mina_tree/proofs/

step.rs

use std::rc::Rc;

use crate::{
    proofs::{
        prover::make_padded_proof_from_p2p,
        public_input::{
            plonk_checks::ShiftingValue,
            prepared_statement::{DeferredValues, PreparedStatement, ProofState},
        },
        unfinalized::dummy_ipa_step_challenges_computed,
        util::proof_evaluation_to_absorption_sequence,
        verifiers::wrap_domains,
        wrap::{
            create_oracle_with_public_input, dummy_ipa_wrap_sg, wrap_verifier, Domain,
            COMMON_MAX_DEGREE_WRAP_LOG2,
        },
    },
    verifier::{get_srs, get_srs_mut},
};
use anyhow::Context;
use ark_ff::{BigInteger256, One, Zero};
use ark_poly::{
    univariate::DensePolynomial, DenseUVPolynomial, EvaluationDomain, Radix2EvaluationDomain,
};
use kimchi::proof::{PointEvaluations, ProverCommitments, RecursionChallenge};
use mina_curves::pasta::{Fp, Fq, Pallas};
use mina_p2p_messages::{bigint::InvalidBigInt, v2};
use poly_commitment::{commitment::b_poly_coefficients, ipa::OpeningProof};

use crate::proofs::{
    public_input::{
        plonk_checks::{derive_plonk, InCircuit},
        prepared_statement::Plonk,
    },
    transaction::endos,
    util::{challenge_polynomial, four_u64_to_field},
    verification::{make_scalars_env, prev_evals_from_p2p},
    wrap::{
        combined_inner_product, evals_of_split_evals, CombinedInnerProductParams,
        COMMON_MAX_DEGREE_STEP_LOG2,
    },
    BACKEND_TICK_ROUNDS_N, BACKEND_TOCK_ROUNDS_N,
};

use super::{
    constants::ProofConstants,
    field::{Boolean, CircuitVar, FieldWitness, GroupAffine},
    public_input::{messages::MessagesForNextWrapProof, plonk_checks::PlonkMinimal},
    to_field_elements::{ToFieldElements, ToFieldElementsDebug},
    transaction::{
        create_proof, make_group, messages_for_next_wrap_proof_padding,
        scalar_challenge::to_field_checked, Check, CircuitPlonkVerificationKeyEvals,
        CreateProofParams, InnerCurve, MessagesForNextStepProof, PlonkVerificationKeyEvals,
        ProofWithPublic, Prover, ReducedMessagesForNextStepProof, StepStatement,
    },
    unfinalized::{evals_from_p2p, AllEvals, EvalsWithPublicInput, Unfinalized},
    util::{extract_bulletproof, two_u64_to_field},
    witness::Witness,
    wrap::Domains,
    ProverProof, VerifierIndex,
};

#[derive(Clone)]
pub struct PreviousProofStatement<'a> {
    pub public_input: Rc<dyn ToFieldElementsDebug>,
    pub proof: &'a v2::PicklesProofProofsVerified2ReprStableV2,
    pub proof_must_verify: CircuitVar<Boolean>,
}

pub struct InductiveRule<'a, const N_PREVIOUS: usize> {
    pub previous_proof_statements: [PreviousProofStatement<'a>; N_PREVIOUS],
    pub public_output: (),
    pub auxiliary_output: (),
}

impl InductiveRule<'_, 0> {
    pub fn empty() -> Self {
        Self {
            previous_proof_statements: [],
            public_output: (),
            auxiliary_output: (),
        }
    }
}

#[derive(Clone, Copy, Debug)]
pub enum OptFlag {
    Yes,
    No,
    Maybe,
}

#[derive(Clone, Debug)]
pub enum Opt<T> {
    Some(T),
    No,
    Maybe(Boolean, T),
}

impl<T> Opt<T> {
    fn map<V>(&self, fun: impl Fn(&T) -> V) -> Opt<V> {
        match self {
            Opt::Some(v) => Opt::Some(fun(v)),
            Opt::No => Opt::No,
            Opt::Maybe(b, v) => Opt::Maybe(*b, fun(v)),
        }
    }
}

#[derive(Clone, Debug)]
pub struct FeatureFlags<Bool> {
    pub range_check0: Bool,
    pub range_check1: Bool,
    pub foreign_field_add: Bool,
    pub foreign_field_mul: Bool,
    pub xor: Bool,
    pub rot: Bool,
    pub lookup: Bool,
    pub runtime_tables: Bool,
}

impl FeatureFlags<Boolean> {
    pub fn empty() -> Self {
        Self {
            range_check0: Boolean::False,
            range_check1: Boolean::False,
            foreign_field_add: Boolean::False,
            foreign_field_mul: Boolean::False,
            xor: Boolean::False,
            rot: Boolean::False,
            lookup: Boolean::False,
            runtime_tables: Boolean::False,
        }
    }
}

impl<F: FieldWitness> ToFieldElements<F> for FeatureFlags<bool> {
    fn to_field_elements(&self, fields: &mut Vec<F>) {
        let Self {
            range_check0,
            range_check1,
            foreign_field_add,
            foreign_field_mul,
            xor,
            rot,
            lookup,
            runtime_tables,
        } = self;

        [
            range_check0,
            range_check1,
            foreign_field_add,
            foreign_field_mul,
            xor,
            rot,
            lookup,
            runtime_tables,
        ]
        .to_field_elements(fields);
    }
}

impl FeatureFlags<bool> {
    pub fn empty_bool() -> Self {
        Self {
            range_check0: false,
            range_check1: false,
            foreign_field_add: false,
            foreign_field_mul: false,
            xor: false,
            rot: false,
            lookup: false,
            runtime_tables: false,
        }
    }

    pub fn to_boolean(&self) -> FeatureFlags<Boolean> {
        use super::field::ToBoolean;

        let Self {
            range_check0,
            range_check1,
            foreign_field_add,
            foreign_field_mul,
            xor,
            rot,
            lookup,
            runtime_tables,
        } = self;

        FeatureFlags {
            range_check0: range_check0.to_boolean(),
            range_check1: range_check1.to_boolean(),
            foreign_field_add: foreign_field_add.to_boolean(),
            foreign_field_mul: foreign_field_mul.to_boolean(),
            xor: xor.to_boolean(),
            rot: rot.to_boolean(),
            lookup: lookup.to_boolean(),
            runtime_tables: runtime_tables.to_boolean(),
        }
    }
}

#[derive(Debug)]
pub struct Basic {
    pub proof_verifieds: Vec<u64>,
    // branches: u64,
    pub wrap_domain: Domains,
    pub step_domains: Box<[Domains]>,
    pub feature_flags: FeatureFlags<OptFlag>,
}

#[derive(Debug)]
pub enum ForStepKind<T, T2 = ()> {
    Known(T),
    SideLoaded(T2),
}

#[derive(Debug)]
pub struct ForStep {
    pub branches: usize,
    pub max_proofs_verified: usize,
    pub proof_verifieds: ForStepKind<Vec<Fp>>,
    pub public_input: (), // Typ
    pub wrap_key: CircuitPlonkVerificationKeyEvals<Fp>,
    pub wrap_domain: ForStepKind<Domain, Box<[Boolean]>>,
    pub step_domains: ForStepKind<Box<[Domains]>>,
    pub feature_flags: FeatureFlags<OptFlag>,
    pub num_chunks: u64,
    pub zk_rows: u64,
}

pub enum Packed {
    Field(CircuitVar<Fq>),
    PackedBits(CircuitVar<Fq>, usize),
}

impl std::fmt::Debug for Packed {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        match self {
            Self::Field(x) => f.write_fmt(format_args!("Field({:?})", x)),
            Self::PackedBits(a, b) => f.write_fmt(format_args!("PackedBits({:?}, {:?})", a, b)),
        }
    }
}

pub struct StatementDeferredValues {
    pub plonk: PlonkMinimal<Fp, 2>,
    pub bulletproof_challenges: [[u64; 2]; 16],
    pub branch_data: v2::CompositionTypesBranchDataStableV1,
}

pub struct StatementProofState {
    pub deferred_values: StatementDeferredValues,
    pub sponge_digest_before_evaluations: [u64; 4],
    pub messages_for_next_wrap_proof: MessagesForNextWrapProof,
}

impl TryFrom<&v2::PicklesProofProofsVerified2ReprStableV2StatementProofState>
    for StatementProofState
{
    type Error = InvalidBigInt;

    fn try_from(
        value: &v2::PicklesProofProofsVerified2ReprStableV2StatementProofState,
    ) -> Result<Self, Self::Error> {
        let v2::PicklesProofProofsVerified2ReprStableV2StatementProofState {
            deferred_values:
                v2::PicklesProofProofsVerified2ReprStableV2StatementProofStateDeferredValues {
                    plonk,
                    bulletproof_challenges,
                    branch_data,
                },
            sponge_digest_before_evaluations,
            messages_for_next_wrap_proof:
                v2::PicklesProofProofsVerified2ReprStableV2MessagesForNextWrapProof {
                    challenge_polynomial_commitment: (c0, c1),
                    old_bulletproof_challenges,
                },
        } = value;

        Ok(Self {
            deferred_values: StatementDeferredValues {
                plonk: plonk.try_into()?,
                bulletproof_challenges: bulletproof_challenges
                    .each_ref()
                    .map(|challenge| challenge.prechallenge.inner.each_ref().map(|v| v.as_u64())),
                branch_data: branch_data.clone(),
            },
            sponge_digest_before_evaluations: sponge_digest_before_evaluations
                .each_ref()
                .map(|v| v.as_u64()),
            messages_for_next_wrap_proof: MessagesForNextWrapProof {
                challenge_polynomial_commitment: InnerCurve::from((
                    c0.to_field::<Fq>()?,
                    c1.to_field()?,
                )),
                old_bulletproof_challenges: old_bulletproof_challenges
                    .iter()
                    .map(|old_bulletproof_challenge| {
                        old_bulletproof_challenge.each_ref().map(|chal| {
                            two_u64_to_field(
                                &chal.prechallenge.inner.each_ref().map(|v| v.as_u64()),
                            )
                        })
                    })
                    .collect(),
            },
        })
    }
}

pub mod step_verifier {
    use std::ops::Neg;

    use super::*;
    use crate::proofs::{
        self,
        field::{field, ToBoolean},
        opt_sponge::OptSponge,
        public_input::plonk_checks::{self, ft_eval0_checked},
        transaction::{poseidon::Sponge, scalar_challenge},
        unfinalized,
        util::{
            challenge_polynomial_checked, proof_evaluation_to_list_opt, to_absorption_sequence_opt,
        },
        wrap::{
            make_scalars_env_checked, one_hot_vector, ones_vector,
            pcs_batch::PcsBatch,
            pseudo::{self, PseudoDomain},
            wrap_verifier::{
                actual_evaluation, chunks_needed, lowest_128_bits, split_commitments::Point,
                Advice, OPS_BITS_PER_CHUNK,
            },
            MakeScalarsEnvParams, PERMUTS_MINUS_1_ADD_N1,
        },
    };
    use itertools::Itertools;
    use kimchi::circuits::wires::PERMUTS;
    use poly_commitment::{ipa::SRS, PolyComm};

    fn squeeze_challenge(s: &mut Sponge<Fp>, w: &mut Witness<Fp>) -> Fp {
        lowest_128_bits(s.squeeze(w), true, w)
    }

    fn squeeze_scalar(s: &mut Sponge<Fp>, w: &mut Witness<Fp>) -> Fp {
        lowest_128_bits(s.squeeze(w), false, w)
    }

    fn absorb_curve(c: &Pallas, sponge: &mut Sponge<Fp>, w: &mut Witness<Fp>) {
        let GroupAffine::<Fp> { x, y, .. } = c;
        sponge.absorb2(&[*x, *y], w);
    }

    pub trait PlonkDomain<F: FieldWitness> {
        fn vanishing_polynomial(&self, x: F, w: &mut Witness<F>) -> F;
        fn generator(&self) -> F;
        fn shifts(&self) -> &[F; PERMUTS];
        fn log2_size(&self) -> u64;
    }

    impl<F: FieldWitness> PlonkDomain<F> for PseudoDomain<F> {
        fn vanishing_polynomial(&self, x: F, w: &mut Witness<F>) -> F {
            self.vanishing_polynomial(x, w)
        }
        fn generator(&self) -> F {
            self.domain.group_gen
        }
        fn shifts(&self) -> &[F; PERMUTS] {
            &self.shifts
        }
        fn log2_size(&self) -> u64 {
            todo!()
        }
    }

