diff --git a/crates/vm/src/arch/extensions.rs b/crates/vm/src/arch/extensions.rs
index f73a6fc461..8c9a6291c5 100644
--- a/crates/vm/src/arch/extensions.rs
+++ b/crates/vm/src/arch/extensions.rs
@@ -31,7 +31,7 @@ use openvm_stark_backend::{
         types::{AirProvingContext, ProvingContext},
     },
     rap::AnyRap,
-    AirRef, AnyChip, Chip,
+    AnyChip, Chip,
 };
 use rustc_hash::FxHashMap;
 use tracing::info_span;
@@ -145,7 +145,7 @@ pub struct AirInventory<SC: StarkGenericConfig> {
     /// Note that the system will ensure that the first AIR in the list is always the
     /// [VariableRangeCheckerAir].
     #[get = "pub"]
-    ext_airs: Vec<AirRef<SC>>,
+    ext_airs: Vec<AirRefWithColumnNames<SC>>,
     /// `ext_start[i]` will have the starting index in `ext_airs` for extension `i`
     ext_start: Vec<usize>,
 
@@ -399,6 +399,16 @@ impl<F, E> ExecutorInventoryBuilder<'_, F, E> {
     }
 }
 
+pub trait ColumnNames {}
+
+impl<T> ColumnNames for T {}
+
+pub trait AnyRapWithColumnNames<SC: StarkGenericConfig>: AnyRap<SC> + ColumnNames {}
+
+pub type AirRefWithColumnNames<SC> = Arc<dyn AnyRapWithColumnNames<SC>>;
+
+impl<SC: StarkGenericConfig, R: AnyRap<SC> + ColumnNames> AnyRapWithColumnNames<SC> for R {}
+
 impl<SC: StarkGenericConfig> AirInventory<SC> {
     /// Outside of this crate, [AirInventory] must be constructed via [SystemConfig].
     pub(crate) fn new(
@@ -434,11 +444,11 @@ impl<SC: StarkGenericConfig> AirInventory<SC> {
             .filter_map(|air| air.as_any().downcast_ref())
     }
 
-    pub fn add_air<A: AnyRap<SC> + 'static>(&mut self, air: A) {
+    pub fn add_air<A: AnyRapWithColumnNames<SC> + 'static>(&mut self, air: A) {
         self.add_air_ref(Arc::new(air));
     }
 
-    pub fn add_air_ref(&mut self, air: AirRef<SC>) {
+    pub fn add_air_ref(&mut self, air: AirRefWithColumnNames<SC>) {
         self.ext_airs.push(air);
     }
 
@@ -452,7 +462,7 @@ impl<SC: StarkGenericConfig> AirInventory<SC> {
     /// This is the system AIRs, followed by the other AIRs in the **reverse** of the order they
     /// were added in the VM extension definitions. In particular, the AIRs that have dependencies
     /// appear later. The system guarantees that the last AIR is the [VariableRangeCheckerAir].
-    pub fn into_airs(self) -> impl Iterator<Item = AirRef<SC>> {
+    pub fn into_airs(self) -> impl Iterator<Item = AirRefWithColumnNames<SC>> {
         self.system
             .into_airs()
             .into_iter()
diff --git a/crates/vm/src/arch/vm.rs b/crates/vm/src/arch/vm.rs
index ad253f733a..85e839d075 100644
--- a/crates/vm/src/arch/vm.rs
+++ b/crates/vm/src/arch/vm.rs
@@ -1315,6 +1315,8 @@ pub fn debug_proving_ctx<E, VB>(
     let (airs, pks, proof_inputs): (Vec<_>, Vec<_>, Vec<_>) =
         multiunzip(ctx.per_air.iter().map(|(air_id, air_ctx)| {
             // Transfer from device **back** to host so the debugger can read the data.
+
+            use openvm_stark_backend::rap::AnyRap;
             let cached_mains = air_ctx
                 .cached_mains
                 .iter()
@@ -1331,7 +1333,7 @@ pub fn debug_proving_ctx<E, VB>(
                 public_values,
             };
             (
-                global_airs[*air_id].clone(),
+                global_airs[*air_id].clone() as Arc<dyn AnyRap<_>>,
                 pk.per_air[*air_id].clone(),
                 raw,
             )
diff --git a/crates/vm/src/system/memory/mod.rs b/crates/vm/src/system/memory/mod.rs
index 411e7a5473..cdff03ef85 100644
--- a/crates/vm/src/system/memory/mod.rs
+++ b/crates/vm/src/system/memory/mod.rs
@@ -7,7 +7,6 @@ use openvm_stark_backend::{
     interaction::PermutationCheckBus,
     p3_field::Field,
     p3_util::{log2_ceil_usize, log2_strict_usize},
-    AirRef,
 };
 
