diff --git a/stwo_cairo_verifier/Scarb.toml b/stwo_cairo_verifier/Scarb.toml
index ab88f3ec..204f4d8e 100644
--- a/stwo_cairo_verifier/Scarb.toml
+++ b/stwo_cairo_verifier/Scarb.toml
@@ -6,6 +6,9 @@ edition = "2024_07"
 [lib]
 casm = true
 
+[tool.fmt]
+sort-module-level-items = true
+
 [dependencies]
 
 [dev-dependencies]
diff --git a/stwo_cairo_verifier/src/channel.cairo b/stwo_cairo_verifier/src/channel.cairo
index 8a098770..4fb25ed9 100644
--- a/stwo_cairo_verifier/src/channel.cairo
+++ b/stwo_cairo_verifier/src/channel.cairo
@@ -1,11 +1,11 @@
 use core::array::SpanTrait;
 use core::poseidon::{poseidon_hash_span, hades_permutation};
 use core::traits::DivRem;
-
-use stwo_cairo_verifier::{BaseField, SecureField};
 use stwo_cairo_verifier::fields::qm31::QM31Trait;
 use stwo_cairo_verifier::utils::pack4;
 
+use stwo_cairo_verifier::{BaseField, SecureField};
+
 const M31_SHIFT: felt252 = 0x80000000; // 2**31.
 const M31_SHIFT_NZ_U256: NonZero<u256> = 0x80000000; // 2**31.
 pub const EXTENSION_FELTS_PER_HASH: usize = 2;
@@ -155,8 +155,8 @@ fn extract_m31<const N: usize>(ref num: u256) -> BaseField {
 
 #[cfg(test)]
 mod tests {
-    use super::{Channel, ChannelTrait};
     use stwo_cairo_verifier::fields::qm31::qm31;
+    use super::ChannelTrait;
 
     #[test]
     fn test_initialize_channel() {
diff --git a/stwo_cairo_verifier/src/circle.cairo b/stwo_cairo_verifier/src/circle.cairo
index d29bf1ce..7040da72 100644
--- a/stwo_cairo_verifier/src/circle.cairo
+++ b/stwo_cairo_verifier/src/circle.cairo
@@ -1,9 +1,10 @@
-use stwo_cairo_verifier::fields::m31::{M31, M31Impl};
+use core::num::traits::one::One;
+use core::num::traits::zero::Zero;
+use core::num::traits::{WrappingAdd, WideMul};
 use stwo_cairo_verifier::fields::cm31::CM31;
+use stwo_cairo_verifier::fields::m31::{M31, M31Impl};
 use stwo_cairo_verifier::fields::qm31::{QM31Impl, QM31, QM31Trait};
 use super::utils::pow;
-use core::num::traits::zero::Zero;
-use core::num::traits::one::One;
 
 pub const M31_CIRCLE_GEN: CirclePoint<M31> =
     CirclePoint { x: M31 { inner: 2 }, y: M31 { inner: 1268011823 }, };
@@ -123,10 +124,10 @@ pub impl CosetImpl of CosetTrait {
     }
 
     fn index_at(self: @Coset, index: usize) -> usize {
-        let index_times_step = (core::integer::u32_wide_mul(*self.step_size, index) & U32_BIT_MASK)
+        let index_times_step = ((*self.step_size).wide_mul(index) & U32_BIT_MASK)
             .try_into()
             .unwrap();
-        let result = core::integer::u32_wrapping_add(*self.initial_index, index_times_step);
+        let result = (*self.initial_index).wrapping_add(index_times_step);
         result & CIRCLE_ORDER_BIT_MASK
     }
 
@@ -178,14 +179,14 @@ pub impl CosetImpl of CosetTrait {
 
 #[cfg(test)]
 mod tests {
-    use super::{M31_CIRCLE_GEN, CIRCLE_ORDER, CirclePoint, CirclePointM31Impl, Coset, CosetImpl};
-    use core::option::OptionTrait;
     use core::array::ArrayTrait;
+    use core::option::OptionTrait;
     use core::traits::TryInto;
-    use super::{CirclePointQM31Impl, QM31_CIRCLE_GEN};
-    use stwo_cairo_verifier::fields::m31::{m31, M31};
-    use stwo_cairo_verifier::fields::qm31::{qm31, QM31, QM31One};
+    use stwo_cairo_verifier::fields::m31::m31;
+    use stwo_cairo_verifier::fields::qm31::QM31One;
     use stwo_cairo_verifier::utils::pow;
+    use super::{CirclePointQM31Impl, QM31_CIRCLE_GEN};
+    use super::{M31_CIRCLE_GEN, CIRCLE_ORDER, CirclePoint, CirclePointM31Impl, Coset, CosetImpl};
 
