diff --git a/crates/proof-of-sql/src/base/proof/error.rs b/crates/proof-of-sql/src/base/proof/error.rs
index 5988aec56..e81edfd22 100644
--- a/crates/proof-of-sql/src/base/proof/error.rs
+++ b/crates/proof-of-sql/src/base/proof/error.rs
@@ -43,4 +43,7 @@ pub enum ProofSizeMismatch {
     /// This error occurs when the proof has too few one lengths.
     #[snafu(display("Proof has too few one lengths"))]
     TooFewOneLengths,
+    /// This error occurs when the proof has too few sumcheck variables.
+    #[snafu(display("Proof has too few sumcheck variables"))]
+    TooFewSumcheckVariables,
 }
diff --git a/crates/proof-of-sql/src/sql/proof/sumcheck_mle_evaluations.rs b/crates/proof-of-sql/src/sql/proof/sumcheck_mle_evaluations.rs
index 14a937250..1b2473fab 100644
--- a/crates/proof-of-sql/src/sql/proof/sumcheck_mle_evaluations.rs
+++ b/crates/proof-of-sql/src/sql/proof/sumcheck_mle_evaluations.rs
@@ -26,6 +26,9 @@ pub struct SumcheckMleEvaluations<'a, S: Scalar> {
     pub random_evaluation: S,
     /// The evaluations (at the random point generated by sumcheck) of the mles that are evaluated by the inner product argument. These are batched together and checked by a single IPA.
     pub pcs_proof_evaluations: &'a [S],
+
+    /// Evaluation (at the random point generated by sumcheck) of the function `rho_256` that is defined by rho_256(x) = x when 0 <= x < 256 and 0 otherwise.
+    pub rho_256_evaluation: Option<S>,
 }
 
 #[allow(
@@ -46,6 +49,22 @@ impl<'a, S: Scalar> SumcheckMleEvaluations<'a, S> {
         sumcheck_random_scalars: &SumcheckRandomScalars<S>,
         pcs_proof_evaluations: &'a [S],
     ) -> Self {
+        let rho_256_evaluation = if evaluation_point.len() < 8 {
+            None
+        } else {
+            let rho_256_intermediate = evaluation_point
+                .iter()
+                .take(8)
+                .rev()
+                .fold(S::ZERO, |acc, &x| acc * S::TWO + x);
+            Some(
+                evaluation_point
+                    .iter()
+                    .skip(8)
+                    .fold(rho_256_intermediate, |acc, &x| acc * (S::ONE - x)),
+            )
+        };
+
         assert_eq!(
             evaluation_point.len(),
             sumcheck_random_scalars.entrywise_point.len()
@@ -74,6 +93,7 @@ impl<'a, S: Scalar> SumcheckMleEvaluations<'a, S> {
             singleton_one_evaluation,
             random_evaluation,
             pcs_proof_evaluations,
+            rho_256_evaluation,
         }
     }
 }
diff --git a/crates/proof-of-sql/src/sql/proof_gadgets/range_check.rs b/crates/proof-of-sql/src/sql/proof_gadgets/range_check.rs
index 7a699b0ce..5ebc7e42e 100644
--- a/crates/proof-of-sql/src/sql/proof_gadgets/range_check.rs
+++ b/crates/proof-of-sql/src/sql/proof_gadgets/range_check.rs
@@ -239,7 +239,6 @@ fn prove_word_values<'a, S: Scalar + 'a>(
     // Allocate from 0 to 255 and pertrub with verifier challenge
     let word_values: &mut [S] =
         alloc.alloc_slice_fill_with(max(256, scalars.len()), |i| S::from(&(i as u8)));
-    builder.produce_intermediate_mle(word_values as &[_]);
 
     // Now produce an intermediate MLE over the inverted word values + verifier challenge alpha
     let word_vals_inv: &mut [S] = alloc.alloc_slice_fill_with(256, |i| {
@@ -274,11 +273,11 @@ fn prove_word_values<'a, S: Scalar + 'a>(
 /// multiplied by the inverted word value, is zero.
 ///
 /// ```text
-/// ∑ (I₀ + I₁ + I₂ + I₃ - (C * IN)) = 0
+/// ∑ (I₀ + I₁ + I₂ ... Iₙ - (C * IN)) = 0
 /// ```
 ///
 /// Where:
-/// - `I₀, I₁, I₂, I₃` are the inverted word columns.
+/// - `I₀ + I₁ + I₂ ... Iₙ` are the inverted word columns.
 /// - `C` is the count of each word.
 /// - `IN` is the inverted word values column.
 #[allow(clippy::missing_panics_doc)]
@@ -378,7 +377,12 @@ where
         "Range check failed, column contains values outside of the selected range"
     );
 
-    let word_vals_eval = builder.try_consume_mle_evaluation()?;
+    let word_vals_eval = builder
+        .mle_evaluations
+        .rho_256_evaluation
+        .ok_or(ProofSizeMismatch::TooFewSumcheckVariables)?;
+    // Ensures that we have enough sumcheck variables
+    let _ = builder.try_consume_one_evaluation()?;
     let word_vals_plus_alpha_inv = builder.try_consume_mle_evaluation()?;
     let word_value_constraint = word_vals_plus_alpha_inv * (word_vals_eval + alpha);
 
diff --git a/crates/proof-of-sql/src/sql/proof_gadgets/range_check_test.rs b/crates/proof-of-sql/src/sql/proof_gadgets/range_check_test.rs
index 8bd046043..1909b2ed6 100644
--- a/crates/proof-of-sql/src/sql/proof_gadgets/range_check_test.rs
+++ b/crates/proof-of-sql/src/sql/proof_gadgets/range_check_test.rs
@@ -27,6 +27,7 @@ impl ProverEvaluate for RangeCheckTestPlan {
         table_map: &IndexMap<TableRef, Table<'a, S>>,
     ) -> Table<'a, S> {
         builder.request_post_result_challenges(1);
+        builder.produce_one_evaluation_length(256);
         table_map[&self.column.table_ref()].clone()
     }