    impl<F: FieldWitness> PlonkDomain<F> for SideloadedDomain<F> {
        fn vanishing_polynomial(&self, x: F, w: &mut Witness<F>) -> F {
            (self.vanishing_polynomial)(x, w)
        }
        fn generator(&self) -> F {
            self.generator
        }
        fn shifts(&self) -> &[F; PERMUTS] {
            &self.shifts
        }
        fn log2_size(&self) -> u64 {
            self.log2_size
        }
    }

    struct SideloadedDomain<F: FieldWitness> {
        generator: F,
        shifts: Box<[F; PERMUTS]>,
        vanishing_polynomial: Box<dyn Fn(F, &mut Witness<F>) -> F>,
        log2_size: u64,
    }

    fn domain_for_compiled(
        domains: &[Domains],
        branch_data: &v2::CompositionTypesBranchDataStableV1,
        w: &mut Witness<Fp>,
    ) -> PseudoDomain<Fp> {
        let unique_domains = domains
            .iter()
            .map(|d| d.h)
            .sorted()
            .dedup()
            .collect::<Vec<_>>();
        let mut which_log2 = unique_domains
            .iter()
            .rev()
            .map(|Domain::Pow2RootsOfUnity(d)| {
                let d = Fp::from(*d);
                let domain_log2 = Fp::from(branch_data.domain_log2.as_u8() as u64);
                field::equal(d, domain_log2, w)
            })
            .collect::<Vec<_>>();

        which_log2.reverse();

        pseudo::to_domain::<Fp>(&which_log2, &unique_domains)
    }

    fn tick_shifts(log2_size: u64) -> Box<[Fp; PERMUTS]> {
        // caml_pasta_fp_plonk_verifier_index_shifts
        use kimchi::circuits::polynomials::permutation::Shifts;

        let num_coeff = 1 << log2_size;
        let domain = Radix2EvaluationDomain::<Fp>::new(num_coeff).unwrap();
        let shifts = Shifts::new(&domain);
        Box::from(*shifts.shifts())
    }

    fn domain_generator(log2_size: u64) -> Fp {
        // caml_pasta_fp_domain_generator
        let num_coeff = 1 << log2_size;
        let domain = Radix2EvaluationDomain::<Fp>::new(num_coeff).unwrap();
        domain.group_gen
    }

    fn side_loaded_domain(log2_size: u64, w: &mut Witness<Fp>) -> SideloadedDomain<Fp> {
        let log2_size_field = Fp::from(log2_size);

        let vanishing_polynomial = |mask: Vec<Boolean>| {
            Box::new(move |x: Fp, w: &mut Witness<Fp>| {
                let result = mask.iter().rev().fold(x, |acc, should_square| {
                    let squared = field::square(acc, w);
                    w.exists_no_check(match should_square {
                        Boolean::True => squared,
                        Boolean::False => acc,
                    })
                });
                result - Fp::one()
            })
        };

        let mut domain = |max: u64| {
            let max_n = max;
            let mask = ones_vector(log2_size_field, max_n, w);

            let s_max_n = max_n + 1;
            let log2_sizes = (
                one_hot_vector::of_index(log2_size_field, s_max_n, w),
                (0..max_n).collect::<Vec<_>>(),
            );
            let shifts = pseudo::shifts(&log2_sizes, tick_shifts);
            let generator = pseudo::generator(&log2_sizes, domain_generator);
            let vanishing_polynomial = vanishing_polynomial(mask);

            SideloadedDomain {
                generator,
                shifts,
                vanishing_polynomial,
                log2_size,
            }
        };

        domain(Domains::max().h.log2_size())
    }

    pub(super) fn proof_verified_to_prefix(
        p: &v2::PicklesBaseProofsVerifiedStableV1,
    ) -> [Boolean; 2] {
        use v2::PicklesBaseProofsVerifiedStableV1::*;

        match p {
            N0 => [Boolean::False, Boolean::False],
            N1 => [Boolean::False, Boolean::True],
            N2 => [Boolean::True, Boolean::True],
        }
    }

    // TODO: This assumes that feature flags are never enabled (we make this assumption everywhere else too)
    fn validate_feature_flags(hack_feature_flags: OptFlag, w: &mut Witness<Fp>) {
        let no = CircuitVar::Var(Boolean::False);

        let range_check0 = no;
        let range_check1 = no;
        let rot = no;
        let xor = no;
        let foreign_field_mul = no;
        let lookup = no;

        if let OptFlag::Maybe = hack_feature_flags {
            let range_check_lookup = {
                let first = range_check0.or(&range_check1, w);
                first.or(&rot, w)
            };
            let lookups_per_row_4 = {
                let first = xor.or(&range_check_lookup, w);
                first.or(&foreign_field_mul, w)
            };
            let _lookups_per_row_3 = lookups_per_row_4.or(&lookup, w);
        };
    }

    pub(super) struct FinalizeOtherProofParams<'a> {
        pub(super) max_proof_verified: usize,
        pub(super) feature_flags: &'a FeatureFlags<OptFlag>,
        pub(super) step_domains: &'a ForStepKind<Box<[Domains]>>,
        pub(super) sponge: Sponge<Fp>,
        pub(super) prev_challenges: &'a [[Fp; Fp::NROUNDS]],
        pub(super) deferred_values: &'a DeferredValues<Fp>,
        pub(super) evals: &'a AllEvals<Fp>,
        pub(super) hack_feature_flags: OptFlag,
        pub(super) zk_rows: u64,
    }

    pub(super) fn finalize_other_proof(
        params: FinalizeOtherProofParams,
        w: &mut Witness<Fp>,
    ) -> anyhow::Result<(Boolean, Vec<Fp>)> {
        let FinalizeOtherProofParams {
            max_proof_verified,
            feature_flags: _,
            step_domains,
            mut sponge,
            prev_challenges,
            deferred_values,
            evals,
            hack_feature_flags,
            zk_rows,
        } = params;

        let DeferredValues {
            plonk,
            combined_inner_product,
            b,
            xi,
            bulletproof_challenges,
            branch_data,
        } = deferred_values;

        validate_feature_flags(hack_feature_flags, w);

        let AllEvals { ft_eval1, evals } = evals;

        let actual_width_mask = &branch_data.proofs_verified;
        let actual_width_mask = proof_verified_to_prefix(actual_width_mask);

        let (_, endo) = endos::<Fq>();
        let scalar = |b: &[u64; 2], w: &mut Witness<Fp>| -> Fp {
            let scalar = two_u64_to_field(b);
            to_field_checked::<Fp, 128>(scalar, endo, w)
        };

        let plonk = {
            let Plonk {
                alpha,
                beta,
                gamma,
                zeta,
                zeta_to_srs_length,
                zeta_to_domain_size,
                perm,
                feature_flags,
                lookup: _,
            } = plonk;

            // We decompose this way because of OCaml evaluation order
            // let lookup = lookup.as_ref().map(|lookup| scalar(lookup, w));
            let lookup = match hack_feature_flags {
                OptFlag::No => None,
                OptFlag::Maybe => {
                    // TODO: Hack
                    // This assumes that `plonk.lookup` (just above) is [0, 0]
                    // <https://github.com/MinaProtocol/mina/blob/a51f09d09e6ae83362ea74eaca072c8e40d08b52/src/lib/pickles/composition_types/composition_types.ml#L131>
                    Some(scalar(&[0, 0], w))
                }
                OptFlag::Yes => todo!(),
            };
            let zeta = scalar(zeta, w);
            let alpha = scalar(alpha, w);

            InCircuit {
                alpha,
                beta: two_u64_to_field(beta),
                gamma: two_u64_to_field(gamma),
                zeta,
                zeta_to_domain_size: zeta_to_domain_size.clone(),
                zeta_to_srs_length: zeta_to_srs_length.clone(),
                perm: perm.clone(),
                lookup,
                feature_flags: feature_flags.clone(),
            }
        };

        let domain: Rc<dyn PlonkDomain<Fp>> = match step_domains {
            ForStepKind::Known(ds) => Rc::new(domain_for_compiled(ds, branch_data, w)),
            ForStepKind::SideLoaded(()) => Rc::new(side_loaded_domain(
                branch_data.domain_log2.as_u8() as u64,
                w,
            )),
        };

        let zetaw = field::mul(domain.generator(), plonk.zeta, w);

        let sg_olds = prev_challenges
            .iter()
            .map(|chals| challenge_polynomial_checked(chals))
            .collect::<Vec<_>>();

        let (sg_evals1, sg_evals2) = {
            let sg_evals = |pt: Fp, w: &mut Witness<Fp>| {
                let ntrim_front = 2 - max_proof_verified;

                let mut sg = sg_olds
                    .iter()
                    .zip(&actual_width_mask[ntrim_front..])
                    .rev()
                    .map(|(f, keep)| (*keep, f(pt, w)))
                    .collect::<Vec<_>>();
                sg.reverse();
                sg
            };

            // We decompose this way because of OCaml evaluation order
            let sg_evals2 = sg_evals(zetaw, w);
            let sg_evals1 = sg_evals(plonk.zeta, w);
            (sg_evals1, sg_evals2)
        };

        // sponge state
        {
            let challenge_digest = {
                let ntrim_front = 2 - max_proof_verified;

                let mut sponge = OptSponge::create();
                prev_challenges
                    .iter()
                    .zip(&actual_width_mask[ntrim_front..])
                    .for_each(|(chals, keep)| {
                        let keep = CircuitVar::Var(*keep);
                        for chal in chals {
                            sponge.absorb((keep, *chal));
                        }
                    });
                sponge.squeeze(w)
            };

            sponge.absorb2(&[challenge_digest], w);
            sponge.absorb(&[*ft_eval1], w);
            sponge.absorb(&evals.public_input.0, w);
            sponge.absorb(&evals.public_input.1, w);

            for eval in &to_absorption_sequence_opt(&evals.evals, hack_feature_flags) {
                match eval {
                    Opt::No => {}
                    Opt::Some(PointEvaluations { zeta, zeta_omega }) => {
                        sponge.absorb(zeta, w);
                        sponge.absorb(zeta_omega, w);
                    }
                    Opt::Maybe(b, PointEvaluations { zeta, zeta_omega }) => {
                        let sponge_state_before = sponge.sponge_state.clone();
                        let state_before = sponge.state;

                        sponge.absorb(zeta, w);
                        sponge.absorb(zeta_omega, w);

                        // TODO: Does it panic in OCaml ?
                        use ::poseidon::SpongeState::{Absorbed, Squeezed};
                        match (sponge_state_before, &sponge.sponge_state) {
                            (Absorbed(x), Absorbed(y)) => assert_eq!(x, *y),
                            (Squeezed(x), Squeezed(y)) => assert_eq!(x, *y),
                            (Absorbed(_), Squeezed(_)) => panic!(),
                            (Squeezed(_), Absorbed(_)) => panic!(),
                        }

