diff --git a/src/lib.rs b/src/lib.rs
index 595276b..7a16ed0 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -33,6 +33,98 @@ static POSEIDON2_24: OnceLock<Poseidon2KoalaBear<24>> = OnceLock::new();
 /// A lazily-initialized, thread-safe cache for the Poseidon2 permutation with a width of 16.
 static POSEIDON2_16: OnceLock<Poseidon2KoalaBear<16>> = OnceLock::new();
 
+/// Errors returned when initializing a custom Poseidon2 permutation.
+///
+/// This crate caches Poseidon2 permutations (width 24 and 16) using `OnceLock`.
+/// Initialization is therefore a one-time operation: attempting to initialize after the
+/// permutation has already been set (or lazily created by first use) returns
+/// `Poseidon2InitError::AlreadyInitialized`.
+#[derive(Debug, thiserror::Error)]
+pub enum Poseidon2InitError {
+    #[error("Poseidon2 permutation for width {width} was already initialized")]
+    AlreadyInitialized { width: usize },
+}
+
+/// Initialize the width-24 Poseidon2 permutation used by this crate.
+///
+/// This must be called before the first use of the permutation (i.e. before any code paths that
+/// compute message/tweak hashes). If not called, the default Plonky3 permutation is used.
+///
+/// # Example
+/// ```no_run
+/// use leansig::init_poseidon2_24;
+/// use p3_koala_bear::Poseidon2KoalaBear;
+///
+/// // Build your custom Poseidon2(24) permutation here.
+/// // For example, from a spec-aligned constant set.
+/// let perm: Poseidon2KoalaBear<24> = unimplemented!();
+/// init_poseidon2_24(perm).unwrap();
+/// ```
+///
+/// For a builder-style API, see [`init_poseidon2_24_with`].
+pub fn init_poseidon2_24(perm: Poseidon2KoalaBear<24>) -> Result<(), Poseidon2InitError> {
+    POSEIDON2_24
+        .set(perm)
+        .map_err(|_| Poseidon2InitError::AlreadyInitialized { width: 24 })
+}
+
+/// Initialize the width-24 Poseidon2 permutation using a builder.
+///
+/// The builder is only called if the permutation has not been initialized yet.
+/// This function is intended for single-threaded initialization at program startup.
+///
+/// # Errors
+/// Returns `Poseidon2InitError::AlreadyInitialized { width: 24 }` if the permutation was already
+/// initialized (including via lazy initialization from first use).
+pub fn init_poseidon2_24_with<B>(builder: B) -> Result<(), Poseidon2InitError>
+where
+    B: FnOnce() -> Poseidon2KoalaBear<24>,
+{
+    if POSEIDON2_24.get().is_some() {
+        return Err(Poseidon2InitError::AlreadyInitialized { width: 24 });
+    }
+    init_poseidon2_24(builder())
+}
+
+/// Initialize the width-16 Poseidon2 permutation used by this crate.
+///
+/// This must be called before the first use of the permutation. If not called, the default
+/// Plonky3 permutation is used.
+///
+/// # Example
+/// ```no_run
+/// use leansig::init_poseidon2_16;
+/// use p3_koala_bear::Poseidon2KoalaBear;
+///
+/// let perm: Poseidon2KoalaBear<16> = unimplemented!();
+/// init_poseidon2_16(perm).unwrap();
+/// ```
+///
+/// For a builder-style API, see [`init_poseidon2_16_with`].
+pub fn init_poseidon2_16(perm: Poseidon2KoalaBear<16>) -> Result<(), Poseidon2InitError> {
+    POSEIDON2_16
+        .set(perm)
+        .map_err(|_| Poseidon2InitError::AlreadyInitialized { width: 16 })
+}
+
+/// Initialize the width-16 Poseidon2 permutation using a builder.
+///
+/// The builder is only called if the permutation has not been initialized yet.
+/// This function is intended for single-threaded initialization at program startup.
+///
+/// # Errors
+/// Returns `Poseidon2InitError::AlreadyInitialized { width: 16 }` if the permutation was already
+/// initialized (including via lazy initialization from first use).
+pub fn init_poseidon2_16_with<B>(builder: B) -> Result<(), Poseidon2InitError>
+where
+    B: FnOnce() -> Poseidon2KoalaBear<16>,
+{
+    if POSEIDON2_16.get().is_some() {
+        return Err(Poseidon2InitError::AlreadyInitialized { width: 16 });
+    }
+    init_poseidon2_16(builder())
+}
+
 /// Poseidon2 permutation (width 24)
 pub(crate) fn poseidon2_24() -> Poseidon2KoalaBear<24> {
     POSEIDON2_24
@@ -46,3 +138,63 @@ pub(crate) fn poseidon2_16() -> Poseidon2KoalaBear<16> {
         .get_or_init(default_koalabear_poseidon2_16)
         .clone()
 }
+
+#[cfg(test)]
+mod poseidon2_init_tests {
+    use std::sync::atomic::{AtomicUsize, Ordering};
+
+    use p3_koala_bear::{default_koalabear_poseidon2_16, default_koalabear_poseidon2_24};
+
+    use crate::{
+        Poseidon2InitError, init_poseidon2_16, init_poseidon2_16_with, init_poseidon2_24,
+        init_poseidon2_24_with, poseidon2_16, poseidon2_24,
+    };
+
+    #[test]
+    fn init_poseidon2_24_returns_already_initialized_and_does_not_call_builder() {
+        // Ensure the OnceLock is initialized (possibly by other tests too).
+        let _ = poseidon2_24();
+
+        let calls = AtomicUsize::new(0);
+        let res = init_poseidon2_24_with(|| {
+            calls.fetch_add(1, Ordering::SeqCst);
+            default_koalabear_poseidon2_24()
+        });
+
+        assert!(matches!(
+            res,
+            Err(Poseidon2InitError::AlreadyInitialized { width: 24 })
+        ));
+        assert_eq!(calls.load(Ordering::SeqCst), 0);
+
+        let res = init_poseidon2_24(default_koalabear_poseidon2_24());
+        assert!(matches!(
+            res,
+            Err(Poseidon2InitError::AlreadyInitialized { width: 24 })
+        ));
+    }
+
+    #[test]
+    fn init_poseidon2_16_returns_already_initialized_and_does_not_call_builder() {
+        // Ensure the OnceLock is initialized (possibly by other tests too).
+        let _ = poseidon2_16();
+
+        let calls = AtomicUsize::new(0);
+        let res = init_poseidon2_16_with(|| {
+            calls.fetch_add(1, Ordering::SeqCst);
+            default_koalabear_poseidon2_16()
+        });
+
+        assert!(matches!(
+            res,
+            Err(Poseidon2InitError::AlreadyInitialized { width: 16 })
+        ));
+        assert_eq!(calls.load(Ordering::SeqCst), 0);
+
+        let res = init_poseidon2_16(default_koalabear_poseidon2_16());
+        assert!(matches!(
+            res,
+            Err(Poseidon2InitError::AlreadyInitialized { width: 16 })
+        ));
+    }
+}