     #[test]
     fn test_add_1() {
diff --git a/stwo_cairo_verifier/src/fields.cairo b/stwo_cairo_verifier/src/fields.cairo
index 8c1737e7..32c0ba18 100644
--- a/stwo_cairo_verifier/src/fields.cairo
+++ b/stwo_cairo_verifier/src/fields.cairo
@@ -1,5 +1,5 @@
-pub mod m31;
 pub mod cm31;
+pub mod m31;
 pub mod qm31;
 
 pub type BaseField = m31::M31;
diff --git a/stwo_cairo_verifier/src/fields/cm31.cairo b/stwo_cairo_verifier/src/fields/cm31.cairo
index 3363d3a0..fef2aa65 100644
--- a/stwo_cairo_verifier/src/fields/cm31.cairo
+++ b/stwo_cairo_verifier/src/fields/cm31.cairo
@@ -71,8 +71,8 @@ pub fn cm31(a: u32, b: u32) -> CM31 {
 
 #[cfg(test)]
 mod tests {
-    use super::{cm31};
     use super::super::m31::{m31, P};
+    use super::{cm31};
 
     #[test]
     fn test_cm31() {
diff --git a/stwo_cairo_verifier/src/fields/m31.cairo b/stwo_cairo_verifier/src/fields/m31.cairo
index 69491fe5..b01ba972 100644
--- a/stwo_cairo_verifier/src/fields/m31.cairo
+++ b/stwo_cairo_verifier/src/fields/m31.cairo
@@ -1,6 +1,6 @@
+use core::num::traits::{WideMul, CheckedSub};
 use core::option::OptionTrait;
 use core::traits::TryInto;
-use core::result::ResultTrait;
 
 pub const P: u32 = 0x7fffffff;
 const P32NZ: NonZero<u32> = 0x7fffffff;
@@ -45,7 +45,7 @@ pub impl M31Impl of M31Trait {
 pub impl M31Add of core::traits::Add<M31> {
     fn add(lhs: M31, rhs: M31) -> M31 {
         let res = lhs.inner + rhs.inner;
-        let res = core::integer::u32_overflowing_sub(res, P).unwrap_or(res);
+        let res = res.checked_sub(P).unwrap_or(res);
         M31 { inner: res }
     }
 }
@@ -56,7 +56,7 @@ pub impl M31Sub of core::traits::Sub<M31> {
 }
 pub impl M31Mul of core::traits::Mul<M31> {
     fn mul(lhs: M31, rhs: M31) -> M31 {
-        M31Impl::reduce_u64(core::integer::u32_wide_mul(lhs.inner, rhs.inner))
+        M31Impl::reduce_u64(lhs.inner.wide_mul(rhs.inner))
     }
 }
 pub impl M31Zero of core::num::traits::Zero<M31> {
@@ -102,7 +102,7 @@ pub fn m31(val: u32) -> M31 {
 
 #[cfg(test)]
 mod tests {
-    use super::{m31, P, M31, M31Trait};
+    use super::{m31, P, M31Trait};
     const POW2_15: u32 = 0b1000000000000000;
     const POW2_16: u32 = 0b10000000000000000;
 
diff --git a/stwo_cairo_verifier/src/fields/qm31.cairo b/stwo_cairo_verifier/src/fields/qm31.cairo
index f8ba678a..f34dd3ba 100644
--- a/stwo_cairo_verifier/src/fields/qm31.cairo
+++ b/stwo_cairo_verifier/src/fields/qm31.cairo
@@ -1,7 +1,7 @@
-use super::m31::{M31, m31, M31Impl};
-use super::cm31::{CM31, cm31, CM31Trait};
-use core::num::traits::zero::Zero;
 use core::num::traits::one::One;
+use core::num::traits::zero::Zero;
+use super::cm31::{CM31, cm31, CM31Trait};
+use super::m31::{M31, M31Impl};
 
 pub const R: CM31 = CM31 { a: M31 { inner: 2 }, b: M31 { inner: 1 } };
 