                        sponge
                            .state
                            .iter_mut()
                            .zip(state_before)
                            .for_each(|(then, else_)| {
                                *then = w.exists_no_check(match b {
                                    Boolean::True => *then,
                                    Boolean::False => else_,
                                })
                            });
                    }
                }
            }
        };

        let xi_actual = lowest_128_bits(sponge.squeeze(w), true, w);
        let r_actual = lowest_128_bits(sponge.squeeze(w), true, w);

        let xi_correct = field::equal(xi_actual, two_u64_to_field(xi), w);

        let xi = scalar(xi, w);
        let r = to_field_checked::<Fp, 128>(r_actual, endo, w);

        let to_bytes = |f: Fp| {
            let bigint: BigInteger256 = f.into();
            bigint.0
        };

        let plonk_mininal = PlonkMinimal::<Fp, 4> {
            alpha: plonk.alpha,
            beta: plonk.beta,
            gamma: plonk.gamma,
            zeta: plonk.zeta,
            joint_combiner: None,
            alpha_bytes: to_bytes(plonk.alpha),
            beta_bytes: to_bytes(plonk.beta),
            gamma_bytes: to_bytes(plonk.gamma),
            zeta_bytes: to_bytes(plonk.zeta),
            joint_combiner_bytes: None,
            feature_flags: FeatureFlags::empty_bool(), // TODO
        };

        let combined_evals = {
            let mut pow2pow =
                |f: Fp| (0..COMMON_MAX_DEGREE_STEP_LOG2).fold(f, |acc, _| field::square(acc, w));

            let zeta_n = pow2pow(plonk.zeta);
            let zetaw_n = pow2pow(zetaw);

            evals
                .evals
                .map_ref(&|PointEvaluations { zeta, zeta_omega }| {
                    let zeta = actual_evaluation(zeta, zeta_n);
                    let zeta_omega = actual_evaluation(zeta_omega, zetaw_n);
                    PointEvaluations { zeta, zeta_omega }
                })
        };

        let srs_length_log2 = COMMON_MAX_DEGREE_STEP_LOG2;
        let env = make_scalars_env_checked(
            MakeScalarsEnvParams {
                minimal: &plonk_mininal,
                domain,
                srs_length_log2,
                hack_feature_flags,
                zk_rows,
            },
            w,
        );
        let combined_inner_product_correct = {
            let p_eval0 = &evals.public_input.0;

            let ft_eval0 = ft_eval0_checked(
                &env,
                &combined_evals,
                &plonk_mininal,
                plonk.lookup,
                p_eval0,
                w,
            );
            let a = proof_evaluation_to_list_opt(&evals.evals, hack_feature_flags)
                .into_iter()
                .filter_map(|v| match v {
                    Opt::No => None,
                    Opt::Some(PointEvaluations { zeta, zeta_omega }) => Some([
                        zeta.into_iter().map(Opt::Some).collect::<Vec<_>>(),
                        zeta_omega.into_iter().map(Opt::Some).collect::<Vec<_>>(),
                    ]),
                    Opt::Maybe(boolean, PointEvaluations { zeta, zeta_omega }) => Some([
                        zeta.into_iter()
                            .map(|a| Opt::Maybe(boolean, a))
                            .collect::<Vec<_>>(),
                        zeta_omega
                            .into_iter()
                            .map(|a| Opt::Maybe(boolean, a))
                            .collect::<Vec<_>>(),
                    ]),
                })
                .collect::<Vec<_>>();

            let actual_combined_inner_product = {
                enum WhichEval {
                    First,
                    Second,
                }

                let combine = |which_eval: WhichEval,
                               sg_evals: &[(Boolean, Fp)],
                               ft_eval: Fp,
                               x_hat: &[Fp],
                               w: &mut Witness<Fp>| {
                    let f = |[a, b]: &[Vec<Opt<Fp>>; 2]| match which_eval {
                        WhichEval::First => a.clone(),
                        WhichEval::Second => b.clone(),
                    };
                    let v = sg_evals
                        .iter()
                        .copied()
                        .map(|(b, v)| Opt::Maybe(b, v))
                        .chain(x_hat.iter().copied().map(Opt::Some).collect::<Vec<_>>())
                        .chain([Opt::Some(ft_eval)])
                        .chain(a.iter().flat_map(f))
                        .rev()
                        .collect::<Vec<_>>();
                    let (init, rest) = v.split_at(1);

                    let init = match init[0] {
                        Opt::Some(x) => x,
                        Opt::No => Fp::zero(),
                        Opt::Maybe(b, x) => field::mul(b.to_field(), x, w),
                    };
                    rest.iter().fold(init, |acc: Fp, fx: &Opt<Fp>| match fx {
                        Opt::No => acc,
                        Opt::Some(fx) => *fx + field::mul(xi, acc, w),
                        Opt::Maybe(b, fx) => {
                            let on_true = *fx + field::mul(xi, acc, w);
                            w.exists_no_check(match b {
                                Boolean::True => on_true,
                                Boolean::False => acc,
                            })
                        }
                    })
                };

                // We decompose this way because of OCaml evaluation order
                let b = combine(
                    WhichEval::Second,
                    &sg_evals2,
                    *ft_eval1,
                    &evals.public_input.1,
                    w,
                );
                let b = field::mul(b, r, w);
                let a = combine(
                    WhichEval::First,
                    &sg_evals1,
                    ft_eval0,
                    &evals.public_input.0,
                    w,
                );
                a + b
            };

            let combined_inner_product =
                ShiftingValue::<Fp>::shifted_to_field(combined_inner_product);
            field::equal(combined_inner_product, actual_combined_inner_product, w)
        };

        let mut bulletproof_challenges = bulletproof_challenges
            .iter()
            .rev()
            .map(|f| to_field_checked::<Fp, 128>(*f, endo, w))
            .collect::<Vec<_>>();
        bulletproof_challenges.reverse();

        let b_correct = {
            let challenge_poly = challenge_polynomial_checked(&bulletproof_challenges);

            // We decompose this way because of OCaml evaluation order
            let r_zetaw = field::mul(r, challenge_poly(zetaw, w), w);
            let b_actual = challenge_poly(plonk.zeta, w) + r_zetaw;

            field::equal(b.shifted_to_field(), b_actual, w)
        };

        let plonk = wrap_verifier::PlonkWithField {
            alpha: plonk.alpha,
            beta: plonk.beta,
            gamma: plonk.gamma,
            zeta: plonk.zeta,
            zeta_to_srs_length: plonk.zeta_to_srs_length,
            zeta_to_domain_size: plonk.zeta_to_domain_size,
            perm: plonk.perm,
            lookup: (),
        };
        let plonk_checks_passed = plonk_checks::checked(&env, &combined_evals, &plonk, w);

        let finalized = Boolean::all(
            &[
                xi_correct,
                b_correct,
                combined_inner_product_correct,
                plonk_checks_passed,
            ],
            w,
        );

        Ok((finalized, bulletproof_challenges))
    }

    pub(super) fn sponge_after_index(
        index: &PlonkVerificationKeyEvals<Fp>,
        w: &mut Witness<Fp>,
    ) -> Sponge<Fp> {
        let mut sponge = Sponge::<Fp>::new();
        let fields = index.to_field_elements_owned();
        sponge.absorb2(&fields, w);
        sponge
    }

    pub(super) fn hash_messages_for_next_step_proof_opt(
        msg: ReducedMessagesForNextStepProof,
        sponge: Sponge<Fp>,
        _widths: &ForStepKind<Vec<Fp>>,
        _max_width: usize,
        proofs_verified_mask: &[Boolean],
        w: &mut Witness<Fp>,
    ) -> Fp {
        enum MaybeOpt<T, T2> {
            Opt(Boolean, T),
            NotOpt(T2),
        }

        let ReducedMessagesForNextStepProof {
            app_state,
            challenge_polynomial_commitments,
            old_bulletproof_challenges,
        } = msg;

        let old_bulletproof_challenges = proofs_verified_mask
            .iter()
            .zip(old_bulletproof_challenges)
            .map(|(b, v)| {
                let b = *b;
                v.map(|v| MaybeOpt::Opt(b, v))
            });

        let challenge_polynomial_commitments = proofs_verified_mask
            .iter()
            .zip(challenge_polynomial_commitments)
            .map(|(b, v)| {
                let b = *b;
                let GroupAffine::<Fp> { x, y, .. } = v.to_affine();
                [MaybeOpt::Opt(b, x), MaybeOpt::Opt(b, y)]
            });

        let app_state = app_state
            .to_field_elements_owned()
            .into_iter()
            .map(MaybeOpt::NotOpt);

        let both = challenge_polynomial_commitments
            .zip(old_bulletproof_challenges)
            .flat_map(|(c, o)| c.into_iter().chain(o));

        let sponge = Box::new(sponge);
        let res = app_state
            .chain(both)
            .fold(MaybeOpt::NotOpt(sponge), |acc, v| match (acc, v) {
                (MaybeOpt::NotOpt(mut sponge), MaybeOpt::NotOpt(v)) => {
                    sponge.absorb(&[v], w);
                    MaybeOpt::NotOpt(sponge)
                }
                (MaybeOpt::NotOpt(sponge), MaybeOpt::Opt(b, v)) => {
                    let mut sponge = Box::new(OptSponge::of_sponge(*sponge, w));
                    sponge.absorb((CircuitVar::Var(b), v));
                    MaybeOpt::Opt(Boolean::True, sponge)
                }
                (MaybeOpt::Opt(_, mut sponge), MaybeOpt::Opt(b, v)) => {
                    sponge.absorb((CircuitVar::Var(b), v));
                    MaybeOpt::Opt(Boolean::True, sponge)
                }
                (MaybeOpt::Opt(_, _), MaybeOpt::NotOpt(_)) => panic!(),
            });

        match res {
            MaybeOpt::NotOpt(mut sponge) => sponge.squeeze(w),
            MaybeOpt::Opt(_, mut sponge) => sponge.squeeze(w),
        }
    }

    // TODO: Dedup with the one in `wrap_verifier`
    fn scale_fast2<F: FieldWitness>(
        g: CircuitVar<GroupAffine<F>>,
        (s_div_2, s_odd): (F, Boolean),
        num_bits: usize,
        w: &mut Witness<F>,
    ) -> GroupAffine<F> {
        use crate::proofs::transaction::plonk_curve_ops::scale_fast_unpack;
        use wrap_verifier::*;

        let s_div_2_bits = num_bits - 1;
        let chunks_needed = chunks_needed(s_div_2_bits);
        let actual_bits_used = chunks_needed * OPS_BITS_PER_CHUNK;

        let g_value = *g.value();
        let shifted = F::Shifting::of_raw(s_div_2);
        let h = match actual_bits_used {
            255 => scale_fast_unpack::<F, F, 255>(g_value, shifted, w).0,
            130 => scale_fast_unpack::<F, F, 130>(g_value, shifted, w).0,
            10 => scale_fast_unpack::<F, F, 10>(g_value, shifted, w).0,
            n => todo!("{:?} param_num_bits={:?}", n, num_bits),
        };

        let on_false = {
            let g_neg = g.value().neg();
            if let CircuitVar::Var(_) = g {
                w.exists(g_neg.y);
            } else {
                // eprintln!("ignoring {:?}", g_neg.y);
            }
            w.add_fast(h, g_neg)
        };

        w.exists_no_check(match s_odd {
            Boolean::True => h,
            Boolean::False => on_false,
        })
    }

    // TODO: Dedup with the one above and in `wrap_verifier`
    fn scale_fast22<F: FieldWitness>(
        g: CircuitVar<GroupAffine<F>>,
        (s_div_2, s_odd): (F, Boolean),
        num_bits: usize,
        w: &mut Witness<F>,
    ) -> GroupAffine<F> {
        use crate::proofs::transaction::plonk_curve_ops::scale_fast_unpack;
        use wrap_verifier::*;

        let s_div_2_bits = num_bits - 1;
        let chunks_needed = chunks_needed(s_div_2_bits);
        let actual_bits_used = chunks_needed * OPS_BITS_PER_CHUNK;

        let g_value = *g.value();
        let shifted = F::Shifting::of_raw(s_div_2);
        let h = match actual_bits_used {
            255 => scale_fast_unpack::<F, F, 255>(g_value, shifted, w).0,
            130 => scale_fast_unpack::<F, F, 130>(g_value, shifted, w).0,
            10 => scale_fast_unpack::<F, F, 10>(g_value, shifted, w).0,
            n => todo!("{:?} param_num_bits={:?}", n, num_bits),
        };

        let on_false = {
            let g_neg = w.exists_no_check(g.value().neg());
            w.add_fast(h, g_neg)
        };

        w.exists_no_check(match s_odd {
            Boolean::True => h,
            Boolean::False => on_false,
        })
    }

    // TODO: Dedup with the one in `wrap_verifier`
    pub(super) fn scale_fast2_prime<F: FieldWitness, F2: FieldWitness>(
        g: CircuitVar<GroupAffine<F>>,
        s: F2,
        num_bits: usize,
        w: &mut Witness<F>,
    ) -> GroupAffine<F> {
        let s_parts = w.exists({
            // TODO: Here `s` is a `F` but needs to be read as a `F::Scalar`
            let bigint: BigInteger256 = s.into();
            let bigint = bigint.0;
            let s_odd = bigint[0] & 1 != 0;
            let v = if s_odd { s - F2::one() } else { s };
            // TODO: Remove this ugly hack
            let v: BigInteger256 = (v / F2::from(2u64)).into();
            (F::from(v), s_odd.to_boolean()) // `unwrap` never fail
        });

        scale_fast2(g, s_parts, num_bits, w)
    }

    // TODO: Dedup with the one in `wrap_verifier`
    pub(super) fn ft_comm<F: FieldWitness, Scale>(
        plonk: &Plonk<<F as proofs::field::FieldWitness>::Scalar>,
        t_comm: &PolyComm<GroupAffine<F>>,
        verification_key: &CircuitPlonkVerificationKeyEvals<F>,
        scale: Scale,
        w: &mut Witness<F>,
    ) -> GroupAffine<F>
    where
        Scale: Fn(
            CircuitVar<GroupAffine<F>>,
            <<F as proofs::field::FieldWitness>::Scalar as FieldWitness>::Shifting,
            &mut Witness<F>,
        ) -> GroupAffine<F>,
    {
        let m = verification_key;
        let [sigma_comm_last] = &m.sigma[PERMUTS_MINUS_1_ADD_N1..] else {
            panic!()
        };

