diff --git a/Cargo.toml b/Cargo.toml
index 88580997d..1462bd9d0 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -60,6 +60,7 @@ rocksdb = { version = "0.19.0", features = ["lz4"] }
 serde = { version = "1.0.137", features = ["derive", "rc"] }
 serde_json = { version = "1.0" }
 sha2 = "0.10.6"
+digest = "0.10.6"
 thiserror = "1.0.38"
 tiny-keccak = "2.0.2"
 tracing = "0.1.37"
diff --git a/adapters/celestia/Cargo.toml b/adapters/celestia/Cargo.toml
index d6154fc73..0a3f2bc33 100644
--- a/adapters/celestia/Cargo.toml
+++ b/adapters/celestia/Cargo.toml
@@ -24,6 +24,7 @@ serde = { workspace = true }
 serde_cbor = "0.11.2"
 serde_json = { workspace = true }
 tokio = { version = "1", features = ["full"], optional = true }
+thiserror = { workspace = true }
 tracing = "0.1.37"
 
 sov-rollup-interface = { path = "../../rollup-interface" }
diff --git a/adapters/celestia/src/celestia.rs b/adapters/celestia/src/celestia.rs
index 5c2a04dce..23a2be2ed 100644
--- a/adapters/celestia/src/celestia.rs
+++ b/adapters/celestia/src/celestia.rs
@@ -33,12 +33,6 @@ pub struct MarshalledDataAvailabilityHeader {
     pub column_roots: Vec<String>,
 }
 
-#[derive(PartialEq, Eq, Debug, Clone, Serialize, Deserialize, BorshDeserialize, BorshSerialize)]
-pub struct PartialBlockId {
-    pub hash: ProtobufHash,
-    pub part_set_header: Vec<u8>,
-}
-
 /// A partially serialized tendermint header. Only fields which are actually inspected by
 /// Jupiter are included in their raw form. Other fields are pre-encoded as protobufs.
 ///
diff --git a/adapters/celestia/src/verifier/mod.rs b/adapters/celestia/src/verifier/mod.rs
index abb4c8b7f..e6c64aed2 100644
--- a/adapters/celestia/src/verifier/mod.rs
+++ b/adapters/celestia/src/verifier/mod.rs
@@ -1,9 +1,13 @@
 use nmt_rs::NamespaceId;
 use serde::{Deserialize, Serialize};
 use sov_rollup_interface::{
+    crypto::SimpleHasher,
     da::{self, BlobTransactionTrait, BlockHashTrait as BlockHash, CountedBufReader, DaSpec},
+    traits::{BlockHeaderTrait, CanonicalHash},
+    zk::traits::ValidityCondition,
     Buf,
 };
+use thiserror::Error;
 
 pub mod address;
 pub mod proofs;
@@ -102,33 +106,61 @@ pub struct RollupParams {
     pub namespace: NamespaceId,
 }
 
+#[derive(Debug, Clone, PartialEq, Eq, Serialize, Deserialize, Hash)]
+/// A validity condition expressing that a chain of DA layer blocks is contiguous and canonical
+pub struct ChainValidityCondition {
+    pub prev_hash: [u8; 32],
+    pub block_hash: [u8; 32],
+}
+#[derive(Error, Debug)]
+pub enum ValidityConditionError {
+    #[error("conditions for validity can only be combined if the blocks are consecutive")]
+    BlocksNotConsecutive,
+}
+
+impl ValidityCondition for ChainValidityCondition {
+    type Error = ValidityConditionError;
+    fn combine<H: SimpleHasher>(&self, rhs: Self) -> Result<Self, Self::Error> {
+        if self.block_hash != rhs.prev_hash {
+            return Err(ValidityConditionError::BlocksNotConsecutive);
+        }
+        Ok(rhs)
+    }
+}
+
 impl da::DaVerifier for CelestiaVerifier {
     type Spec = CelestiaSpec;
 
     type Error = ValidationError;
 
+    type ValidityCondition = ChainValidityCondition;
+
     fn new(params: <Self::Spec as DaSpec>::ChainParams) -> Self {
         Self {
             rollup_namespace: params.namespace,
         }
     }
 
