diff --git a/evm/src/all_stark.rs b/evm/src/all_stark.rs
index 68b65d41..fd9ce01f 100644
--- a/evm/src/all_stark.rs
+++ b/evm/src/all_stark.rs
@@ -755,12 +755,13 @@ mod tests {
 
         let circuit_config = CircuitConfig::standard_recursion_config();
         let mut builder = CircuitBuilder::<F, D>::new(circuit_config);
-        let mut pw = PartialWitness::new();
-        recursive_all_proof.verify_circuit(&mut builder, &mut pw);
-
-        let data = builder.build::<C>();
-        let proof = data.prove(pw)?;
-        data.verify(proof)
+        // let mut pw = PartialWitness::new();
+        recursive_all_proof.verify(inner_config)
+        // recursive_all_proof.verify_circuit(&mut builder, &mut pw);
+        //
+        // let data = builder.build::<C>();
+        // let proof = data.prove(pw)?;
+        // data.verify(proof)
     }
 
     fn init_logger() {
diff --git a/evm/src/get_challenges.rs b/evm/src/get_challenges.rs
index 8b254ee4..e39e3e23 100644
--- a/evm/src/get_challenges.rs
+++ b/evm/src/get_challenges.rs
@@ -229,6 +229,7 @@ impl<const D: usize> StarkProofTarget<D> {
 
         challenger.observe_cap(quotient_polys_cap);
         let stark_zeta = challenger.get_extension_challenge(builder);
+        dbg!(stark_zeta);
 
         challenger.observe_openings(&openings.to_fri_openings(builder.zero()));
 
diff --git a/evm/src/permutation.rs b/evm/src/permutation.rs
index 0bb8ab1d..b081c309 100644
--- a/evm/src/permutation.rs
+++ b/evm/src/permutation.rs
@@ -1,5 +1,7 @@
 //! Permutation arguments.
 
+use std::fmt::Debug;
+
 use itertools::Itertools;
 use maybe_rayon::*;
 use plonky2::field::batch_util::batch_multiply_inplace;
@@ -42,14 +44,14 @@ impl PermutationPair {
 }
 
 /// A single instance of a permutation check protocol.
-pub(crate) struct PermutationInstance<'a, T: Copy> {
+pub(crate) struct PermutationInstance<'a, T: Copy + Eq + PartialEq + Debug> {
     pub(crate) pair: &'a PermutationPair,
     pub(crate) challenge: GrandProductChallenge<T>,
 }
 
 /// Randomness for a single instance of a permutation check protocol.
-#[derive(Copy, Clone)]
-pub(crate) struct GrandProductChallenge<T: Copy> {
+#[derive(Copy, Clone, Eq, PartialEq, Debug)]
+pub(crate) struct GrandProductChallenge<T: Copy + Eq + PartialEq + Debug> {
     /// Randomness used to combine multiple columns into one.
     pub(crate) beta: T,
     /// Random offset that's added to the beta-reduced column values.
@@ -92,8 +94,8 @@ impl GrandProductChallenge<Target> {
 }
 
 /// Like `PermutationChallenge`, but with `num_challenges` copies to boost soundness.
-#[derive(Clone)]
-pub(crate) struct GrandProductChallengeSet<T: Copy> {
+#[derive(Clone, Eq, PartialEq, Debug)]
+pub(crate) struct GrandProductChallengeSet<T: Copy + Eq + PartialEq + Debug> {
     pub(crate) challenges: Vec<GrandProductChallenge<T>>,
 }
 