        // We decompose this way because of OCaml evaluation order (reversed)
        let f_comm = [scale(*sigma_comm_last, plonk.perm.clone(), w)]
            .into_iter()
            .rev()
            .reduce(|acc, v| w.add_fast(acc, v))
            .unwrap();

        let chunked_t_comm = t_comm
            .chunks
            .iter()
            .rev()
            .copied()
            .reduce(|acc, v| {
                let scaled = scale(CircuitVar::Var(acc), plonk.zeta_to_srs_length.clone(), w);
                w.add_fast(v, scaled)
            })
            .unwrap();

        // We decompose this way because of OCaml evaluation order
        let scaled = scale(
            CircuitVar::Var(chunked_t_comm),
            plonk.zeta_to_domain_size.clone(),
            w,
        )
        .neg();
        let v = w.add_fast(f_comm, chunked_t_comm);

        // Because of `neg()` above
        w.exists_no_check(scaled.y);

        w.add_fast(v, scaled)
    }

    fn public_input_commitment_dynamic(
        which: &[Boolean],
        srs: &mut poly_commitment::ipa::SRS<Pallas>,
        domains: Vec<Domains>,
        public_input: Vec<Packed>,
        w: &mut Witness<Fp>,
    ) -> GroupAffine<Fp> {
        let lagrange_commitment =
            |d: &Domains, i: usize, srs: &mut poly_commitment::ipa::SRS<Pallas>| {
                let d = 2u64.pow(d.h.log2_size() as u32);
                let elems = wrap_verifier::lagrange_commitment::<Fp>(srs, d, i).chunks;
                assert_eq!(elems.len(), 1);
                InnerCurve::<Fp>::of_affine(elems[0])
            };

        fn select_curve_points(
            domains: &[Domains],
            which: &[Boolean],
            srs: &mut poly_commitment::ipa::SRS<Pallas>,
            w: &mut Witness<Fp>,
            points_for_domain: impl Fn(
                &Domains,
                &mut poly_commitment::ipa::SRS<Pallas>,
            ) -> Vec<InnerCurve<Fp>>,
        ) -> Vec<InnerCurve<Fp>> {
            let (d, ds) = domains.split_first().unwrap();
            if ds.iter().all(|d2| d2.h == d.h) {
                points_for_domain(d, srs)
            } else {
                let index = which.iter().position(|b| b.as_bool()).unwrap();
                let domain = &domains[index];
                let points = points_for_domain(domain, srs);
                for p in points.iter().rev() {
                    let GroupAffine::<Fp> { x, y, .. } = p.to_affine();
                    w.exists_no_check([y, x]);
                }
                points
            }
        }

        let lagrange =
            |i: usize, srs: &mut poly_commitment::ipa::SRS<Pallas>, w: &mut Witness<Fp>| {
                let vec = select_curve_points(&domains, which, srs, w, |d, srs| {
                    vec![lagrange_commitment(d, i, srs)]
                });
                vec[0].clone()
            };

        let pow2pow = |x: InnerCurve<Fp>, n: usize| (0..n).fold(x, |acc, _| acc.clone() + acc);

        let lagrange_with_correction = |input_length: usize,
                                        i: usize,
                                        srs: &mut poly_commitment::ipa::SRS<Pallas>,
                                        w: &mut Witness<Fp>|
         -> Vec<InnerCurve<Fp>> {
            let actual_shift = OPS_BITS_PER_CHUNK * chunks_needed(input_length);

            select_curve_points(&domains, which, srs, w, |d, srs| {
                let g = lagrange_commitment(d, i, srs);
                let powed = pow2pow(g.clone(), actual_shift);
                let powed = powed.to_affine().neg();
                vec![g, InnerCurve::of_affine(powed)]
            })
        };

        let x_hat = {
            let (constant_part, non_constant_part): (Vec<_>, Vec<_>) = public_input
                .into_iter()
                .enumerate()
                .partition_map(|(i, t)| {
                    use itertools::Either::{Left, Right};
                    use CircuitVar::Constant;
                    use Packed::{Field, PackedBits};

                    match t {
                        Field(Constant(c)) | PackedBits(Constant(c), _) => Left(if c.is_zero() {
                            None
                        } else if c.is_one() {
                            Some(lagrange(i, srs, w))
                        } else {
                            todo!()
                        }),
                        Field(x) => Right((i, (x, 255))),
                        PackedBits(x, n) => Right((i, (x, n))),
                    }
                });

            #[derive(Debug)]
            enum CondOrAdd {
                CondAdd(CircuitVar<Boolean>, InnerCurve<Fp>),
                AddWithCorrection((CircuitVar<Fq>, usize), Vec<InnerCurve<Fp>>),
            }

            let terms = non_constant_part
                .into_iter()
                .map(|(i, x)| match x {
                    (b, 1) => CondOrAdd::CondAdd(CircuitVar::of_cvar(b), lagrange(i, srs, w)),
                    (x, n) => {
                        CondOrAdd::AddWithCorrection((x, n), lagrange_with_correction(n, i, srs, w))
                    }
                })
                .collect::<Vec<_>>();

            let correction = terms
                .iter()
                .filter_map(|term| match term {
                    CondOrAdd::CondAdd(_, _) => None,
                    CondOrAdd::AddWithCorrection(_, v) => {
                        let [_, corr] = v.as_slice() else { panic!() };
                        Some(corr.to_affine())
                    }
                })
                .reduce(|a, b| w.add_fast(a, b))
                .unwrap();

            let init =
                constant_part
                    .iter()
                    .filter_map(|term| term.as_ref())
                    .fold(correction, |acc, v| {
                        let v = v.to_affine();
                        w.add_fast(acc, v)
                    });

            let result = terms.iter().fold(init, |acc, term| match term {
                CondOrAdd::CondAdd(b, g) => {
                    let on_true = w.add_fast(g.to_affine(), acc);
                    w.exists_no_check(match b.value() {
                        Boolean::True => on_true,
                        Boolean::False => acc,
                    })
                }
                CondOrAdd::AddWithCorrection((x, num_bits), slice) => {
                    let g = &slice[0];
                    let g = CircuitVar::Var(g.to_affine());
                    let acc2 = scale_fast2_prime(g, *x.value(), *num_bits, w);
                    w.add_fast(acc, acc2)
                }
            });
            result.neg()
        };

        x_hat
    }

    fn multiscale_known(ts: &[(&Packed, InnerCurve<Fp>)], w: &mut Witness<Fp>) -> GroupAffine<Fp> {
        let pow2pow = |x: InnerCurve<Fp>, n: usize| (0..n).fold(x, |acc, _| acc.clone() + acc);

        let (constant_part, non_constant_part): (Vec<_>, Vec<_>) =
            ts.iter().partition_map(|(t, g)| {
                use itertools::Either::{Left, Right};
                use CircuitVar::Constant;
                use Packed::{Field, PackedBits};

                match t {
                    Field(Constant(c)) | PackedBits(Constant(c), _) => Left(if c.is_zero() {
                        None
                    } else if c.is_one() {
                        Some(g)
                    } else {
                        todo!()
                    }),
                    Field(x) => Right((Field(*x), g)),
                    PackedBits(x, n) => Right((PackedBits(*x, *n), g)),
                }
            });

        let add_opt = |xo: Option<InnerCurve<Fp>>, y: &InnerCurve<Fp>| match xo {
            Some(x) => x + y.clone(),
            None => y.clone(),
        };

        let constant_part = constant_part
            .iter()
            .filter_map(|c| c.as_ref())
            .fold(None, |acc, x| Some(add_opt(acc, x)));

        let (correction, acc) = {
            non_constant_part
                .iter()
                .map(|(s, x)| {
                    let (rr, n) = match s {
                        Packed::PackedBits(s, n) => {
                            let x = CircuitVar::Constant(x.to_affine());
                            let c = scale_fast2_prime(x, s.as_field(), *n, w);
                            (c, *n)
                        }
                        Packed::Field(s) => {
                            let x = CircuitVar::Constant(x.to_affine());
                            let c = scale_fast2_prime(x, s.as_field(), 255, w);
                            (c, 255)
                        }
                    };

                    let n = wrap_verifier::OPS_BITS_PER_CHUNK * wrap_verifier::chunks_needed(n - 1);
                    let cc = pow2pow((*x).clone(), n);
                    (cc, rr)
                })
                .collect::<Vec<_>>() // We need to collect because `w` is borrowed :(
                .into_iter()
                .reduce(|(a1, b1), (a2, b2)| ((a1 + a2), w.add_fast(b1, b2)))
                .unwrap()
        };

        let correction = InnerCurve::of_affine(correction.to_affine().neg());
        w.add_fast(acc, add_opt(constant_part, &correction).to_affine())
    }

    fn lagrange_commitment<F: FieldWitness>(
        srs: &mut SRS<GroupAffine<F>>,
        domain: &Domain,
        i: usize,
    ) -> InnerCurve<F> {
        let d = domain.size();
        let elems = wrap_verifier::lagrange_commitment::<F>(srs, d, i).chunks;

        assert_eq!(elems.len(), 1);
        InnerCurve::of_affine(elems[0])
    }

    fn to_high_low(f: Fq) -> (Fp, Boolean) {
        fn of_bits<F: FieldWitness>(bs: &[bool; 254]) -> F {
            bs.iter().rev().fold(F::zero(), |acc, b| {
                let acc = acc + acc;
                if *b {
                    acc + F::one()
                } else {
                    acc
                }
            })
        }
        let to_high_low = |fq: Fq| {
            let [low, high @ ..] = crate::proofs::transaction::field_to_bits::<Fq, 255>(fq);
            (of_bits::<Fp>(&high), low.to_boolean())
        };
        to_high_low(f)
    }

    fn scale_for_ft_comm(
        g: CircuitVar<GroupAffine<Fp>>,
        f: <Fq as FieldWitness>::Shifting,
        w: &mut Witness<Fp>,
    ) -> GroupAffine<Fp> {
        let scalar = to_high_low(f.shifted_raw());
        scale_fast2(g, scalar, 255, w)
    }

    struct CheckBulletProofParams<'a> {
        pcs_batch: PcsBatch,
        sponge: Sponge<Fp>,
        xi: [u64; 2],
        advice: &'a Advice<Fp>,
        openings_proof: &'a OpeningProof<GroupAffine<Fp>>,
        srs: &'a SRS<GroupAffine<Fp>>,
        polynomials: (Vec<CircuitVar<GroupAffine<Fp>>>, Vec<()>),
    }

    fn check_bulletproof(
        params: CheckBulletProofParams,
        w: &mut Witness<Fp>,
    ) -> anyhow::Result<(Boolean, Vec<Fp>)> {
        let CheckBulletProofParams {
            pcs_batch: _,
            mut sponge,
            xi,
            advice,
            openings_proof:
                OpeningProof {
                    lr,
                    delta,
                    z1,
                    z2,
                    sg,
                },
            srs,
            polynomials,
        } = params;

        let (without_degree_bound, _with_degree_bound) = polynomials;

        let (high, low) = to_high_low(advice.combined_inner_product.shifted_raw());
        sponge.absorb2(&[high, low.to_field()], w);

        let u = {
            let t = sponge.squeeze(w);
            wrap_verifier::group_map(t, w)
        };

        let xi_field: Fq = two_u64_to_field(&xi);

        let point: Point<Fp> = PcsBatch::combine_split_commitments::<Fp, _, _, _, _>(
            |p, _w| p.clone(),
            |acc, _xi, p, w| match acc {
                Point::MaybeFinite(acc_is_finite, acc) => match p {
                    Point::MaybeFinite(p_is_finite, p) => {
                        let is_finite = p_is_finite.or(&acc_is_finite, w);
                        let xi_acc = scalar_challenge::endo_cvar::<Fp, _, 128>(acc, xi_field, w);

                        let on_true = CircuitVar::Var(w.add_fast(*p.value(), xi_acc));

                        let v = match acc_is_finite.as_boolean() {
                            Boolean::True => on_true,
                            Boolean::False => *p,
                        };
                        if let CircuitVar::Var(_) = acc_is_finite {
                            w.exists_no_check(v.value());
                        };
                        Point::<Fp>::MaybeFinite(is_finite, v)
                    }
                    Point::Finite(p) => {
                        let xi_acc = scalar_challenge::endo_cvar::<Fp, _, 128>(acc, xi_field, w);
                        let on_true = CircuitVar::Var(w.add_fast(*p.value(), xi_acc));

