product identity check (product_check) and the LogUp sum check (sum_check), combining all three checks into a single root with gamma:

root = constraint_check + gamma * product_check + gamma^2 * sum_check

Returns the new DAG with the batched root.