-    fn verify_relevant_tx_list(
+    fn verify_relevant_tx_list<H: SimpleHasher>(
         &self,
         block_header: &<Self::Spec as DaSpec>::BlockHeader,
         txs: &[<Self::Spec as DaSpec>::BlobTransaction],
         inclusion_proof: <Self::Spec as DaSpec>::InclusionMultiProof,
         completeness_proof: <Self::Spec as DaSpec>::CompletenessProof,
-    ) -> Result<(), Self::Error> {
+    ) -> Result<Self::ValidityCondition, Self::Error> {
         // Validate that the provided DAH is well-formed
         block_header.validate_dah()?;
+        let validity_condition = ChainValidityCondition {
+            prev_hash: *block_header.prev_hash().inner(),
+            block_hash: *block_header.hash().inner(),
+        };
 
         // Check the validity and completeness of the rollup row proofs, against the DAH.
         // Extract the data from the row proofs and build a namespace_group from it
         let rollup_shares_u8 = self.verify_row_proofs(completeness_proof, &block_header.dah)?;
         if rollup_shares_u8.is_empty() {
             if txs.is_empty() {
-                return Ok(());
+                return Ok(validity_condition);
             }
             return Err(ValidationError::MissingTx);
         }
@@ -218,7 +250,7 @@ impl da::DaVerifier for CelestiaVerifier {
             }
         }
 
-        Ok(())
+        Ok(validity_condition)
     }
 }
 
diff --git a/adapters/risc0/src/guest.rs b/adapters/risc0/src/guest.rs
index 5f717f457..24a67e1b5 100644
--- a/adapters/risc0/src/guest.rs
+++ b/adapters/risc0/src/guest.rs
@@ -11,6 +11,10 @@ impl ZkvmGuest for Risc0Guest {
     fn read_from_host<T: serde::de::DeserializeOwned>(&self) -> T {
         env::read()
     }
+
+    fn commit<T: serde::Serialize>(&self, item: &T) {
+        env::commit(item);
+    }
 }
 
 #[cfg(not(target_os = "zkvm"))]
@@ -18,6 +22,10 @@ impl ZkvmGuest for Risc0Guest {
     fn read_from_host<T: serde::de::DeserializeOwned>(&self) -> T {
         unimplemented!("This method should only be called in zkvm mode")
     }
+
+    fn commit<T: serde::Serialize>(&self, _item: &T) {
+        unimplemented!("This method should only be called in zkvm mode")
+    }
 }
 
 impl Zkvm for Risc0Guest {
diff --git a/examples/demo-prover/methods/guest/src/bin/rollup.rs b/examples/demo-prover/methods/guest/src/bin/rollup.rs
index b927d0e4c..0a2b9d63f 100644
--- a/examples/demo-prover/methods/guest/src/bin/rollup.rs
+++ b/examples/demo-prover/methods/guest/src/bin/rollup.rs
@@ -11,10 +11,11 @@ use jupiter::{BlobWithSender, CelestiaHeader};
 use log::info;
 use risc0_adapter::guest::Risc0Guest;
 use risc0_zkvm::guest::env;
+use sov_rollup_interface::crypto::NoOpHasher;
 use sov_rollup_interface::da::{DaSpec, DaVerifier};
 use sov_rollup_interface::services::stf_runner::StateTransitionRunner;
 use sov_rollup_interface::stf::{StateTransitionFunction, ZkConfig};
-use sov_rollup_interface::zk::traits::ZkvmGuest;
+use sov_rollup_interface::zk::traits::{StateTransition, ValidityCondition, ZkvmGuest};
 
 // The rollup stores its data in the namespace b"sov-test" on Celestia
 const ROLLUP_NAMESPACE: NamespaceId = NamespaceId(ROLLUP_NAMESPACE_RAW);
@@ -46,17 +47,20 @@ pub fn main() {
     let completeness_proof: <CelestiaSpec as DaSpec>::CompletenessProof = guest.read_from_host();
 