                        let v = match acc_is_finite.as_boolean() {
                            Boolean::True => on_true,
                            Boolean::False => *p,
                        };
                        if let CircuitVar::Var(_) = acc_is_finite {
                            w.exists_no_check(v.value());
                        };
                        Point::<Fp>::Finite(v)
                    }
                },
                Point::Finite(acc) => {
                    let xi_acc = scalar_challenge::endo_cvar::<Fp, _, 128>(acc, xi_field, w);

                    let v = match p {
                        Point::Finite(p) => CircuitVar::Var(w.add_fast(*p.value(), xi_acc)),
                        Point::MaybeFinite(p_is_finite, p) => {
                            let p = *p;
                            let on_true = CircuitVar::Var(w.add_fast(*p.value(), xi_acc));

                            let v = match p_is_finite.as_boolean() {
                                Boolean::True => on_true,
                                Boolean::False => CircuitVar::Var(xi_acc),
                            };
                            if let CircuitVar::Var(_) = p_is_finite {
                                w.exists_no_check(v.value());
                            };
                            v
                        }
                    };

                    Point::Finite(v)
                }
            },
            xi,
            &without_degree_bound
                .into_iter()
                .map(Point::Finite)
                .collect::<Vec<_>>(),
            &[],
            w,
        );

        let Point::Finite(combined_polynomial) = point else {
            panic!("invalid state");
        };
        let combined_polynomial = *combined_polynomial.value();

        let (lr_prod, challenges) = wrap_verifier::bullet_reduce(&mut sponge, lr, w);

        let p_prime = {
            w.exists_no_check(&u); // Made by `plonk_curve_ops.seal` in `scale_fast`
            let combined_inner_product = to_high_low(advice.combined_inner_product.shifted_raw());
            let uc = scale_fast22(CircuitVar::Var(u), combined_inner_product, 255, w);
            w.add_fast(combined_polynomial, uc)
        };

        let q = w.add_fast(p_prime, lr_prod);
        absorb_curve(delta, &mut sponge, w);
        let c = squeeze_scalar(&mut sponge, w);

        let lhs = {
            let cq = scalar_challenge::endo::<Fp, Fp, 128>(q, c, w);
            w.add_fast(cq, *delta)
        };

        let rhs = {
            let b_u = {
                w.exists_no_check(&u); // Made by `plonk_curve_ops.seal` in `scale_fast`
                let b = to_high_low(advice.b.shifted_raw());
                scale_fast22(CircuitVar::Var(u), b, 255, w)
            };

            let z_1_g_plus_b_u = {
                use plonk_checks::ShiftedValue;

                let z1 = to_high_low(ShiftedValue::<Fq>::of_field(*z1).shifted);
                scale_fast2(CircuitVar::Var(w.add_fast(*sg, b_u)), z1, 255, w)
            };

            let z2_h = {
                use plonk_checks::ShiftedValue;

                let z2 = to_high_low(ShiftedValue::<Fq>::of_field(*z2).shifted);
                scale_fast2(CircuitVar::Constant(srs.h), z2, 255, w)
            };

            w.add_fast(z_1_g_plus_b_u, z2_h)
        };

        Ok((wrap_verifier::equal_g(lhs, rhs, w), challenges))
    }

    struct IncrementallyVerifyProofParams<'a> {
        pub proofs_verified: usize,
        pub srs: &'a mut poly_commitment::ipa::SRS<Pallas>,
        pub wrap_domain: &'a ForStepKind<Domain, Box<[Boolean]>>,
        pub sponge: Sponge<Fp>,
        pub sponge_after_index: Sponge<Fp>,
        pub wrap_verification_key: &'a CircuitPlonkVerificationKeyEvals<Fp>,
        pub xi: [u64; 2],
        pub public_input: Vec<Packed>,
        pub sg_old: &'a Vec<GroupAffine<Fp>>,
        pub advice: &'a Advice<Fp>,
        pub proof: &'a ProverProof<Fq>,
        pub plonk: &'a Plonk<Fq>,
    }

    fn incrementally_verify_proof(
        params: IncrementallyVerifyProofParams,
        w: &mut Witness<Fp>,
    ) -> anyhow::Result<(Fp, (Boolean, Vec<Fp>))> {
        let IncrementallyVerifyProofParams {
            proofs_verified: _,
            srs,
            wrap_domain,
            mut sponge,
            sponge_after_index,
            wrap_verification_key,
            xi,
            public_input,
            sg_old,
            advice,
            proof,
            plonk,
        } = params;

        let ProverProof::<Fq> {
            commitments: messages,
            proof: openings_proof,
            ..
            // evals,
            // ft_eval1,
            // prev_challenges
        } = proof;

        let sample = squeeze_challenge;
        let sample_scalar = squeeze_scalar;

        let index_digest = {
            let mut index_sponge = sponge_after_index.clone();
            index_sponge.squeeze(w)
        };

        sponge.absorb2(&[index_digest], w);

        // Or padding
        assert_eq!(sg_old.len(), 2);
        for v in sg_old {
            absorb_curve(v, &mut sponge, w);
        }

        let x_hat = match wrap_domain {
            ForStepKind::Known(domain) => {
                let ts = public_input
                    .iter()
                    .enumerate()
                    .map(|(i, x)| (x, lagrange_commitment::<Fp>(srs, domain, i)))
                    .collect::<Vec<_>>();
                multiscale_known(&ts, w).neg()
            }
            ForStepKind::SideLoaded(which) => {
                let domains = [0, 1, 2].into_iter().map(wrap_domains).collect();
                public_input_commitment_dynamic(which, srs, domains, public_input, w)
            }
        };

        let x_hat = {
            w.exists(x_hat.y); // Because of `.neg()` above
            w.add_fast(x_hat, srs.h)
        };

        absorb_curve(&x_hat, &mut sponge, w);

        let w_comm = &messages.w_comm;
        for g in w_comm.iter().flat_map(|w| &w.chunks) {
            absorb_curve(g, &mut sponge, w);
        }

        let _beta = sample(&mut sponge, w);
        let _gamma = sample(&mut sponge, w);

        let z_comm = &messages.z_comm;
        for z in z_comm.chunks.iter() {
            absorb_curve(z, &mut sponge, w);
        }

        let _alpha = sample_scalar(&mut sponge, w);

        let t_comm = &messages.t_comm;
        for t in t_comm.chunks.iter() {
            absorb_curve(t, &mut sponge, w);
        }

        let _zeta = sample_scalar(&mut sponge, w);

        let sponge_before_evaluations = sponge.clone();
        let sponge_digest_before_evaluations = sponge.squeeze(w);

        let sigma_comm_init = &wrap_verification_key.sigma[..PERMUTS_MINUS_1_ADD_N1];

        let ft_comm = ft_comm(plonk, t_comm, wrap_verification_key, scale_for_ft_comm, w);

        let bulletproof_challenges = {
            /// Wrap_hack.Padded_length
            const WRAP_HACK_PADDED_LENGTH: usize = 2;
            const NUM_COMMITMENTS_WITHOUT_DEGREE_BOUND: usize = 45;

            let cvar = CircuitVar::Var;

            let without_degree_bound = {
                let sg_old = sg_old.iter().copied().map(cvar);
                let rest = [cvar(x_hat), cvar(ft_comm)]
                    .into_iter()
                    .chain(z_comm.chunks.iter().cloned().map(cvar))
                    .chain([
                        wrap_verification_key.generic,
                        wrap_verification_key.psm,
                        wrap_verification_key.complete_add,
                        wrap_verification_key.mul,
                        wrap_verification_key.emul,
                        wrap_verification_key.endomul_scalar,
                    ])
                    .chain(
                        w_comm
                            .iter()
                            .flat_map(|w| w.chunks.iter().cloned().map(cvar)),
                    )
                    .chain(wrap_verification_key.coefficients)
                    .chain(sigma_comm_init.iter().cloned());
                sg_old.chain(rest).collect::<Vec<_>>()
            };

            check_bulletproof(
                CheckBulletProofParams {
                    pcs_batch: PcsBatch::create(
                        WRAP_HACK_PADDED_LENGTH + NUM_COMMITMENTS_WITHOUT_DEGREE_BOUND,
                    ),
                    sponge: sponge_before_evaluations,
                    xi,
                    advice,
                    openings_proof,
                    srs,
                    polynomials: (without_degree_bound, vec![]),
                },
                w,
            )?
        };

        Ok((sponge_digest_before_evaluations, bulletproof_challenges))
    }

    pub(super) struct VerifyParams<'a> {
        pub(super) srs: &'a mut poly_commitment::ipa::SRS<Pallas>,
        pub(super) feature_flags: &'a FeatureFlags<OptFlag>,
        pub(super) lookup_parameters: (),
        pub(super) proofs_verified: usize,
        pub(super) wrap_domain: &'a ForStepKind<Domain, Box<[Boolean]>>,
        pub(super) is_base_case: CircuitVar<Boolean>,
        pub(super) sponge_after_index: Sponge<Fp>,
        pub(super) sg_old: &'a Vec<GroupAffine<Fp>>,
        pub(super) proof: &'a ProverProof<Fq>,
        pub(super) wrap_verification_key: &'a CircuitPlonkVerificationKeyEvals<Fp>,
        pub(super) statement: &'a PreparedStatement,
        pub(super) hack_feature_flags: OptFlag,
        pub(super) unfinalized: &'a Unfinalized,
    }

    pub(super) fn verify(params: VerifyParams, w: &mut Witness<Fp>) -> anyhow::Result<Boolean> {
        let VerifyParams {
            srs,
            feature_flags: _,
            lookup_parameters: _,
            proofs_verified,
            wrap_domain,
            is_base_case,
            sponge_after_index,
            sg_old,
            proof,
            wrap_verification_key,
            statement,
            hack_feature_flags,
            unfinalized,
        } = params;

        let public_input = {
            let npublic_input = match hack_feature_flags {
                OptFlag::No => 39,
                OptFlag::Maybe => 40,
                OptFlag::Yes => todo!(),
            };
            statement.to_public_input_cvar(hack_feature_flags, npublic_input)?
        };

        let unfinalized::DeferredValues {
            plonk,
            combined_inner_product,
            b,
            xi,
            bulletproof_challenges: _,
        } = &unfinalized.deferred_values;

        let b = b.clone();
        let combined_inner_product = combined_inner_product.clone();
        let sponge = Sponge::new();

        let (
            _sponge_digest_before_evaluations_actual,
            (bulletproof_success, bulletproof_challenges_actual),
        ) = incrementally_verify_proof(
            IncrementallyVerifyProofParams {
                proofs_verified,
                srs,
                wrap_domain,
                sponge,
                sponge_after_index,
                wrap_verification_key,
                xi: *xi,
                public_input,
                sg_old,
                advice: &Advice {
                    b,
                    combined_inner_product,
                },
                proof,
                plonk,
            },
            w,
        )?;

        for (c1, c2) in unfinalized
            .deferred_values
            .bulletproof_challenges
            .iter()
            .zip(&bulletproof_challenges_actual)
        {
            let v = match is_base_case.value() {
                Boolean::True => two_u64_to_field(c1),
                Boolean::False => *c2,
            };
            if let CircuitVar::Var(_) = is_base_case {
                w.exists_no_check(v);
            };
        }

        Ok(bulletproof_success)
    }
}

struct VerifyOneParams<'a> {
    srs: &'a mut poly_commitment::ipa::SRS<Pallas>,
    proof: &'a PerProofWitness,
    data: &'a ForStep,
    messages_for_next_wrap_proof: Fp,
    unfinalized: &'a Unfinalized,
    should_verify: CircuitVar<Boolean>,
}

fn verify_one(params: VerifyOneParams, w: &mut Witness<Fp>) -> anyhow::Result<(Vec<Fp>, Boolean)> {
    let VerifyOneParams {
        srs,
        proof,
        data,
        messages_for_next_wrap_proof,
        unfinalized,
        should_verify,
    } = params;

    let PerProofWitness {
        app_state,
        wrap_proof,
        proof_state,
        prev_proof_evals,
        prev_challenges,
        prev_challenge_polynomial_commitments,
        hack_feature_flags,
    } = proof;

    let deferred_values = &proof_state.deferred_values;

    let (finalized, chals) = {
        let sponge_digest = proof_state.sponge_digest_before_evaluations;

        let sponge = {
            let mut sponge = crate::proofs::transaction::poseidon::Sponge::<Fp>::new();
            sponge.absorb2(&[four_u64_to_field(&sponge_digest)?], w);
            sponge
        };

        step_verifier::finalize_other_proof(
            step_verifier::FinalizeOtherProofParams {
                max_proof_verified: data.max_proofs_verified,
                feature_flags: &data.feature_flags,
                step_domains: &data.step_domains,
                sponge,
                prev_challenges,
                deferred_values,
                evals: prev_proof_evals,
                hack_feature_flags: *hack_feature_flags,
                zk_rows: data.zk_rows,
            },
            w,
        )?
    };

    let branch_data = &deferred_values.branch_data;

    let sponge_after_index = step_verifier::sponge_after_index(&data.wrap_key.to_non_cvar(), w);

    let statement = {
        let msg = ReducedMessagesForNextStepProof {
            app_state: app_state.clone().unwrap(),
            challenge_polynomial_commitments: prev_challenge_polynomial_commitments
                .iter()
                .map(|g| InnerCurve::of_affine(*g))
                .collect(),
            old_bulletproof_challenges: prev_challenges.clone(),
        };

        let ntrim_front = 2 - prev_challenge_polynomial_commitments.len();
        let proofs_verified_mask = {
            let proofs_verified_mask = &branch_data.proofs_verified;
            step_verifier::proof_verified_to_prefix(proofs_verified_mask)
        };
        let proofs_verified_mask = &proofs_verified_mask[ntrim_front..];

        let prev_messages_for_next_step_proof =
            step_verifier::hash_messages_for_next_step_proof_opt(
                msg,
                sponge_after_index.clone(),
                &data.proof_verifieds,
                data.max_proofs_verified,
                proofs_verified_mask,
                w,
            );