@@ -261,7 +263,7 @@ pub(crate) fn get_n_grand_product_challenge_sets_target<
 /// Before batching, each permutation pair leads to `num_challenges` permutation arguments, so we
 /// start with the cartesian product of `permutation_pairs` and `0..num_challenges`. Then we
 /// chunk these arguments based on our batch size.
-pub(crate) fn get_permutation_batches<'a, T: Copy>(
+pub(crate) fn get_permutation_batches<'a, T: Copy + Eq + PartialEq + Debug>(
     permutation_pairs: &'a [PermutationPair],
     permutation_challenge_sets: &[GrandProductChallengeSet<T>],
     num_challenges: usize,
diff --git a/evm/src/recursive_verifier.rs b/evm/src/recursive_verifier.rs
index 4f08a053..fca634a7 100644
--- a/evm/src/recursive_verifier.rs
+++ b/evm/src/recursive_verifier.rs
@@ -1,16 +1,19 @@
-use anyhow::Result;
+use anyhow::{ensure, Result};
 use itertools::Itertools;
 use plonky2::field::extension::Extendable;
 use plonky2::field::types::Field;
 use plonky2::fri::witness_util::set_fri_proof_target;
-use plonky2::hash::hash_types::RichField;
+use plonky2::hash::hash_types::{HashOut, RichField};
 use plonky2::hash::hashing::SPONGE_WIDTH;
-use plonky2::iop::challenger::RecursiveChallenger;
+use plonky2::hash::merkle_tree::MerkleCap;
+use plonky2::hash::poseidon::PoseidonHash;
+use plonky2::iop::challenger::{Challenger, RecursiveChallenger};
 use plonky2::iop::ext_target::ExtensionTarget;
 use plonky2::iop::target::Target;
 use plonky2::iop::witness::{PartialWitness, Witness};
 use plonky2::plonk::circuit_builder::CircuitBuilder;
 use plonky2::plonk::circuit_data::{CircuitConfig, VerifierCircuitData, VerifierCircuitTarget};
+use plonky2::plonk::config::GenericHashOut;
 use plonky2::plonk::config::Hasher;
 use plonky2::plonk::config::{AlgebraicHasher, GenericConfig};
 use plonky2::plonk::proof::ProofWithPublicInputs;
@@ -29,7 +32,8 @@ use crate::keccak_memory::keccak_memory_stark::KeccakMemoryStark;
 use crate::logic::LogicStark;
 use crate::memory::memory_stark::MemoryStark;
 use crate::permutation::{
-    GrandProductChallenge, GrandProductChallengeSet, PermutationCheckDataTarget,
+    get_grand_product_challenge_set, GrandProductChallenge, GrandProductChallengeSet,
+    PermutationCheckDataTarget,
 };
 use crate::proof::{
     AllChallengerState, AllProof, AllProofChallengesTarget, AllProofTarget, BlockMetadata,
@@ -52,14 +56,88 @@ pub struct RecursiveAllProof<
         [(ProofWithPublicInputs<F, C, D>, VerifierCircuitData<F, C, D>); NUM_TABLES],
 }
 
+struct PublicInputs<F: RichField + Extendable<D>, C: GenericConfig<D, F = F>, const D: usize> {
+    trace_cap: MerkleCap<F, C::Hasher>,
+    ctl_zs_last: Vec<F>,
+    ctl_challenges: GrandProductChallengeSet<F>,
+    challenger_state_before: [F; SPONGE_WIDTH],
+    challenger_state_after: [F; SPONGE_WIDTH],
+}
+
+impl<F: RichField + Extendable<D>, C: GenericConfig<D, F = F>, const D: usize>
+    PublicInputs<F, C, D>
+{
+    fn from_vec(v: &[F], config: &StarkConfig) -> Self {
+        let mut start = 0;
+        let trace_cap = MerkleCap(
+            v[start..4 * (1 << config.fri_config.cap_height)]
+                .chunks(4)
+                .map(|chunk| <C::Hasher as Hasher<F>>::Hash::from_vec(chunk))
+                .collect(),
+        );
+        start += 4 * (1 << config.fri_config.cap_height);
+        let ctl_challenges = GrandProductChallengeSet {
+            challenges: (0..config.num_challenges)
+                .map(|i| GrandProductChallenge {
+                    beta: v[start + 2 * i],
+                    gamma: v[start + 2 * i + 1],
+                })
+                .collect(),
+        };
+        start += 2 * config.num_challenges;
+        let challenger_state_before = v[start..start + SPONGE_WIDTH].try_into().unwrap();
+        let challenger_state_after = v[start + SPONGE_WIDTH..start + 2 * SPONGE_WIDTH]
+            .try_into()
+            .unwrap();
+
+        start += 2 * SPONGE_WIDTH;
+        let ctl_zs_last = v[start..].to_vec();
+
+        Self {
+            trace_cap,
+            ctl_zs_last,
+            ctl_challenges,
+            challenger_state_before,
+            challenger_state_after,
+        }
+    }
+}
+
 impl<F: RichField + Extendable<D>, C: GenericConfig<D, F = F>, const D: usize>
     RecursiveAllProof<F, C, D>
 {
     /// Verify every recursive proof.
-    pub fn verify(self) -> Result<()>
+    pub fn verify(self, inner_config: &StarkConfig) -> Result<()>
     where
         [(); C::Hasher::HASH_SIZE]:,
     {
+        let pis: [_; NUM_TABLES] = std::array::from_fn(|i| {
+            PublicInputs::<F, C, D>::from_vec(
+                &self.recursive_proofs[i].0.public_inputs,
+                inner_config,
+            )
+        });
+
+        let mut challenger = Challenger::<F, C::Hasher>::new();
+        for pi in &pis {
+            challenger.observe_cap(&pi.trace_cap);
+        }
+        let ctl_challenges =
+            get_grand_product_challenge_set(&mut challenger, inner_config.num_challenges);
+        for pi in &pis {
+            ensure!(ctl_challenges == pi.ctl_challenges);
+        }
+        challenger.duplexing();
+        let state = challenger.state();
+        ensure!(state == pis[0].challenger_state_before);
+        for i in 1..NUM_TABLES {
+            dbg!(i);
+            dbg!(
+                pis[i].challenger_state_before,
+                pis[i - 1].challenger_state_after
+            );
+            ensure!(pis[i].challenger_state_before == pis[i - 1].challenger_state_after);
+        }
         for (proof, verifier_data) in self.recursive_proofs {
             verifier_data.verify(proof)?;
         }
@@ -124,6 +202,14 @@ where
         proof.num_ctl_zs(),
     );
     set_stark_proof_target(&mut pw, &proof_target, proof, builder.zero());
+    builder.register_public_inputs(
+        &proof_target
+            .trace_cap
+            .0
+            .iter()
+            .flat_map(|h| h.elements)
+            .collect::<Vec<_>>(),
+    );
 