     // Step 2: Verify tx list
-    verifier
-        .verify_relevant_tx_list(&header, &txs, inclusion_proof, completeness_proof)
+    let validity_condition = verifier
+        .verify_relevant_tx_list::<NoOpHasher>(&header, &txs, inclusion_proof, completeness_proof)
         .expect("Transaction list must be correct");
     env::write(&"Relevant txs verified\n");
 
-    state_transition(&guest, txs);
+    state_transition(&guest, txs, validity_condition);
 }
 
-fn state_transition(guest: &Risc0Guest, batches: Vec<BlobWithSender>) {
+fn state_transition(
+    guest: &Risc0Guest,
+    batches: Vec<BlobWithSender>,
+    validity_condition: impl ValidityCondition,
+) {
     let prev_state_root_hash: [u8; 32] = guest.read_from_host();
-    env::commit_slice(&prev_state_root_hash[..]);
     env::write(&"Prev root hash read\n");
 
     let mut demo_runner = <ZkAppRunner<Risc0Guest> as StateTransitionRunner<
@@ -77,7 +81,12 @@ fn state_transition(guest: &Risc0Guest, batches: Vec<BlobWithSender>) {
     }
     let (state_root, _) = demo.end_slot();
     env::write(&"Slot has ended\n");
-    env::commit(&state_root);
+    let output = StateTransition {
+        initial_state_root: prev_state_root_hash,
+        final_state_root: state_root.0,
+        validity_condition,
+    };
+    env::commit(&output);
     env::write(&"new state root committed\n");
 }
 
diff --git a/examples/demo-rollup/src/main.rs b/examples/demo-rollup/src/main.rs
index cf64ae790..d87823d32 100644
--- a/examples/demo-rollup/src/main.rs
+++ b/examples/demo-rollup/src/main.rs
@@ -16,14 +16,17 @@ use demo_stf::runtime::GenesisConfig;
 use jsonrpsee::core::server::rpc_module::Methods;
 use jupiter::da_service::CelestiaService;
 use jupiter::types::NamespaceId;
-use jupiter::verifier::CelestiaVerifier;
 use jupiter::verifier::RollupParams;
+use jupiter::verifier::{CelestiaVerifier, ChainValidityCondition};
 use risc0_adapter::host::Risc0Verifier;
 use sov_db::ledger_db::{LedgerDB, SlotCommit};
+use sov_rollup_interface::crypto::NoOpHasher;
 use sov_rollup_interface::da::DaVerifier;
 use sov_rollup_interface::services::da::{DaService, SlotData};
 use sov_rollup_interface::services::stf_runner::StateTransitionRunner;
 use sov_rollup_interface::stf::StateTransitionFunction;
+use sov_rollup_interface::traits::CanonicalHash;
+use sov_rollup_interface::zk::traits::ValidityConditionChecker;
 use sov_state::Storage;
 use std::env;
 use std::net::SocketAddr;
@@ -74,6 +77,22 @@ pub fn get_genesis_config() -> GenesisConfig<DefaultContext> {
     )
 }
 
+pub struct CelestiaChainChecker {
+    current_block_hash: [u8; 32],
+}
+
+impl ValidityConditionChecker<ChainValidityCondition> for CelestiaChainChecker {
+    type Error = anyhow::Error;
+
+    fn check(&mut self, condition: &ChainValidityCondition) -> Result<(), anyhow::Error> {
+        anyhow::ensure!(
+            condition.block_hash == self.current_block_hash,
+            "Invalid block hash"
+        );
+        Ok(())
+    }
+}
+
 #[tokio::main]
 async fn main() -> Result<(), anyhow::Error> {
     let rollup_config_path = env::args()
@@ -188,9 +207,22 @@ async fn main() -> Result<(), anyhow::Error> {
         let (inclusion_proof, completeness_proof) =
             da_service.get_extraction_proof(&filtered_block, &blob_txs);
 
-        assert!(da_verifier
-            .verify_relevant_tx_list(header, &blob_txs, inclusion_proof, completeness_proof)
-            .is_ok());
+        let validity_condition = da_verifier
+            .verify_relevant_tx_list::<NoOpHasher>(
+                header,
+                &blob_txs,
+                inclusion_proof,
+                completeness_proof,
+            )
+            .expect("Failed to verify relevant tx list but prover is honest");
+
+        // For demonstration purposes, we also show how you would check the extra validity condition
+        // imposed by celestia (that the Celestia block processed be the next one from the canonical chain).
+        // In a real rollup, this check would only be made by light clients.
+        let mut checker = CelestiaChainChecker {
+            current_block_hash: *header.hash().inner(),
+        };
+        checker.check(&validity_condition)?;
 
