diff --git a/folding-schemes/src/folding/hypernova/circuits.rs b/folding-schemes/src/folding/hypernova/circuits.rs
index 319bb0f6..2ebc4ef0 100644
--- a/folding-schemes/src/folding/hypernova/circuits.rs
+++ b/folding-schemes/src/folding/hypernova/circuits.rs
@@ -414,8 +414,8 @@ impl<C: CurveGroup> NIMFSGadget<C> {
 /// Computes c from the step 5 in section 5 of HyperNova, adapted to multiple LCCCS & CCCS
 /// instances:
 /// $$
-/// c = \sum_{i \in [\mu]} \left(\sum_{j \in [t]} \gamma^{i \cdot t + j} \cdot e_i \cdot \sigma_{i,j} \right)
-/// + \sum_{k \in [\nu]} \gamma^{\mu \cdot t+k} \cdot e_k \cdot \left( \sum_{i=1}^q c_i \cdot \prod_{j \in S_i}
+/// c = \sum_{i \in [\mu]} \left(\sum_{j \in [t]} \gamma^{i \cdot t + j} \cdot e_i \cdot \sigma_{i,j} \right) +
+/// \sum_{k \in [\nu]} \gamma^{\mu \cdot t+k} \cdot e_k \cdot \left( \sum_{i=1}^q c_i \cdot \prod_{j \in S_i}
 /// \theta_{k,j} \right)
 /// $$
 #[allow(clippy::too_many_arguments)]
diff --git a/folding-schemes/src/folding/hypernova/utils.rs b/folding-schemes/src/folding/hypernova/utils.rs
index b2df2147..71b9108e 100644
--- a/folding-schemes/src/folding/hypernova/utils.rs
+++ b/folding-schemes/src/folding/hypernova/utils.rs
@@ -52,8 +52,8 @@ pub fn compute_sigmas_thetas<F: PrimeField>(
 /// Computes c from the step 5 in section 5 of HyperNova, adapted to multiple LCCCS & CCCS
 /// instances:
 /// $$
-/// c = \sum_{i \in [\mu]} \left(\sum_{j \in [t]} \gamma^{i \cdot t + j} \cdot e_i \cdot \sigma_{i,j} \right)
-/// + \sum_{k \in [\nu]} \gamma^{\mu \cdot t+k} \cdot e_k \cdot \left( \sum_{i=1}^q c_i \cdot \prod_{j \in S_i}
+/// c = \sum_{i \in [\mu]} \left(\sum_{j \in [t]} \gamma^{i \cdot t + j} \cdot e_i \cdot \sigma_{i,j} \right) +
+/// \sum_{k \in [\nu]} \gamma^{\mu \cdot t+k} \cdot e_k \cdot \left( \sum_{i=1}^q c_i \cdot \prod_{j \in S_i}
 /// \theta_{k,j} \right)
 /// $$
 pub fn compute_c<F: PrimeField>(
diff --git a/folding-schemes/src/folding/nova/nifs/mod.rs b/folding-schemes/src/folding/nova/nifs/mod.rs
index e233e3d5..ad3e4fa0 100644
--- a/folding-schemes/src/folding/nova/nifs/mod.rs
+++ b/folding-schemes/src/folding/nova/nifs/mod.rs
@@ -1,9 +1,11 @@
 /// This module defines the traits related to the NIFS (Non-Interactive Folding Scheme).
 /// - NIFSTrait, which implements the NIFS interface
 /// - NIFSGadget, which implements the NIFS in-circuit
-/// both traits implemented by the various Nova variants schemes; ie.
-/// [Nova](https://eprint.iacr.org/2021/370.pdf), [Ova](https://hackmd.io/V4838nnlRKal9ZiTHiGYzw),
-/// [Mova](https://eprint.iacr.org/2024/1220.pdf).
+///
+/// Both traits implemented by the various Nova variants schemes; ie.
