diff --git a/starky/src/recursive_verifier.rs b/starky/src/recursive_verifier.rs
index ea7ffb70..c1071b5a 100644
--- a/starky/src/recursive_verifier.rs
+++ b/starky/src/recursive_verifier.rs
@@ -187,24 +187,29 @@ pub fn add_virtual_stark_proof<F: RichField + Extendable<D>, S: Stark<F, D>, con
     let fri_params = config.fri_params(degree_bits);
     let cap_height = fri_params.config.cap_height;
 
-    let num_leaves_per_oracle = &[
-        S::COLUMNS,
-        // TODO: permutation polys
-        stark.quotient_degree_factor() * config.num_challenges,
-    ];
-
-    let permutation_zs_cap = if stark.uses_permutation_args() {
-        Some(builder.add_virtual_cap(cap_height))
+    let num_leaves_per_oracle = if stark.uses_permutation_args() {
+        vec![
+            S::COLUMNS,
+            stark.num_permutation_batches(config),
+            stark.quotient_degree_factor() * config.num_challenges,
+        ]
     } else {
-        None
+        vec![
+            S::COLUMNS,
+            stark.quotient_degree_factor() * config.num_challenges,
+        ]
     };
 
+    let permutation_zs_cap = stark
+        .uses_permutation_args()
+        .then(|| builder.add_virtual_cap(cap_height));
+
     StarkProofTarget {
         trace_cap: builder.add_virtual_cap(cap_height),
         permutation_zs_cap,
         quotient_polys_cap: builder.add_virtual_cap(cap_height),
         openings: add_stark_opening_set::<F, S, D>(builder, stark, config),
-        opening_proof: builder.add_virtual_fri_proof(num_leaves_per_oracle, &fri_params),
+        opening_proof: builder.add_virtual_fri_proof(&num_leaves_per_oracle, &fri_params),
     }
 }
 
@@ -217,8 +222,10 @@ fn add_stark_opening_set<F: RichField + Extendable<D>, S: Stark<F, D>, const D:
     StarkOpeningSetTarget {
         local_values: builder.add_virtual_extension_targets(S::COLUMNS),
         next_values: builder.add_virtual_extension_targets(S::COLUMNS),
-        permutation_zs: vec![/*TODO*/],
-        permutation_zs_right: vec![/*TODO*/],
+        permutation_zs: builder
+            .add_virtual_extension_targets(stark.num_permutation_batches(config)),
+        permutation_zs_right: builder
+            .add_virtual_extension_targets(stark.num_permutation_batches(config)),
         quotient_polys: builder
             .add_virtual_extension_targets(stark.quotient_degree_factor() * num_challenges),
     }