         // Store the resulting receipts in the ledger database
         ledger_db.commit_slot(data_to_commit)?;
diff --git a/module-system/sov-modules-api/src/default_context.rs b/module-system/sov-modules-api/src/default_context.rs
index 340b2dd61..88df2e8ec 100644
--- a/module-system/sov-modules-api/src/default_context.rs
+++ b/module-system/sov-modules-api/src/default_context.rs
@@ -1,7 +1,7 @@
 use crate::default_signature::{DefaultPublicKey, DefaultSignature};
 use crate::{Address, AddressTrait, Context, PublicKey, Spec};
+use sov_rollup_interface::crypto::SimpleHasher;
 
-use jmt::SimpleHasher;
 #[cfg(feature = "native")]
 use serde::{Deserialize, Serialize};
 use sov_state::DefaultStorageSpec;
diff --git a/module-system/sov-modules-api/src/lib.rs b/module-system/sov-modules-api/src/lib.rs
index 37fa0ce8a..57edd7204 100644
--- a/module-system/sov-modules-api/src/lib.rs
+++ b/module-system/sov-modules-api/src/lib.rs
@@ -19,10 +19,10 @@ use borsh::{BorshDeserialize, BorshSerialize};
 use core::fmt::{self, Debug, Display};
 pub use dispatch::{DispatchCall, Genesis};
 pub use error::Error;
-pub use jmt::SimpleHasher as Hasher;
 pub use prefix::Prefix;
 pub use response::CallResponse;
 use serde::{Deserialize, Serialize};
+pub use sov_rollup_interface::crypto::SimpleHasher as Hasher;
 pub use sov_rollup_interface::traits::AddressTrait;
 use sov_state::{Storage, Witness, WorkingSet};
 use thiserror::Error;
diff --git a/module-system/sov-state/src/lib.rs b/module-system/sov-state/src/lib.rs
index d836390cc..7dc3b543e 100644
--- a/module-system/sov-state/src/lib.rs
+++ b/module-system/sov-state/src/lib.rs
@@ -78,7 +78,7 @@ pub trait MerkleProofSpec {
     /// The structure that accumulates the witness data
     type Witness: Witness;
     /// The hash function used to compute the merkle root
-    type Hasher: jmt::SimpleHasher;
+    type Hasher: sov_rollup_interface::crypto::SimpleHasher;
 }
 
 use sha2::Sha256;
diff --git a/module-system/sov-state/src/prover_storage.rs b/module-system/sov-state/src/prover_storage.rs
index 826480994..1a8d8f599 100644
--- a/module-system/sov-state/src/prover_storage.rs
+++ b/module-system/sov-state/src/prover_storage.rs
@@ -1,3 +1,4 @@
+use std::marker::PhantomData;
 use std::{fs, path::Path, sync::Arc};
 
 use crate::config::Config;
@@ -8,12 +9,13 @@ use crate::{
     tree_db::TreeReadLogger,
     MerkleProofSpec, Storage,
 };
-use jmt::{storage::TreeWriter, JellyfishMerkleTree, KeyHash, PhantomHasher, SimpleHasher};
+use jmt::{storage::TreeWriter, JellyfishMerkleTree, KeyHash};
 use sov_db::state_db::StateDB;
+use sov_rollup_interface::crypto::SimpleHasher;
 
 pub struct ProverStorage<S: MerkleProofSpec> {
     db: StateDB,
-    _phantom_hasher: PhantomHasher<S::Hasher>,
+    _phantom_hasher: PhantomData<S::Hasher>,
 }
 
 impl<S: MerkleProofSpec> Clone for ProverStorage<S> {
diff --git a/module-system/sov-state/src/zk_storage.rs b/module-system/sov-state/src/zk_storage.rs
index ed92cd511..1e6684252 100644
--- a/module-system/sov-state/src/zk_storage.rs
+++ b/module-system/sov-state/src/zk_storage.rs
@@ -1,7 +1,8 @@
-use std::sync::Arc;
+use std::{marker::PhantomData, sync::Arc};
 