@@ -113,9 +113,9 @@ pub fn qm31(a: u32, b: u32, c: u32, d: u32) -> QM31 {
 
 #[cfg(test)]
 mod tests {
-    use super::{QM31, qm31, QM31Trait, QM31Impl};
-    use super::{CM31, cm31};
+    use super::CM31;
     use super::super::m31::{m31, P, M31Trait};
+    use super::{QM31, qm31, QM31Trait, QM31Impl};
 
     #[test]
     fn test_QM31() {
diff --git a/stwo_cairo_verifier/src/fri.cairo b/stwo_cairo_verifier/src/fri.cairo
index 23fe23b8..d2ee8b0c 100644
--- a/stwo_cairo_verifier/src/fri.cairo
+++ b/stwo_cairo_verifier/src/fri.cairo
@@ -1,23 +1,23 @@
 use core::dict::Felt252Dict;
-use stwo_cairo_verifier::fields::m31::M31Trait;
-use stwo_cairo_verifier::circle::{Coset, CosetImpl};
-use stwo_cairo_verifier::poly::line::{LineDomain, LineDomainImpl};
-use stwo_cairo_verifier::fields::qm31::{QM31, qm31, QM31Trait};
-use stwo_cairo_verifier::queries::SparseSubCircleDomain;
+use stwo_cairo_verifier::channel::{Channel, ChannelTrait};
+use stwo_cairo_verifier::circle::CosetImpl;
 use stwo_cairo_verifier::fields::m31::M31;
-use stwo_cairo_verifier::utils::{bit_reverse_index, pow, pow_qm31, qm31_zero_array, find};
-use stwo_cairo_verifier::poly::line::{
-    LineEvaluation, LineEvaluationImpl, SparseLineEvaluation, SparseLineEvaluationImpl
-};
+use stwo_cairo_verifier::fields::m31::M31Trait;
+use stwo_cairo_verifier::fields::qm31::{QM31, QM31Trait};
+use stwo_cairo_verifier::poly::circle::CircleDomainImpl;
 use stwo_cairo_verifier::poly::circle::{
     CircleEvaluation, SparseCircleEvaluation, SparseCircleEvaluationImpl
 };
-use stwo_cairo_verifier::poly::circle::{CircleDomain, CircleDomainImpl};
+use stwo_cairo_verifier::poly::line::{
+    LineEvaluation, LineEvaluationImpl, SparseLineEvaluation, SparseLineEvaluationImpl
+};
+use stwo_cairo_verifier::poly::line::{LineDomain, LineDomainImpl};
+use stwo_cairo_verifier::poly::line::{LinePoly, LinePolyImpl};
+use stwo_cairo_verifier::queries::SparseSubCircleDomain;
 use stwo_cairo_verifier::queries::{Queries, QueriesImpl};
-use stwo_cairo_verifier::vcs::verifier::{MerkleDecommitment, MerkleVerifier, MerkleVerifierTrait};
+use stwo_cairo_verifier::utils::{bit_reverse_index, pow, pow_qm31, qm31_zero_array, find};
 use stwo_cairo_verifier::vcs::hasher::PoseidonMerkleHasher;
-use stwo_cairo_verifier::poly::line::{LinePoly, LinePolyImpl};
-use stwo_cairo_verifier::channel::{Channel, ChannelTrait};
+use stwo_cairo_verifier::vcs::verifier::{MerkleDecommitment, MerkleVerifier, MerkleVerifierTrait};
 
 pub const CIRCLE_TO_LINE_FOLD_STEP: u32 = 1;
 pub const FOLD_STEP: u32 = 1;
@@ -531,27 +531,20 @@ pub fn ibutterfly(v0: QM31, v1: QM31, itwid: M31) -> (QM31, QM31) {
 