        PreparedStatement {
            proof_state: ProofState {
                messages_for_next_wrap_proof: { to_bytes(messages_for_next_wrap_proof) },
                ..proof_state.clone()
            },
            messages_for_next_step_proof: { to_bytes(prev_messages_for_next_step_proof) },
        }
    };

    let verified = step_verifier::verify(
        step_verifier::VerifyParams {
            srs,
            feature_flags: &data.feature_flags,
            lookup_parameters: (),
            proofs_verified: data.max_proofs_verified,
            wrap_domain: &data.wrap_domain,
            is_base_case: should_verify.neg(),
            sponge_after_index,
            sg_old: prev_challenge_polynomial_commitments,
            proof: wrap_proof,
            wrap_verification_key: &data.wrap_key,
            statement: &statement,
            hack_feature_flags: *hack_feature_flags,
            unfinalized,
        },
        w,
    )?;

    let a = verified.and(&finalized, w);
    let b = CircuitVar::Var(a).or(&should_verify.neg(), w);

    Ok((chals, b.as_boolean()))
}

fn to_bytes(f: Fp) -> [u64; 4] {
    let bigint: BigInteger256 = f.into();
    bigint.0
}

fn to_4limbs(v: [u64; 2]) -> [u64; 4] {
    [v[0], v[1], 0, 0]
}

pub struct ExpandDeferredParams<'a> {
    pub evals: &'a AllEvals<Fp>,
    pub old_bulletproof_challenges: &'a Vec<[Fp; 16]>,
    pub proof_state: &'a StatementProofState,
    pub zk_rows: u64,
}

pub fn expand_deferred(params: ExpandDeferredParams) -> anyhow::Result<DeferredValues<Fp>> {
    let ExpandDeferredParams {
        evals,
        old_bulletproof_challenges,
        proof_state,
        zk_rows,
    } = params;

    use super::public_input::scalar_challenge::ScalarChallenge;

    let (_, endo) = endos::<Fq>();

    let plonk0 = &proof_state.deferred_values.plonk;

    let zeta = ScalarChallenge::limbs_to_field(&plonk0.zeta_bytes);
    let alpha = ScalarChallenge::limbs_to_field(&plonk0.alpha_bytes);
    let step_domain: u8 = proof_state.deferred_values.branch_data.domain_log2.as_u8();

    let Some(num_coeffs) = 1u64.checked_shl(step_domain as u32) else {
        return Err(InvalidBigInt)?;
    };

    let Some(domain) = Radix2EvaluationDomain::<Fp>::new(num_coeffs as usize) else {
        return Err(InvalidBigInt)?;
    };

    let zetaw = zeta * domain.group_gen;

    let plonk_minimal = PlonkMinimal::<Fp, 4> {
        alpha,
        beta: plonk0.beta,
        gamma: plonk0.gamma,
        zeta,
        // joint_combiner: plonk0.joint_combiner,
        joint_combiner: plonk0
            .joint_combiner_bytes
            .as_ref()
            .map(ScalarChallenge::limbs_to_field),
        alpha_bytes: to_bytes(alpha),
        beta_bytes: to_4limbs(plonk0.beta_bytes),
        gamma_bytes: to_4limbs(plonk0.gamma_bytes),
        zeta_bytes: to_bytes(zeta),
        joint_combiner_bytes: plonk0.joint_combiner_bytes.map(to_4limbs),
        feature_flags: plonk0.feature_flags.clone(),
    };

    let combined_evals =
        evals_of_split_evals(zeta, zetaw, &evals.evals.evals, BACKEND_TICK_ROUNDS_N);

    let srs_length_log2 = COMMON_MAX_DEGREE_STEP_LOG2;
    let env = make_scalars_env(&plonk_minimal, step_domain, srs_length_log2, zk_rows);

    let plonk = {
        let InCircuit {
            alpha: _,
            beta: _,
            gamma: _,
            zeta: _,
            zeta_to_domain_size,
            zeta_to_srs_length,
            perm,
            lookup,
            feature_flags,
        } = derive_plonk(&env, &combined_evals, &plonk_minimal);

        Plonk {
            alpha: plonk0.alpha_bytes,
            beta: plonk0.beta_bytes,
            gamma: plonk0.gamma_bytes,
            zeta: plonk0.zeta_bytes,
            zeta_to_srs_length,
            zeta_to_domain_size,
            perm,
            feature_flags,
            lookup: lookup.map(|_| plonk0.joint_combiner_bytes.unwrap()),
        }
    };

    let xs = proof_evaluation_to_absorption_sequence(&evals.evals.evals);
    let (x1, x2) = &evals.evals.public_input;

    let old_bulletproof_challenges: Vec<_> = old_bulletproof_challenges
        .iter()
        .map(ScalarChallenge::array_to_fields)
        .collect();

    let challenges_digest = {
        let mut sponge = poseidon::Sponge::<Fp>::default();
        for old_bulletproof_challenges in &old_bulletproof_challenges {
            sponge.absorb(old_bulletproof_challenges);
        }
        sponge.squeeze()
    };

    let mut sponge = poseidon::FqSponge::default();
    sponge.absorb_fq(&[four_u64_to_field(
        &proof_state.sponge_digest_before_evaluations,
    )?]);
    sponge.absorb_fq(&[challenges_digest]);
    sponge.absorb_fq(&[evals.ft_eval1]);
    sponge.absorb_fq(x1);
    sponge.absorb_fq(x2);
    xs.iter().for_each(|PointEvaluations { zeta, zeta_omega }| {
        sponge.absorb_fq(zeta);
        sponge.absorb_fq(zeta_omega);
    });
    let xi_chal: [u64; 2] = sponge.squeeze_limbs();
    let r_chal: [u64; 2] = sponge.squeeze_limbs();

    let xi = ScalarChallenge::from(xi_chal).to_field(&endo);
    let r = ScalarChallenge::from(r_chal).to_field(&endo);

    let public_input = &evals.evals.public_input;

    let es = &evals.evals.evals;
    let tick_combined_evals = evals_of_split_evals(zeta, zetaw, es, super::BACKEND_TICK_ROUNDS_N);
    let public = PointEvaluations {
        zeta: public_input.0.clone(),
        zeta_omega: public_input.1.clone(),
    };

    let combined_inner_product_actual =
        combined_inner_product(CombinedInnerProductParams::<_, { Fp::NROUNDS }, 4> {
            env: &env,
            evals: es,
            combined_evals: &tick_combined_evals,
            public: &public,
            minimal: &plonk_minimal,
            ft_eval1: evals.ft_eval1,
            r,
            old_bulletproof_challenges: &old_bulletproof_challenges,
            xi,
            zetaw,
        });

    let bulletproof_challenges: Vec<_> = proof_state
        .deferred_values
        .bulletproof_challenges
        .iter()
        .map(ScalarChallenge::limbs_to_field)
        .collect();

    let b_actual = {
        let challenge_polys = challenge_polynomial(&bulletproof_challenges);
        challenge_polys(zeta) + (r * challenge_polys(zetaw))
    };

    let to_shifted = |f: Fp| <Fp as FieldWitness>::Shifting::of_field(f);

    Ok(DeferredValues {
        plonk,
        combined_inner_product: to_shifted(combined_inner_product_actual),
        b: to_shifted(b_actual),
        xi: xi_chal,
        bulletproof_challenges,
        branch_data: proof_state.deferred_values.branch_data.clone(),
    })
}

/// Ipa.Wrap.compute_sg
fn wrap_compute_sg(challenges: &[[u64; 2]]) -> GroupAffine<Fp> {
    use super::public_input::scalar_challenge::ScalarChallenge;

    let challenges = challenges
        .iter()
        .map(ScalarChallenge::limbs_to_field)
        .collect::<Vec<_>>();

    let coeffs = b_poly_coefficients(&challenges);
    let p = DensePolynomial::from_coefficients_vec(coeffs);

    let comm = {
        use poly_commitment::SRS;

        let srs = get_srs::<Fq>();
        srs.commit_non_hiding(&p, 1)
    };
    comm.chunks[0]
}

struct ExpandProofParams<'a> {
    dlog_vk: &'a VerifierIndex<Fq>,
    dlog_plonk_index: &'a CircuitPlonkVerificationKeyEvals<Fp>,
    app_state: &'a Rc<dyn ToFieldElementsDebug>,
    t: &'a v2::PicklesProofProofsVerified2ReprStableV2,
    public_input_length: usize,
    tag: (),
    must_verify: CircuitVar<Boolean>,
    hack_feature_flags: OptFlag,
    zk_rows: u64,
}

fn expand_proof(params: ExpandProofParams) -> anyhow::Result<ExpandedProof> {
    let ExpandProofParams {
        dlog_vk,
        dlog_plonk_index,
        app_state,
        t,
        public_input_length,
        tag: _,
        must_verify,
        hack_feature_flags,
        zk_rows,
    } = params;

    use super::public_input::scalar_challenge::ScalarChallenge;

    let plonk0: PlonkMinimal<Fp> = (&t.statement.proof_state.deferred_values.plonk).try_into()?;

    let plonk = {
        let domain: u8 = t
            .statement
            .proof_state
            .deferred_values
            .branch_data
            .domain_log2
            .as_u8();

        let alpha = ScalarChallenge::limbs_to_field(&plonk0.alpha_bytes);
        let zeta = ScalarChallenge::limbs_to_field(&plonk0.zeta_bytes);
        let w: Fp = Radix2EvaluationDomain::new(1 << domain).unwrap().group_gen;
        let zetaw = zeta * w;

