diff --git a/examples/Cargo.toml b/examples/Cargo.toml
index 8c75f8ee3..2fda1d952 100644
--- a/examples/Cargo.toml
+++ b/examples/Cargo.toml
@@ -26,7 +26,6 @@ default = ["std"]
 std = ["core-utils/std", "hex/std", "rand-utils", "winterfell/std"]
 
 [dependencies]
-air = { version = "0.9", path = "../air", package = "winter-air", default-features = false }
 blake3 = { version = "1.5", default-features = false }
 core-utils = { version = "0.9", path = "../utils/core", package = "winter-utils", default-features = false }
 hex = { version = "0.4", optional = true }
diff --git a/prover/src/logup_gkr/prover.rs b/prover/src/logup_gkr/prover.rs
index f3f0b6c4f..3ad6fb0d4 100644
--- a/prover/src/logup_gkr/prover.rs
+++ b/prover/src/logup_gkr/prover.rs
@@ -156,7 +156,7 @@ fn build_mls_from_main_trace_segment<E: FieldElement>(
                 let ml = MultiLinearPoly::from_evaluations(values);
                 mls.push(ml)
             },
-            air::LogUpGkrOracle::PeriodicValue(values) => periodic_values.push(values.to_vec()),
+            LogUpGkrOracle::PeriodicValue(values) => periodic_values.push(values.to_vec()),
         };
     }
     Ok((mls, PeriodicTable::new(periodic_values)))
diff --git a/sumcheck/src/prover/high_degree.rs b/sumcheck/src/prover/high_degree.rs
index 867000a69..eeb6b7e4e 100644
--- a/sumcheck/src/prover/high_degree.rs
+++ b/sumcheck/src/prover/high_degree.rs
@@ -241,9 +241,6 @@ pub fn sum_check_prove_higher_degree<
         .for_each(|ml| ml.bind_least_significant_variable(round_challenge));
     eq_nu.bind_least_significant_variable(round_challenge);
 
-    // fold each periodic multi-linear using the round challenge
-    periodic_table.bind_least_significant_variable(round_challenge);
-
     let SumCheckRoundClaim { eval_point, claim: _claim } =
         reduce_claim(&round_proofs[num_rounds - 1], current_round_claim, round_challenge);
 
diff --git a/winterfell/src/tests/logup_gkr_simple.rs b/winterfell/src/tests/logup_gkr_simple.rs
index 508a14816..1a6119e64 100644
--- a/winterfell/src/tests/logup_gkr_simple.rs
+++ b/winterfell/src/tests/logup_gkr_simple.rs
@@ -17,7 +17,7 @@ use crate::{
 
 #[test]
 fn test_logup_gkr() {
-    let aux_trace_width = 2;
+    let aux_trace_width = 1;
     let trace = LogUpGkrSimple::new(2_usize.pow(7), aux_trace_width);
     let prover = LogUpGkrSimpleProver::new(aux_trace_width);
 
@@ -264,7 +264,7 @@ impl LogUpGkrSimpleProver {
     fn new(aux_trace_width: usize) -> Self {
         Self {
             aux_trace_width,
-            options: ProofOptions::new(1, 8, 0, FieldExtension::None, 2, 1),
+            options: ProofOptions::new(1, 8, 0, FieldExtension::Quadratic, 2, 1),
         }
     }
 }