diff --git a/src/gkr/circuit/mod.rs b/src/gkr/circuit/mod.rs
index d599081..77f65f1 100644
--- a/src/gkr/circuit/mod.rs
+++ b/src/gkr/circuit/mod.rs
@@ -541,19 +541,19 @@ impl<E: FieldElement<BaseField = BaseElement> + 'static> CircuitProof<E> {
         H: ElementHasher<BaseField = BaseElement>,
     >(
         &self,
-        claims_sum_vec: &(E, E, E, E),
+        claims_sum_vec: &[E],
         transcript: &mut C,
     ) -> ((E, E), Vec<E>) {
         let num_layers = self.proof.len() as usize - 1;
         let mut rand: Vec<E> = Vec::new();
 
-        let data = vec![claims_sum_vec.0, claims_sum_vec.1, claims_sum_vec.2, claims_sum_vec.3];
+        let data = claims_sum_vec;
         transcript.reseed(H::hash_elements(&data));
 
         let r_cord = transcript.draw().unwrap();
 
-        let p_poly_coef = vec![claims_sum_vec.0, claims_sum_vec.1];
-        let q_poly_coef = vec![claims_sum_vec.2, claims_sum_vec.3];
+        let p_poly_coef = vec![claims_sum_vec[0], claims_sum_vec[1]];
+        let q_poly_coef = vec![claims_sum_vec[2], claims_sum_vec[3]];
 
         let p_poly = MultiLinear::new(p_poly_coef);
         let q_poly = MultiLinear::new(q_poly_coef);
@@ -619,27 +619,27 @@ impl<E: FieldElement<BaseField = BaseElement> + 'static> CircuitProof<E> {
         &self,
         composition_polys: Vec<Vec<Arc<dyn CompositionPolynomial<E>>>>,
         final_layer_proof: super::sumcheck::FullProof<E>,
-        claims_sum_vec: &(E, E, E, E),
+        claims_sum_vec: &[E],
         transcript: &mut C,
     ) -> (FinalEvaluationClaim<E>, Vec<E>) {
         let num_layers = self.proof.len() as usize;
         let mut rand: Vec<E> = Vec::new();
 
         // Check that a/b + d/e is equal to 0
-        assert_ne!(claims_sum_vec.2, E::ZERO);
-        assert_ne!(claims_sum_vec.3, E::ZERO);
+        assert_ne!(claims_sum_vec[2], E::ZERO);
+        assert_ne!(claims_sum_vec[3], E::ZERO);
         assert_eq!(
-            claims_sum_vec.0 * claims_sum_vec.3 + claims_sum_vec.1 * claims_sum_vec.2,
+            claims_sum_vec[0] * claims_sum_vec[3] + claims_sum_vec[1] * claims_sum_vec[2],
             E::ZERO
         );
 
-        let data = vec![claims_sum_vec.0, claims_sum_vec.1, claims_sum_vec.2, claims_sum_vec.3];
+        let data = claims_sum_vec;
         transcript.reseed(H::hash_elements(&data));
 
         let r_cord = transcript.draw().unwrap();
 
-        let p_poly_coef = vec![claims_sum_vec.0, claims_sum_vec.1];
-        let q_poly_coef = vec![claims_sum_vec.2, claims_sum_vec.3];
+        let p_poly_coef = vec![claims_sum_vec[0], claims_sum_vec[1]];
+        let q_poly_coef = vec![claims_sum_vec[2], claims_sum_vec[3]];
 
         let p_poly = MultiLinear::new(p_poly_coef);
         let q_poly = MultiLinear::new(q_poly_coef);
@@ -905,7 +905,7 @@ mod sum_circuit_tests {
 
         let seed = [BaseElement::ZERO; 4];
         let mut transcript = RpoRandomCoin::new(seed.into());
-        let claims = (p0, p1, q0, q1);
+        let claims = vec![p0, p1, q0, q1];
         proof.verify(&claims, &mut transcript);
     }
 
@@ -971,7 +971,7 @@ mod sum_circuit_tests {
 
         let seed = [BaseElement::ZERO; 4];
         let mut transcript = RpoRandomCoin::new(seed.into());
-        let claims = (p0, p1, q0, q1);
+        let claims = vec![p0, p1, q0, q1];
         proof.verify(&claims, &mut transcript);
     }
 }
diff --git a/src/gkr/sumcheck/tests.rs b/src/gkr/sumcheck/tests.rs
index 2ed161d..7d8bfbe 100644
--- a/src/gkr/sumcheck/tests.rs
+++ b/src/gkr/sumcheck/tests.rs
@@ -59,8 +59,6 @@ fn gkr_workflow() {
     // 2. Randomness defining the Lagrange kernel in the final sum-check protocol. Note that this
     // Lagrange kernel is different from the one used by the STARK (outer) prover to open the MLs
     // at the evaluation point.
-    let circuit_outputs =
-        (circuit_outputs[0], circuit_outputs[1], circuit_outputs[2], circuit_outputs[3]);
     let (final_eval_claim, gkr_lagrange_kernel_rand) = gkr_before_last_proof.verify_virtual_bus(
         composition_polys.clone(),
         final_layer_proof,
@@ -101,7 +99,7 @@ fn gkr_workflow() {
     let left_den_eval = mls[2].evaluate(&evaluation_point);
     let right_den_eval = mls[3].evaluate(&evaluation_point);
 
-    // The verifier absorbs the claimed openings and generates batching randomness
+    // The verifier absorbs the claimed openings and generates batching randomness lambda
     let mut query = vec![left_num_eval, right_num_eval, left_den_eval, right_den_eval];
     transcript.reseed(Rpo256::hash_elements(&query));
     let lambdas: Vec<BaseElement> = vec![
@@ -112,17 +110,17 @@ fn gkr_workflow() {
     let batched_query =
         query[0] + query[1] * lambdas[0] + query[2] * lambdas[1] + query[3] * lambdas[2];
 
-    // The prover generates the Lagrange kernel
+    // The prover generates the Lagrange kernel as an auxiliary column
     let mut rev_evaluation_point = evaluation_point;
     rev_evaluation_point.reverse();
     let lagrange_kernel = EqPolynomial::new(rev_evaluation_point).evaluations();
+
+    // The prover generates the additional auxiliary column for the inner product
     let tmp_col: Vec<BaseElement> = (0..mls[0].len())
         .map(|i| {
             mls[0][i] + mls[1][i] * lambdas[0] + mls[2][i] * lambdas[1] + mls[3][i] * lambdas[2]
         })
         .collect();
-
-    // The prover generates the additional auxiliary column for the inner product
     let mut running_sum_col = vec![BaseElement::ZERO; tmp_col.len() + 1];
     running_sum_col[0] = BaseElement::ZERO;
     for i in 1..(tmp_col.len() + 1) {