        // dbg!(alpha, zeta, zetaw, dlog_vk.domain.log_size_of_group, domain);

        let es = prev_evals_from_p2p(&t.prev_evals.evals.evals)?;
        let combined_evals = evals_of_split_evals(zeta, zetaw, &es, BACKEND_TICK_ROUNDS_N);

        let plonk_minimal = PlonkMinimal::<Fp, 4> {
            alpha,
            beta: plonk0.beta,
            gamma: plonk0.gamma,
            zeta,
            joint_combiner: plonk0.joint_combiner,
            // joint_combiner: plonk0.joint_combiner_bytes.as_ref().map(ScalarChallenge::limbs_to_field),
            alpha_bytes: to_bytes(alpha),
            beta_bytes: to_4limbs(plonk0.beta_bytes),
            gamma_bytes: to_4limbs(plonk0.gamma_bytes),
            zeta_bytes: to_bytes(zeta),
            joint_combiner_bytes: plonk0.joint_combiner_bytes.map(to_4limbs),
            feature_flags: plonk0.feature_flags.clone(),
        };

        let srs_length_log2 = COMMON_MAX_DEGREE_STEP_LOG2;
        let env = make_scalars_env(&plonk_minimal, domain, srs_length_log2, zk_rows);

        derive_plonk(&env, &combined_evals, &plonk_minimal)
    };

    let statement = &t.statement;

    let prev_challenges: Vec<[Fq; BACKEND_TOCK_ROUNDS_N]> = {
        let old_bulletproof_challenges = &statement
            .proof_state
            .messages_for_next_wrap_proof
            .old_bulletproof_challenges;
        extract_bulletproof(&[
            old_bulletproof_challenges.0[0].0.clone(),
            old_bulletproof_challenges.0[1].0.clone(),
        ])
    };

    let old_bulletproof_challenges: Vec<[Fp; 16]> = statement
        .messages_for_next_step_proof
        .old_bulletproof_challenges
        .iter()
        .map(|v| {
            v.0.clone()
                .map(|v| two_u64_to_field(&v.prechallenge.inner.0.map(|v| v.as_u64())))
        })
        .collect();

    let deferred_values_computed = {
        let evals: AllEvals<Fp> = (&t.prev_evals).try_into()?;
        let proof_state: StatementProofState = (&statement.proof_state).try_into()?;

        expand_deferred(ExpandDeferredParams {
            evals: &evals,
            old_bulletproof_challenges: &old_bulletproof_challenges,
            proof_state: &proof_state,
            zk_rows,
        })?
    };

    let old_bulletproof_challenges: Vec<_> = old_bulletproof_challenges
        .iter()
        .map(ScalarChallenge::array_to_fields)
        .collect();

    let messages_for_next_step_proof = MessagesForNextStepProof {
        app_state: Rc::clone(app_state),
        dlog_plonk_index: &dlog_plonk_index.to_non_cvar(),
        challenge_polynomial_commitments: statement
            .messages_for_next_step_proof
            .challenge_polynomial_commitments
            .iter()
            .map(|(x, y)| {
                Ok(InnerCurve::of_affine(make_group(
                    x.to_field::<Fp>()?,
                    y.to_field()?,
                )))
            })
            .collect::<Result<_, InvalidBigInt>>()?,
        old_bulletproof_challenges: old_bulletproof_challenges.clone(),
    }
    .hash();

    let deferred_values = deferred_values_computed;
    let prev_statement_with_hashes = PreparedStatement {
        proof_state: ProofState {
            deferred_values: DeferredValues {
                plonk: Plonk {
                    alpha: plonk0.alpha_bytes,
                    beta: plonk0.beta_bytes,
                    gamma: plonk0.gamma_bytes,
                    zeta: plonk0.zeta_bytes,
                    zeta_to_srs_length: plonk.zeta_to_srs_length,
                    zeta_to_domain_size: plonk.zeta_to_domain_size,
                    perm: plonk.perm,
                    lookup: match plonk.lookup {
                        None => None,
                        Some(_) => Some(plonk0.joint_combiner_bytes.unwrap()),
                    },
                    feature_flags: plonk.feature_flags,
                },
                combined_inner_product: deferred_values.combined_inner_product,
                b: deferred_values.b,
                xi: deferred_values.xi,
                bulletproof_challenges: statement
                    .proof_state
                    .deferred_values
                    .bulletproof_challenges
                    .iter()
                    .map(|challenge| {
                        two_u64_to_field(
                            &challenge.prechallenge.inner.each_ref().map(|v| v.as_u64()),
                        )
                    })
                    .collect(),
                branch_data: deferred_values.branch_data,
            },
            sponge_digest_before_evaluations: statement
                .proof_state
                .sponge_digest_before_evaluations
                .each_ref()
                .map(|v| v.as_u64()),
            messages_for_next_wrap_proof: MessagesForNextWrapProof {
                old_bulletproof_challenges: prev_challenges.clone(),
                challenge_polynomial_commitment: {
                    let (x, y) = &statement
                        .proof_state
                        .messages_for_next_wrap_proof
                        .challenge_polynomial_commitment;
                    InnerCurve::from((x.to_field::<Fq>()?, y.to_field()?))
                },
            }
            .hash(),
        },
        messages_for_next_step_proof,
    };

    let mut proof = make_padded_proof_from_p2p(t)?;
    let oracle = {
        let public_input = prev_statement_with_hashes.to_public_input(public_input_length)?;
        create_oracle_with_public_input(dlog_vk, &proof, &public_input)
    };

    let x_hat = PointEvaluations {
        zeta: oracle.p_eval_1(),
        zeta_omega: oracle.p_eval_2(),
    };

    let alpha = oracle.alpha();
    let beta = oracle.beta();
    let gamma = oracle.gamma();
    let zeta = oracle.zeta();

    let to_bytes = |f: Fq| {
        let bigint: BigInteger256 = f.into();
        let [a, b, c, d] = bigint.0;
        assert_eq!([c, d], [0, 0]);
        [a, b]
    };

    let plonk0 = PlonkMinimal {
        alpha,
        beta,
        gamma,
        zeta,
        joint_combiner: None,
        alpha_bytes: to_bytes(alpha),
        beta_bytes: to_bytes(beta),
        gamma_bytes: to_bytes(gamma),
        zeta_bytes: to_bytes(zeta),
        joint_combiner_bytes: None, // TODO
        feature_flags: FeatureFlags::empty_bool(),
    };

    let xi = oracle.v();
    let r = oracle.u();
    let sponge_digest_before_evaluations = oracle.digest_before_evaluations;

    let (_, endo) = endos::<Fp>();
    let to_field = |bytes: [u64; 2]| -> Fq { ScalarChallenge::from(bytes).to_field(&endo) };

    let w = dlog_vk.domain.group_gen;

    let zeta = to_field(plonk0.zeta_bytes);
    let zetaw = { zeta * w };

    let (new_bulletproof_challenges, b) = {
        let chals = oracle
            .opening_prechallenges
            .iter()
            .map(|v| to_field(to_bytes(*v)))
            .collect::<Vec<_>>();

        let r = to_field(to_bytes(r.0));
        // let zeta = to_field(plonk0.zeta_bytes);
        let challenge_poly = challenge_polynomial(&chals);
        let b = challenge_poly(zeta) + (r * challenge_poly(zetaw));

        let prechals = oracle
            .opening_prechallenges
            .iter()
            .copied()
            .map(to_bytes)
            .collect::<Vec<_>>();

        (prechals, b)
    };

    let challenge_polynomial_commitment = match must_verify.value() {
        Boolean::False => wrap_compute_sg(&new_bulletproof_challenges),
        Boolean::True => proof.proof.sg,
    };

    let witness = PerProofWitness {
        app_state: None,
        proof_state: prev_statement_with_hashes.proof_state.clone(),
        prev_proof_evals: (&t.prev_evals).try_into()?,
        prev_challenge_polynomial_commitments: {
            let mut challenge_polynomial_commitments = t
                .statement
                .messages_for_next_step_proof
                .challenge_polynomial_commitments
                .iter()
                .map(|(x, y)| Ok(make_group::<Fp>(x.to_field()?, y.to_field()?)))
                .collect::<Result<Vec<_>, InvalidBigInt>>()?;

            while challenge_polynomial_commitments.len() < 2 {
                challenge_polynomial_commitments.insert(0, dummy_ipa_wrap_sg());
            }

            challenge_polynomial_commitments
        },
        prev_challenges: {
            let mut prev_challenges = old_bulletproof_challenges.clone();
            while prev_challenges.len() < 2 {
                prev_challenges.insert(0, dummy_ipa_step_challenges_computed())
            }

            prev_challenges
        },
        wrap_proof: {
            proof.proof.sg = challenge_polynomial_commitment;
            proof.clone()
        },
        hack_feature_flags,
    };

    let tock_combined_evals = {
        let zeta = to_field(plonk0.zeta_bytes);
        evals_of_split_evals(zeta, zetaw, &proof.evals, BACKEND_TOCK_ROUNDS_N)
    };

    let tock_plonk_minimal = {
        let alpha = to_field(plonk0.alpha_bytes);
        let zeta = to_field(plonk0.zeta_bytes);

        let to_bytes = |f: Fq| {
            let bigint: BigInteger256 = f.into();
            bigint.0
        };

        PlonkMinimal {
            alpha,
            beta,
            gamma,
            zeta,
            joint_combiner: None,
            alpha_bytes: to_bytes(alpha),
            beta_bytes: to_4limbs(plonk0.beta_bytes),
            gamma_bytes: to_4limbs(plonk0.gamma_bytes),
            zeta_bytes: to_bytes(alpha),
            joint_combiner_bytes: None, // TODO
            feature_flags: FeatureFlags::empty_bool(),
        }
    };

    let domain_log2 = dlog_vk.domain.log_size_of_group;
    let srs_length_log2 = COMMON_MAX_DEGREE_WRAP_LOG2;
    let tock_env = make_scalars_env(
        &tock_plonk_minimal,
        domain_log2 as u8,
        srs_length_log2 as u64,
        zk_rows,
    );

    let public = {
        let PointEvaluations { zeta, zeta_omega } = &x_hat;
        PointEvaluations {
            zeta: vec![*zeta],
            zeta_omega: vec![*zeta_omega],
        }
    };

    let combined_inner_product = combined_inner_product(CombinedInnerProductParams {
        env: &tock_env,
        evals: &proof.evals,
        combined_evals: &tock_combined_evals,
        public: &public,
        minimal: &tock_plonk_minimal,
        ft_eval1: proof.ft_eval1,
        r: to_field(to_bytes(r.0)),
        old_bulletproof_challenges: &prev_challenges,
        xi: to_field(to_bytes(xi.0)),
        zetaw,
    });

    let plonk = derive_plonk(&tock_env, &tock_combined_evals, &tock_plonk_minimal);

    let shift = |f: Fq| <Fq as FieldWitness>::Shifting::of_field(f);

    let unfinalized = Unfinalized {
        deferred_values: crate::proofs::unfinalized::DeferredValues {
            plonk: Plonk {
                alpha: to_bytes(plonk0.alpha),
                beta: to_bytes(plonk0.beta),
                gamma: to_bytes(plonk0.gamma),
                zeta: to_bytes(plonk0.zeta),
                zeta_to_srs_length: plonk.zeta_to_srs_length,
                zeta_to_domain_size: plonk.zeta_to_domain_size,
                perm: plonk.perm,
                lookup: None,
                feature_flags: plonk.feature_flags,
            },
            combined_inner_product: shift(combined_inner_product),
            b: shift(b),
            xi: to_bytes(xi.0),
            bulletproof_challenges: new_bulletproof_challenges,
        },
        should_finalize: must_verify.value().as_bool(),
        sponge_digest_before_evaluations: {
            let bigint: BigInteger256 = sponge_digest_before_evaluations.into();
            bigint.0
        },
    };

    Ok(ExpandedProof {
        sg: challenge_polynomial_commitment,
        unfinalized,
        prev_statement_with_hashes,
        x_hat,
        witness,
        actual_wrap_domain: dlog_vk.domain.log_size_of_group,
    })
}

#[derive(Debug)]
struct ExpandedProof {
    sg: GroupAffine<Fp>,
    unfinalized: Unfinalized,
    prev_statement_with_hashes: PreparedStatement,
    x_hat: PointEvaluations<Fq>,
    witness: PerProofWitness,
    actual_wrap_domain: u32,
}

#[derive(Clone, Debug)]
pub struct PerProofWitness {
    pub app_state: Option<Rc<dyn ToFieldElementsDebug>>,
    // app_state: AppState,
    pub wrap_proof: ProverProof<Fq>,
    pub proof_state: ProofState,
    pub prev_proof_evals: AllEvals<Fp>,
    pub prev_challenges: Vec<[Fp; 16]>,
    pub prev_challenge_polynomial_commitments: Vec<GroupAffine<Fp>>,
    /// Hack until I understand how feature flags are used.
    /// So far they are always `OptFlag::No`, except for zkapps using proof authorization, in that
    /// case they are `OptFlag::Maybe`.
    pub hack_feature_flags: OptFlag,
}

impl PerProofWitness {
    pub fn with_app_state(self, app_state: Rc<dyn ToFieldElementsDebug>) -> PerProofWitness {
        let Self {
            app_state: old,
            wrap_proof,
            proof_state,
            prev_proof_evals,
            prev_challenges,
            prev_challenge_polynomial_commitments,
            hack_feature_flags,
        } = self;
        assert!(old.is_none());