 use crate::witness::{TreeWitnessReader, Witness};
-use jmt::{JellyfishMerkleTree, KeyHash, PhantomHasher, SimpleHasher, Version};
+use jmt::{JellyfishMerkleTree, KeyHash, Version};
+use sov_rollup_interface::crypto::SimpleHasher;
 
 use crate::{
     internal_cache::OrderedReadsAndWrites,
@@ -11,7 +12,7 @@ use crate::{
 
 pub struct ZkStorage<S: MerkleProofSpec> {
     prev_state_root: [u8; 32],
-    _phantom_hasher: PhantomHasher<S::Hasher>,
+    _phantom_hasher: PhantomData<S::Hasher>,
 }
 
 impl<S: MerkleProofSpec> Clone for ZkStorage<S> {
diff --git a/rollup-interface/Cargo.toml b/rollup-interface/Cargo.toml
index 5951b70b3..bd351e464 100644
--- a/rollup-interface/Cargo.toml
+++ b/rollup-interface/Cargo.toml
@@ -22,8 +22,9 @@ borsh = { workspace = true, features = ["rc"] }
 serde = { workspace = true }
 bytes = { workspace = true }
 hex = { workspace = true, features = ["serde"] }
+jmt = { workspace = true }
 
-sha2 = { workspace = true }
+sha2 = { workspace = true, optional = true }
 tendermint = "0.32"
 
 anyhow = { workspace = true }
@@ -38,4 +39,4 @@ serde_json = "1"
 [features]
 default = []
 fuzzing = ["proptest"]
-mocks = []
+mocks = ["sha2"]
diff --git a/rollup-interface/src/state_machine/crypto/mod.rs b/rollup-interface/src/state_machine/crypto/mod.rs
new file mode 100644
index 000000000..b550dba93
--- /dev/null
+++ b/rollup-interface/src/state_machine/crypto/mod.rs
@@ -0,0 +1,2 @@
+mod simple_hasher;
+pub use simple_hasher::{NoOpHasher, SimpleHasher};
diff --git a/rollup-interface/src/state_machine/crypto/simple_hasher.rs b/rollup-interface/src/state_machine/crypto/simple_hasher.rs
new file mode 100644
index 000000000..4ce358146
--- /dev/null
+++ b/rollup-interface/src/state_machine/crypto/simple_hasher.rs
@@ -0,0 +1,15 @@
+pub use jmt::SimpleHasher;
+
+/// A SimpleHasher implementation which always returns the digest [0;32]
+pub struct NoOpHasher;
+impl SimpleHasher for NoOpHasher {
+    fn new() -> Self {
+        Self
+    }
+
+    fn update(&mut self, _data: &[u8]) {}
+
+    fn finalize(self) -> [u8; 32] {
+        [0u8; 32]
+    }
+}
diff --git a/rollup-interface/src/state_machine/da.rs b/rollup-interface/src/state_machine/da.rs
index 80a329a8d..80bb8fefd 100644
--- a/rollup-interface/src/state_machine/da.rs
+++ b/rollup-interface/src/state_machine/da.rs
@@ -1,4 +1,6 @@
+use crate::crypto::SimpleHasher;
 use crate::traits::{AddressTrait, BlockHeaderTrait};
+use crate::zk::traits::ValidityCondition;
 use borsh::{BorshDeserialize, BorshSerialize};
 use bytes::Buf;
 use core::fmt::Debug;
@@ -46,16 +48,20 @@ pub trait DaVerifier {
     /// TODO: Should we add `std::Error` bound so it can be `()?` ?
     type Error: Debug;
 
+    /// Any conditions imposed by the DA layer which need to be checked outside of the SNARK
+    type ValidityCondition: ValidityCondition;
+
+    /// Create a new da verifier with the given chain parameters
     fn new(params: <Self::Spec as DaSpec>::ChainParams) -> Self;
 