 #[cfg(test)]
 mod test {
-    use stwo_cairo_verifier::poly::line::{
-        LineEvaluation, SparseLineEvaluation, SparseLineEvaluationImpl
-    };
-    use stwo_cairo_verifier::fields::m31::M31Trait;
+    use stwo_cairo_verifier::channel::ChannelTrait;
     use stwo_cairo_verifier::circle::{Coset, CosetImpl};
-    use stwo_cairo_verifier::poly::line::{LineDomain, LineDomainImpl};
-    use stwo_cairo_verifier::fields::qm31::{QM31, qm31};
-    use stwo_cairo_verifier::fields::m31::M31;
-    use stwo_cairo_verifier::utils::{bit_reverse_index, pow};
+    use stwo_cairo_verifier::fields::qm31::qm31;
     use stwo_cairo_verifier::poly::circle::{
-        CircleEvaluation, CircleEvaluationTrait, CircleDomain, CircleEvaluationImpl,
-        SparseCircleEvaluation, SparseCircleEvaluationImpl
+        CircleDomain, CircleEvaluationImpl, SparseCircleEvaluation, SparseCircleEvaluationImpl
     };
-    use stwo_cairo_verifier::queries::{Queries, QueriesImpl};
-    use stwo_cairo_verifier::channel::ChannelTrait;
+    use stwo_cairo_verifier::poly::line::LineDomainImpl;
     use stwo_cairo_verifier::poly::line::LinePoly;
-    use stwo_cairo_verifier::vcs::verifier::MerkleDecommitment;
-    use super::{
-        FOLD_STEP, CIRCLE_TO_LINE_FOLD_STEP, FriConfig, FriProof, FriVerifierImpl,
-        FriVerificationError, FriLayerProof
+    use stwo_cairo_verifier::poly::line::{
+        LineEvaluation, SparseLineEvaluation, SparseLineEvaluationImpl
     };
+    use stwo_cairo_verifier::queries::{Queries, QueriesImpl};
+    use stwo_cairo_verifier::vcs::verifier::MerkleDecommitment;
+    use super::{FriConfig, FriProof, FriVerifierImpl, FriVerificationError, FriLayerProof};
 
     #[test]
     fn test_fold_line_1() {
diff --git a/stwo_cairo_verifier/src/lib.cairo b/stwo_cairo_verifier/src/lib.cairo
index 9dbe333c..1f422bbc 100644
--- a/stwo_cairo_verifier/src/lib.cairo
+++ b/stwo_cairo_verifier/src/lib.cairo
@@ -1,12 +1,12 @@
 mod channel;
 mod circle;
 mod fields;
+mod fri;
 mod poly;
+mod queries;
+mod sort;
 mod utils;
 mod vcs;
-mod fri;
-mod sort;
-mod queries;
 
 pub use fields::{BaseField, SecureField};
 
diff --git a/stwo_cairo_verifier/src/poly/circle.cairo b/stwo_cairo_verifier/src/poly/circle.cairo
index 34668fd4..65e63d9f 100644
--- a/stwo_cairo_verifier/src/poly/circle.cairo
+++ b/stwo_cairo_verifier/src/poly/circle.cairo
@@ -1,15 +1,12 @@
+use core::num::traits::ops::wrapping::WrappingSub;
 use stwo_cairo_verifier::circle::CirclePointTrait;
-use core::option::OptionTrait;
-use core::clone::Clone;
-use core::result::ResultTrait;
-use stwo_cairo_verifier::fields::qm31::{QM31, qm31};
-use stwo_cairo_verifier::fields::m31::{M31, m31};
-use stwo_cairo_verifier::utils::pow;
 use stwo_cairo_verifier::circle::{
     Coset, CosetImpl, CirclePoint, CirclePointM31Impl, M31_CIRCLE_GEN, CIRCLE_ORDER
 };
+use stwo_cairo_verifier::fields::m31::M31;
+use stwo_cairo_verifier::fields::qm31::QM31;
 use stwo_cairo_verifier::fri::fold_circle_into_line;
-use core::num::traits::ops::wrapping::WrappingSub;
+use stwo_cairo_verifier::utils::pow;
 
 /// A valid domain for circle polynomial interpolation and evaluation.
 ///
@@ -127,13 +124,13 @@ pub impl SparseCircleEvaluationImpl of SparseCircleEvaluationImplTrait {
 