        PerProofWitness {
            app_state: Some(app_state),
            wrap_proof,
            proof_state,
            prev_proof_evals,
            prev_challenges,
            prev_challenge_polynomial_commitments,
            hack_feature_flags,
        }
    }
}

impl Check<Fp> for PerProofWitness {
    fn check(&self, w: &mut Witness<Fp>) {
        let Self {
            app_state,
            wrap_proof,
            proof_state,
            prev_proof_evals: _,
            prev_challenges: _,
            prev_challenge_polynomial_commitments,
            hack_feature_flags: _,
        } = self;

        assert!(app_state.is_none());

        let ProverProof::<Fq> {
            commitments:
                ProverCommitments {
                    w_comm,
                    z_comm,
                    t_comm,
                    lookup: _,
                },
            proof:
                OpeningProof {
                    lr,
                    delta,
                    z1,
                    z2,
                    sg,
                },
            evals: _,
            ft_eval1: _,
            prev_challenges: _,
        } = wrap_proof;

        for poly in w_comm {
            poly.chunks.check(w);
        }
        z_comm.chunks.check(w);
        t_comm.chunks.check(w);
        lr.check(w);

        let shift = |f: Fq| <Fq as FieldWitness>::Shifting::of_field(f);

        shift(*z1).check(w);
        shift(*z2).check(w);

        delta.check(w);
        sg.check(w);

        let ProofState {
            deferred_values:
                DeferredValues {
                    plonk:
                        Plonk {
                            alpha: _,
                            beta: _,
                            gamma: _,
                            zeta: _,
                            zeta_to_srs_length,
                            zeta_to_domain_size,
                            perm,
                            lookup: _,
                            feature_flags: _,
                        },
                    combined_inner_product,
                    b,
                    xi,
                    bulletproof_challenges,
                    branch_data,
                },
            sponge_digest_before_evaluations: _,
            messages_for_next_wrap_proof: _,
        } = proof_state;

        zeta_to_srs_length.check(w);
        zeta_to_domain_size.check(w);
        perm.check(w);
        combined_inner_product.check(w);
        b.check(w);
        two_u64_to_field::<Fp, _>(xi).check(w);
        bulletproof_challenges.check(w);

        {
            let v2::CompositionTypesBranchDataStableV1 {
                proofs_verified: _,
                domain_log2,
            } = branch_data;
            let domain_log2: u64 = domain_log2.0.as_u8() as u64;

            // Assert 16 bits
            const NBITS: usize = 16;
            let (_, endo) = endos::<Fq>();
            to_field_checked::<Fp, NBITS>(Fp::from(domain_log2), endo, w);
        }

        prev_challenge_polynomial_commitments.check(w);
    }
}

pub fn extract_recursion_challenges<const N: usize>(
    proofs: &[&v2::PicklesProofProofsVerified2ReprStableV2; N],
) -> anyhow::Result<Vec<RecursionChallenge<GroupAffine<Fq>>>> {
    use poly_commitment::PolyComm;

    let comms: [(Fq, Fq); N] =
        crate::try_array_into_with(proofs, |proof| -> Result<_, InvalidBigInt> {
            let (a, b) = &proof
                .statement
                .proof_state
                .messages_for_next_wrap_proof
                .challenge_polynomial_commitment;
            Ok((a.to_field::<Fq>()?, b.to_field::<Fq>()?))
        })?;

    let challs = proofs
        .iter()
        .map(|p| {
            p.statement
                .proof_state
                .deferred_values
                .bulletproof_challenges
                .clone()
        })
        .collect::<Vec<_>>();
    let challs = extract_bulletproof(&challs);

    Ok(challs
        .into_iter()
        .zip(comms)
        .map(|(chals, (x, y))| {
            let comm = PolyComm::<mina_curves::pasta::Vesta> {
                chunks: vec![make_group(x, y)],
            };
            RecursionChallenge {
                chals: chals.to_vec(),
                comm,
            }
        })
        .collect())
}

/// `N_PREVIOUS`: Number of previous proofs.
///  - For block and merge proofs, the number is 2
///  - For zkapp with proof authorization, it's 1
///  - For other proofs, it's 0
pub struct StepParams<'a, const N_PREVIOUS: usize> {
    pub app_state: Rc<dyn ToFieldElementsDebug>,
    pub rule: InductiveRule<'a, N_PREVIOUS>,
    pub for_step_datas: [&'a ForStep; N_PREVIOUS],
    pub indexes: [(
        &'a VerifierIndex<Fq>,
        &'a CircuitPlonkVerificationKeyEvals<Fp>,
    ); N_PREVIOUS],
    pub prev_challenge_polynomial_commitments: Vec<RecursionChallenge<GroupAffine<Fq>>>,
    /// TODO: Remove this. See documentation in `PerProofWitness` struct.
    pub hack_feature_flags: OptFlag,
    pub step_prover: &'a Prover<Fp>,
    pub wrap_prover: &'a Prover<Fq>,
    pub only_verify_constraints: bool,
}

pub struct StepProof {
    pub statement: StepStatement,
    pub prev_evals: Vec<AllEvals<Fq>>,
    pub proof_with_public: ProofWithPublic<Fp>,
}

pub fn step<C: ProofConstants, const N_PREVIOUS: usize>(
    params: StepParams<N_PREVIOUS>,
    w: &mut Witness<Fp>,
) -> anyhow::Result<StepProof> {
    let StepParams {
        app_state,
        rule,
        for_step_datas,
        indexes,
        prev_challenge_polynomial_commitments,
        hack_feature_flags,
        step_prover,
        wrap_prover,
        only_verify_constraints,
    } = params;

    let dlog_plonk_index = w.exists(super::merge::dlog_plonk_index(wrap_prover));

    let expanded_proofs: Box<[ExpandedProof; N_PREVIOUS]> = rule
        .previous_proof_statements
        .iter()
        .zip(indexes)
        .zip(for_step_datas)
        .map(|((statement, (verifier_index, dlog_plonk_index)), data)| {
            let PreviousProofStatement {
                public_input,
                proof,
                proof_must_verify,
            } = statement;

            expand_proof(ExpandProofParams {
                dlog_vk: verifier_index,
                dlog_plonk_index,
                app_state: public_input,
                t: proof,
                public_input_length: 40,
                tag: (),
                must_verify: *proof_must_verify,
                hack_feature_flags,
                zk_rows: data.zk_rows,
            })
        })
        .collect::<Result<Vec<_>, _>>()
        .context("expand_proof")?
        .try_into()
        .unwrap();

    let prevs: [&PerProofWitness; N_PREVIOUS] =
        w.exists(expanded_proofs.each_ref().map(|p| &p.witness));
    let unfinalized_proofs_unextended: [&Unfinalized; N_PREVIOUS] =
        w.exists(expanded_proofs.each_ref().map(|p| &p.unfinalized));

    let messages_for_next_wrap_proof: [Fp; N_PREVIOUS] = {
        let f = four_u64_to_field::<Fp, _>;

        crate::try_array_into_with(&expanded_proofs, |p| {
            f(&p.prev_statement_with_hashes
                .proof_state
                .messages_for_next_wrap_proof)
        })?
    };

    let messages_for_next_wrap_proof_padded: [Fp; 2] = w.exists({
        let n_padding = 2 - expanded_proofs.len();
        std::array::from_fn(|i| {
            if i < n_padding {
                messages_for_next_wrap_proof_padding()
            } else {
                messages_for_next_wrap_proof[i - n_padding]
            }
        })
    });

    let actual_wrap_domains: [usize; N_PREVIOUS] = {
        let all_possible_domains = wrap_verifier::all_possible_domains();

        let actuals_wrap_domain: [u32; N_PREVIOUS] =
            expanded_proofs.each_ref().map(|p| p.actual_wrap_domain);

        actuals_wrap_domain.map(|domain_size| {
            let domain_size = domain_size as u64;
            all_possible_domains
                .iter()
                .position(|Domain::Pow2RootsOfUnity(d)| *d == domain_size)
                .unwrap_or(0)
        })
    };

    let prevs: [PerProofWitness; N_PREVIOUS] = rule
        .previous_proof_statements
        .iter()
        .zip(prevs)
        .map(|(stmt, proof)| proof.clone().with_app_state(stmt.public_input.clone()))
        .collect::<Vec<_>>()
        .try_into()
        .unwrap();

    let srs = get_srs_mut::<Fq>();
    let mut srs = srs.lock().unwrap();

    let bulletproof_challenges = prevs
        .iter()
        .zip(messages_for_next_wrap_proof)
        .zip(unfinalized_proofs_unextended)
        .zip(&rule.previous_proof_statements)
        .zip(actual_wrap_domains)
        .zip(for_step_datas)
        .map(
            |(
                ((((proof, msg_for_next_wrap_proof), unfinalized), stmt), actual_wrap_domain),
                data,
            )| {
                let PreviousProofStatement {
                    proof_must_verify: should_verify,
                    ..
                } = stmt;

                match data.wrap_domain {
                    ForStepKind::SideLoaded(_) => {} // Nothing
                    ForStepKind::Known(wrap_domain) => {
                        let actual_wrap_domain = wrap_domains(actual_wrap_domain);
                        assert_eq!(actual_wrap_domain.h, wrap_domain);
                    }
                }
                let (chals, _verified) = verify_one(
                    VerifyOneParams {
                        srs: &mut srs,
                        proof,
                        data,
                        messages_for_next_wrap_proof: msg_for_next_wrap_proof,
                        unfinalized,
                        should_verify: *should_verify,
                    },
                    w,
                )?;
                Ok(chals.try_into().unwrap()) // Never fail, we know it's 16
            },
        )
        .collect::<Result<Vec<[Fp; 16]>, anyhow::Error>>()
        .context("verify_one")?;

    std::mem::drop(srs);

    let messages_for_next_step_proof = {
        let msg = MessagesForNextStepProof {
            app_state: Rc::clone(&app_state),
            dlog_plonk_index: &dlog_plonk_index,
            challenge_polynomial_commitments: prevs
                .iter()
                .map(|v| InnerCurve::of_affine(v.wrap_proof.proof.sg))
                .collect(),
            old_bulletproof_challenges: bulletproof_challenges,
        };
        crate::proofs::transaction::checked_hash2(&msg.to_fields(), w)
    };

    let unfinalized_proofs = {
        let mut unfinalized_proofs: Vec<_> =
            unfinalized_proofs_unextended.into_iter().cloned().collect();
        while unfinalized_proofs.len() < 2 {
            unfinalized_proofs.insert(0, Unfinalized::dummy());
        }
        unfinalized_proofs
    };

    let statement = crate::proofs::transaction::StepMainStatement {
        proof_state: crate::proofs::transaction::StepMainProofState {
            unfinalized_proofs,
            messages_for_next_step_proof,
        },
        messages_for_next_wrap_proof: messages_for_next_wrap_proof_padded.to_vec(),
    };

    w.primary = statement.to_field_elements_owned();

    let proof = create_proof::<C, Fp>(
        CreateProofParams {
            prover: step_prover,
            prev_challenges: prev_challenge_polynomial_commitments,
            only_verify_constraints,
        },
        w,
    )
    .context("create_proof")?;

    let proofs: [&v2::PicklesProofProofsVerified2ReprStableV2; N_PREVIOUS] = rule
        .previous_proof_statements
        .each_ref()
        .map(|stmt| stmt.proof);

    let prev_evals = proofs
        .iter()
        .zip(&*expanded_proofs)
        .map(|(p, expanded)| {
            let evals = evals_from_p2p(&p.proof.evaluations)?;
            let ft_eval1 = p.proof.ft_eval1.to_field()?;
            let PointEvaluations { zeta, zeta_omega } = expanded.x_hat;

            Ok(AllEvals {
                ft_eval1,
                evals: EvalsWithPublicInput {
                    evals,
                    public_input: (vec![zeta], vec![zeta_omega]),
                },
            })
        })
        .collect::<anyhow::Result<Vec<_>>>()
        .context("prev_evals")?;

    let challenge_polynomial_commitments = expanded_proofs
        .iter()
        .map(|v| InnerCurve::of_affine(v.sg))
        .collect();

    let (old_bulletproof_challenges, messages_for_next_wrap_proof): (Vec<_>, Vec<_>) = proofs
        .iter()
        .map(|v| {
            let StatementProofState {
                deferred_values,
                messages_for_next_wrap_proof,
                ..
            } = (&v.statement.proof_state).try_into()?;
            Ok((
                deferred_values.bulletproof_challenges,
                messages_for_next_wrap_proof,
            ))
        })
        .collect::<Result<Vec<_>, InvalidBigInt>>() // TODO: Refactor when `try_unzip` is stable
        .context("unzip proof state")?
        .into_iter()
        .unzip();

    let old_bulletproof_challenges = old_bulletproof_challenges
        .into_iter()
        .map(|v: [[u64; 2]; 16]| v.each_ref().map(two_u64_to_field))
        .collect();

    let step_statement = crate::proofs::transaction::StepStatement {
        proof_state: crate::proofs::transaction::StepProofState {
            unfinalized_proofs: statement.proof_state.unfinalized_proofs,
            messages_for_next_step_proof: ReducedMessagesForNextStepProof {
                app_state: Rc::clone(&app_state),
                challenge_polynomial_commitments,
                old_bulletproof_challenges,
            },
        },
        messages_for_next_wrap_proof,
    };

    Ok(StepProof {
        statement: step_statement,
        prev_evals,
        proof_with_public: proof,
    })
}