     /// Verify a claimed set of transactions against a block header.
-    fn verify_relevant_tx_list(
+    fn verify_relevant_tx_list<H: SimpleHasher>(
         &self,
         block_header: &<Self::Spec as DaSpec>::BlockHeader,
         txs: &[<Self::Spec as DaSpec>::BlobTransaction],
         inclusion_proof: <Self::Spec as DaSpec>::InclusionMultiProof,
         completeness_proof: <Self::Spec as DaSpec>::CompletenessProof,
-    ) -> Result<(), Self::Error>;
+    ) -> Result<Self::ValidityCondition, Self::Error>;
 }
 
 #[derive(Debug, Clone, Serialize, Deserialize, BorshDeserialize, BorshSerialize, PartialEq)]
diff --git a/rollup-interface/src/state_machine/mod.rs b/rollup-interface/src/state_machine/mod.rs
index 8be2f4d54..88b02df5a 100644
--- a/rollup-interface/src/state_machine/mod.rs
+++ b/rollup-interface/src/state_machine/mod.rs
@@ -1,6 +1,6 @@
+pub mod crypto;
 pub mod da;
 pub mod stf;
-
 pub mod zk;
 
 pub use bytes::{Buf, BufMut, Bytes, BytesMut};
diff --git a/rollup-interface/src/state_machine/zk/traits.rs b/rollup-interface/src/state_machine/zk/traits.rs
index 7dcb6ea9d..7bb954a85 100644
--- a/rollup-interface/src/state_machine/zk/traits.rs
+++ b/rollup-interface/src/state_machine/zk/traits.rs
@@ -1,7 +1,9 @@
 use core::fmt::Debug;
 
 use serde::de::DeserializeOwned;
-use serde::Serialize;
+use serde::{Deserialize, Serialize};
+
+use crate::crypto::SimpleHasher;
 
 /// A trait implemented by the prover ("host") of a zkVM program.
 pub trait ZkvmHost: Zkvm {
@@ -31,14 +33,42 @@ pub trait Zkvm {
 pub trait ZkvmGuest: Zkvm {
     /// Obtain "advice" non-deterministically from the host
     fn read_from_host<T: DeserializeOwned>(&self) -> T;
+    /// Add a public output to the zkVM proof
+    fn commit<T: Serialize>(&self, item: &T);
 }
 
-pub trait Matches<T> {
-    fn matches(&self, other: &T) -> bool;
+/// This trait is implemented on the struct/enum which expresses the validity condition
+pub trait ValidityCondition: Serialize + DeserializeOwned {
+    type Error: Into<anyhow::Error>;
+    /// Combine two conditions into one (typically run inside a recursive proof).
+    /// Returns an error if the two conditions cannot be combined
+    fn combine<H: SimpleHasher>(&self, rhs: Self) -> Result<Self, Self::Error>;
+}
+
+/// The public output of a SNARK proof in Sovereign, this struct makes a claim that
+/// the state of the rollup has transitioned from `initial_state_root` to `final_state_root`
+/// if and only if the condition `validity_condition` is satisfied.
+///
+/// The period of time covered by a state transition proof may be a single slot, or a range of slots on the DA layer.
+#[derive(Clone, Debug, Serialize, Deserialize)]
+pub struct StateTransition<C> {
+    /// The state of the rollup before the transition
+    pub initial_state_root: [u8; 32],
+    /// The state of the rollup after the transition
+    pub final_state_root: [u8; 32],
+    /// An additional validity condition for the state transition which needs
+    /// to be checked outside of the zkVM circuit. This typically corresponds to
+    /// some claim about the DA layer history, such as (X) is a valid block on the DA layer
+    pub validity_condition: C,
 }
 
-// TODO!
-mod risc0 {
-    #[allow(unused)]
-    struct MethodId([u8; 32]);
+/// This trait expresses that a type can check a validity condition.
+pub trait ValidityConditionChecker<Condition: ValidityCondition> {
+    type Error: Into<anyhow::Error>;
+    /// Check a validity condition
+    fn check(&mut self, condition: &Condition) -> Result<(), Self::Error>;
+}
+
+pub trait Matches<T> {
+    fn matches(&self, other: &T) -> bool;
 }