 #[cfg(test)]
 mod tests {
-    use super::{
-        CircleDomain, CircleDomainTrait, CircleEvaluation, CircleEvaluationImpl,
-        SparseCircleEvaluation, SparseCircleEvaluationImplTrait
-    };
     use stwo_cairo_verifier::circle::{Coset, CosetImpl, CirclePoint};
     use stwo_cairo_verifier::fields::m31::m31;
     use stwo_cairo_verifier::fields::qm31::qm31;
+    use super::{
+        CircleDomain, CircleDomainTrait, CircleEvaluationImpl, SparseCircleEvaluation,
+        SparseCircleEvaluationImplTrait
+    };
 
     #[test]
     fn test_circle_domain_at_1() {
diff --git a/stwo_cairo_verifier/src/poly/line.cairo b/stwo_cairo_verifier/src/poly/line.cairo
index 83af45b6..7f55d511 100644
--- a/stwo_cairo_verifier/src/poly/line.cairo
+++ b/stwo_cairo_verifier/src/poly/line.cairo
@@ -1,13 +1,9 @@
-use core::option::OptionTrait;
-use core::clone::Clone;
-use core::result::ResultTrait;
-use stwo_cairo_verifier::poly::utils::fold;
-use stwo_cairo_verifier::fields::SecureField;
-use stwo_cairo_verifier::fields::m31::{M31, m31, M31Trait};
-use stwo_cairo_verifier::fields::qm31::{QM31, qm31, QM31Zero};
-use stwo_cairo_verifier::utils::pow;
 use stwo_cairo_verifier::circle::{Coset, CosetImpl, CirclePointTrait, M31_CIRCLE_GEN};
+use stwo_cairo_verifier::fields::SecureField;
+use stwo_cairo_verifier::fields::m31::{M31, m31};
+use stwo_cairo_verifier::fields::qm31::{QM31, QM31Zero};
 use stwo_cairo_verifier::fri::fold_line;
+use stwo_cairo_verifier::poly::utils::fold;
 
 /// A univariate polynomial defined on a [LineDomain].
 #[derive(Debug, Drop, Clone)]
@@ -138,11 +134,11 @@ pub impl SparseLineEvaluationImpl of SparseLineEvaluationTrait {
 
 #[cfg(test)]
 mod tests {
-    use super::{LinePoly, LinePolyTrait, LineDomain, LineDomainImpl};
-    use stwo_cairo_verifier::fields::qm31::qm31;
+    use stwo_cairo_verifier::circle::{CosetImpl, CIRCLE_LOG_ORDER};
     use stwo_cairo_verifier::fields::m31::m31;
-    use stwo_cairo_verifier::circle::{Coset, CosetImpl, CIRCLE_LOG_ORDER};
+    use stwo_cairo_verifier::fields::qm31::qm31;
     use stwo_cairo_verifier::utils::pow;
+    use super::{LinePoly, LinePolyTrait, LineDomainImpl};
 
     #[test]
     #[should_panic]
diff --git a/stwo_cairo_verifier/src/queries.cairo b/stwo_cairo_verifier/src/queries.cairo
index 279b701f..67d64bff 100644
--- a/stwo_cairo_verifier/src/queries.cairo
+++ b/stwo_cairo_verifier/src/queries.cairo
@@ -1,11 +1,8 @@
-use super::utils::{pow, bit_reverse_index, find};
-use core::traits::Copy;
-use core::nullable::{NullableTrait, match_nullable, FromNullableResult};
-use core::dict::Felt252DictEntryTrait;
-use stwo_cairo_verifier::poly::circle::{CircleDomain, CircleDomainImpl};
-use stwo_cairo_verifier::circle::{Coset, CosetImpl};
 use stwo_cairo_verifier::channel::{Channel, ChannelTrait};
+use stwo_cairo_verifier::circle::CosetImpl;
+use stwo_cairo_verifier::poly::circle::{CircleDomain, CircleDomainImpl};
 use stwo_cairo_verifier::sort::MinimumToMaximumSortedIterator;
+use super::utils::{pow, bit_reverse_index, find};
 
 
 /// An ordered set of query indices over a bit reversed [CircleDomain].
@@ -161,8 +158,8 @@ pub impl SparseSubCircleDomainImpl of SparseSubCircleDomainTrait {
 
 #[cfg(test)]
 mod test {
+    use stwo_cairo_verifier::channel::ChannelTrait;
     use super::{Queries, QueriesImpl};
-    use stwo_cairo_verifier::channel::{Channel, ChannelTrait};
 