+/// - [Nova](https://eprint.iacr.org/2021/370.pdf)
+/// - [Ova](https://hackmd.io/V4838nnlRKal9ZiTHiGYzw)
+/// - [Mova](https://eprint.iacr.org/2024/1220.pdf)
 use ark_crypto_primitives::sponge::{constraints::AbsorbGadget, Absorb, CryptographicSponge};
 use ark_ec::CurveGroup;
 use ark_r1cs_std::{alloc::AllocVar, boolean::Boolean, fields::fp::FpVar};
diff --git a/folding-schemes/src/folding/nova/zk.rs b/folding-schemes/src/folding/nova/zk.rs
index 206d3025..a560396a 100644
--- a/folding-schemes/src/folding/nova/zk.rs
+++ b/folding-schemes/src/folding/nova/zk.rs
@@ -73,7 +73,7 @@ where
     /// For further details on why folding is hiding, see lemma 9
     pub fn new<
         GC1: CurveVar<C1, CF2<C1>> + ToConstraintFieldGadget<CF2<C1>>,
-        GC2: CurveVar<C2, CF2<C2>>,
+        GC2: CurveVar<C2, CF2<C2>> + ToConstraintFieldGadget<CF2<C2>>,
         FC: FCircuit<C1::ScalarField>,
         CS1: CommitmentScheme<C1, true>,
         CS2: CommitmentScheme<C2, true>,
@@ -87,7 +87,6 @@ where
         <C2 as Group>::ScalarField: PrimeField,
         <C2 as CurveGroup>::BaseField: PrimeField,
         <C2 as CurveGroup>::BaseField: Absorb,
-        GC2: ToConstraintFieldGadget<<C2 as CurveGroup>::BaseField>,
         C1: CurveGroup<BaseField = C2::ScalarField, ScalarField = C2::BaseField>,
     {
         let mut transcript = PoseidonSponge::<C1::ScalarField>::new(&nova.poseidon_config);
@@ -140,7 +139,7 @@ where
     #[allow(clippy::too_many_arguments)]
     pub fn verify<
         CS1: CommitmentScheme<C1, true>,
-        GC2: CurveVar<C2, CF2<C2>>,
+        GC2: CurveVar<C2, CF2<C2>> + ToConstraintFieldGadget<CF2<C2>>,
         CS2: CommitmentScheme<C2, true>,
     >(
         r1cs: &R1CS<C1::ScalarField>,
@@ -157,7 +156,6 @@ where
         <C2 as Group>::ScalarField: Absorb,
         <C2 as CurveGroup>::BaseField: PrimeField,
         <C2 as CurveGroup>::BaseField: Absorb,
-        GC2: ToConstraintFieldGadget<<C2 as CurveGroup>::BaseField>,
         C1: CurveGroup<BaseField = C2::ScalarField, ScalarField = C2::BaseField>,
     {
         // Handles case where i=0
diff --git a/folding-schemes/src/lib.rs b/folding-schemes/src/lib.rs
index a829fe6d..890d6543 100644
--- a/folding-schemes/src/lib.rs
+++ b/folding-schemes/src/lib.rs
@@ -118,7 +118,8 @@ pub enum Error {
 /// over a cycle of curves (C1, C2), where:
 /// - C1 is the main curve, which ScalarField we use as our F for all the field operations
 /// - C2 is the auxiliary curve, which we use for the commitments, whose BaseField (for point
-/// coordinates) are in the C1::ScalarField.
+///   coordinates) are in the C1::ScalarField.
+///
 /// In other words, C1.Fq == C2.Fr, and C1.Fr == C2.Fq.
 pub trait FoldingScheme<C1: CurveGroup, C2: CurveGroup, FC>: Clone + Debug
 where
diff --git a/folding-schemes/src/utils/espresso/virtual_polynomial.rs b/folding-schemes/src/utils/espresso/virtual_polynomial.rs
index acc843b9..85296156 100644
--- a/folding-schemes/src/utils/espresso/virtual_polynomial.rs
+++ b/folding-schemes/src/utils/espresso/virtual_polynomial.rs
@@ -192,6 +192,7 @@ impl<F: PrimeField> VirtualPolynomial<F> {
     /// Multiple the current VirtualPolynomial by an MLE:
     /// - add the MLE to the MLE list;
     /// - multiple each product by MLE and its coefficient.
+    ///
     /// Returns an error if the MLE has a different `num_vars` from self.
     pub fn mul_by_mle(
         &mut self,