     let ctl_challenges_target = GrandProductChallengeSet {
         challenges: (0..inner_config.num_challenges)
@@ -166,6 +252,8 @@ where
     let challenger_state = challenger.state();
     builder.register_public_inputs(&challenger_state);
 
+    builder.register_public_inputs(&proof_target.openings.ctl_zs_last);
+
     verify_stark_proof_with_challenges_circuit::<F, C, _, D>(
         &mut builder,
         &stark,
diff --git a/plonky2/src/hash/hash_types.rs b/plonky2/src/hash/hash_types.rs
index 14303ad3..955f539a 100644
--- a/plonky2/src/hash/hash_types.rs
+++ b/plonky2/src/hash/hash_types.rs
@@ -78,6 +78,12 @@ impl<F: RichField> GenericHashOut<F> for HashOut<F> {
     fn to_vec(&self) -> Vec<F> {
         self.elements.to_vec()
     }
+
+    fn from_vec(v: &[F]) -> Self {
+        Self {
+            elements: v.try_into().unwrap(),
+        }
+    }
 }
 
 impl<F: Field> Default for HashOut<F> {
@@ -148,6 +154,10 @@ impl<F: RichField, const N: usize> GenericHashOut<F> for BytesHash<N> {
             })
             .collect()
     }
+
+    fn from_vec(_v: &[F]) -> Self {
+        todo!()
+    }
 }
 
 impl<const N: usize> Serialize for BytesHash<N> {
diff --git a/plonky2/src/iop/challenger.rs b/plonky2/src/iop/challenger.rs
index 4e83b1c6..1a9e3f13 100644
--- a/plonky2/src/iop/challenger.rs
+++ b/plonky2/src/iop/challenger.rs
@@ -287,16 +287,20 @@ impl<F: RichField + Extendable<D>, H: AlgebraicHasher<F>, const D: usize>
     }
 
     pub fn duplexing(&mut self, builder: &mut CircuitBuilder<F, D>) {
-        for input_chunk in self.input_buffer.chunks(SPONGE_RATE) {
-            // Overwrite the first r elements with the inputs. This differs from a standard sponge,
-            // where we would xor or add in the inputs. This is a well-known variant, though,
-            // sometimes called "overwrite mode".
-            for (i, &input) in input_chunk.iter().enumerate() {
-                self.sponge_state[i] = input;
-            }
-
-            // Apply the permutation.
+        if self.input_buffer.is_empty() {
             self.sponge_state = builder.permute::<H>(self.sponge_state);
+        } else {
+            for input_chunk in self.input_buffer.chunks(SPONGE_RATE) {
+                // Overwrite the first r elements with the inputs. This differs from a standard sponge,
+                // where we would xor or add in the inputs. This is a well-known variant, though,
+                // sometimes called "overwrite mode".
+                for (i, &input) in input_chunk.iter().enumerate() {
+                    self.sponge_state[i] = input;
+                }
+
+                // Apply the permutation.
+                self.sponge_state = builder.permute::<H>(self.sponge_state);
+            }
         }
 
         self.output_buffer = self.sponge_state[0..SPONGE_RATE].to_vec();
diff --git a/plonky2/src/plonk/config.rs b/plonky2/src/plonk/config.rs
index f55bad1f..51dacdde 100644
--- a/plonky2/src/plonk/config.rs
+++ b/plonky2/src/plonk/config.rs
@@ -20,6 +20,7 @@ pub trait GenericHashOut<F: RichField>:
     fn from_bytes(bytes: &[u8]) -> Self;
 
     fn to_vec(&self) -> Vec<F>;
+    fn from_vec(v: &[F]) -> Self;
 }
 
 /// Trait for hash functions.