     #[test]
     fn test_fold_1() {
diff --git a/stwo_cairo_verifier/src/sort.cairo b/stwo_cairo_verifier/src/sort.cairo
index 0e873fc5..9f4851c8 100644
--- a/stwo_cairo_verifier/src/sort.cairo
+++ b/stwo_cairo_verifier/src/sort.cairo
@@ -1,5 +1,5 @@
-use core::array::ToSpanTrait;
 use core::array::ArrayTrait;
+use core::array::ToSpanTrait;
 use core::option::OptionTrait;
 
 trait Compare<T, C> {
diff --git a/stwo_cairo_verifier/src/utils.cairo b/stwo_cairo_verifier/src/utils.cairo
index 3b5e32f3..ea791d39 100644
--- a/stwo_cairo_verifier/src/utils.cairo
+++ b/stwo_cairo_verifier/src/utils.cairo
@@ -1,15 +1,13 @@
 use core::array::SpanTrait;
-use core::dict::Felt252Dict;
-use core::traits::PanicDestruct;
-use core::option::OptionTrait;
 use core::box::BoxTrait;
+use core::dict::Felt252Dict;
 use core::dict::Felt252DictEntryTrait;
 use core::dict::Felt252DictTrait;
-use core::iter::Iterator;
 use core::num::traits::BitSize;
-use stwo_cairo_verifier::fields::qm31::{QM31, qm31};
-use stwo_cairo_verifier::BaseField;
 use core::traits::DivRem;
+use core::traits::PanicDestruct;
+use stwo_cairo_verifier::BaseField;
+use stwo_cairo_verifier::fields::qm31::{QM31, qm31};
 
 #[generate_trait]
 pub impl DictImpl<T, +Felt252DictValue<T>, +PanicDestruct<T>> of DictTrait<T> {
diff --git a/stwo_cairo_verifier/src/vcs/hasher.cairo b/stwo_cairo_verifier/src/vcs/hasher.cairo
index 6f5f2f89..3050d81d 100644
--- a/stwo_cairo_verifier/src/vcs/hasher.cairo
+++ b/stwo_cairo_verifier/src/vcs/hasher.cairo
@@ -2,8 +2,6 @@ use core::array::ArrayTrait;
 use core::option::OptionTrait;
 use core::poseidon::poseidon_hash_span;
 use stwo_cairo_verifier::BaseField;
-use core::hash::HashStateTrait;
-use core::poseidon::{hades_permutation, HashState};
 
 // A Merkle node hash is a hash of:
 //   [left_child_hash, right_child_hash], column0_value, column1_value, ...
@@ -65,8 +63,8 @@ pub impl PoseidonMerkleHasher of MerkleHasher {
 
 #[cfg(test)]
 mod tests {
-    use super::PoseidonMerkleHasher;
     use stwo_cairo_verifier::fields::m31::{m31};
+    use super::PoseidonMerkleHasher;
 
     #[test]
     fn test_m31() {
diff --git a/stwo_cairo_verifier/src/vcs/verifier.cairo b/stwo_cairo_verifier/src/vcs/verifier.cairo
index d252e793..43cd1477 100644
--- a/stwo_cairo_verifier/src/vcs/verifier.cairo
+++ b/stwo_cairo_verifier/src/vcs/verifier.cairo
@@ -1,17 +1,17 @@
-use core::dict::Felt252DictTrait;
-use core::result::ResultTrait;
-use stwo_cairo_verifier::utils::SpanExTrait;
-use core::option::OptionTrait;
 use core::array::ArrayTrait;
 use core::array::SpanTrait;
 use core::array::ToSpanTrait;
+use core::cmp::min;
 use core::dict::Felt252Dict;
 use core::dict::Felt252DictEntryTrait;
-use core::nullable::NullableTrait;
-use core::cmp::min;
+use core::dict::Felt252DictTrait;
 use core::fmt::{Debug, Formatter, Error};
+use core::nullable::NullableTrait;
+use core::option::OptionTrait;
+use core::result::ResultTrait;
 use stwo_cairo_verifier::BaseField;
 use stwo_cairo_verifier::fields::m31::m31;
+use stwo_cairo_verifier::utils::SpanExTrait;
 use stwo_cairo_verifier::utils::{ArrayExTrait, DictTrait, OptBoxTrait};
 use stwo_cairo_verifier::vcs::hasher::MerkleHasher;