 pub mod adapter;
@@ -24,7 +23,7 @@ pub use controller::*;
 pub use online::{Address, AddressMap, INITIAL_TIMESTAMP};
 
 use crate::{
-    arch::{MemoryConfig, ADDR_SPACE_OFFSET},
+    arch::{AirRefWithColumnNames, MemoryConfig, ADDR_SPACE_OFFSET},
     system::memory::{
         adapter::AccessAdapterAir, dimensions::MemoryDimensions, interface::MemoryInterfaceAirs,
         merkle::MemoryMerkleAir, offline_checker::MemoryBridge, persistent::PersistentBoundaryAir,
@@ -75,7 +74,7 @@ impl<S, T> MemoryAddress<S, T> {
 pub struct MemoryAirInventory<SC: StarkGenericConfig> {
     pub bridge: MemoryBridge,
     pub interface: MemoryInterfaceAirs,
-    pub access_adapters: Vec<AirRef<SC>>,
+    pub access_adapters: Vec<AirRefWithColumnNames<SC>>,
 }
 
 impl<SC: StarkGenericConfig> MemoryAirInventory<SC> {
@@ -122,12 +121,12 @@ impl<SC: StarkGenericConfig> MemoryAirInventory<SC> {
         let lt_air = IsLtSubAir::new(range_bus, mem_config.timestamp_max_bits);
         let maan = mem_config.max_access_adapter_n;
         assert!(matches!(maan, 2 | 4 | 8 | 16 | 32));
-        let access_adapters: Vec<AirRef<SC>> = [
-            Arc::new(AccessAdapterAir::<2> { memory_bus, lt_air }) as AirRef<SC>,
-            Arc::new(AccessAdapterAir::<4> { memory_bus, lt_air }) as AirRef<SC>,
-            Arc::new(AccessAdapterAir::<8> { memory_bus, lt_air }) as AirRef<SC>,
-            Arc::new(AccessAdapterAir::<16> { memory_bus, lt_air }) as AirRef<SC>,
-            Arc::new(AccessAdapterAir::<32> { memory_bus, lt_air }) as AirRef<SC>,
+        let access_adapters: Vec<AirRefWithColumnNames<SC>> = [
+            Arc::new(AccessAdapterAir::<2> { memory_bus, lt_air }) as AirRefWithColumnNames<SC>,
+            Arc::new(AccessAdapterAir::<4> { memory_bus, lt_air }) as AirRefWithColumnNames<SC>,
+            Arc::new(AccessAdapterAir::<8> { memory_bus, lt_air }) as AirRefWithColumnNames<SC>,
+            Arc::new(AccessAdapterAir::<16> { memory_bus, lt_air }) as AirRefWithColumnNames<SC>,
+            Arc::new(AccessAdapterAir::<32> { memory_bus, lt_air }) as AirRefWithColumnNames<SC>,
         ]
         .into_iter()
         .take(log2_strict_usize(maan))
@@ -141,8 +140,8 @@ impl<SC: StarkGenericConfig> MemoryAirInventory<SC> {
     }
 
     /// The order of memory AIRs is boundary, merkle (if exists), access adapters
-    pub fn into_airs(self) -> Vec<AirRef<SC>> {
-        let mut airs: Vec<AirRef<SC>> = Vec::new();
+    pub fn into_airs(self) -> Vec<AirRefWithColumnNames<SC>> {
+        let mut airs: Vec<AirRefWithColumnNames<SC>> = Vec::new();
         match self.interface {
             MemoryInterfaceAirs::Volatile { boundary } => {
                 airs.push(Arc::new(boundary));
diff --git a/crates/vm/src/system/mod.rs b/crates/vm/src/system/mod.rs
index 8c0d2a3d37..50b2cc1170 100644
--- a/crates/vm/src/system/mod.rs
+++ b/crates/vm/src/system/mod.rs
@@ -19,18 +19,19 @@ use openvm_stark_backend::{
         hal::{MatrixDimensions, ProverBackend},
         types::{AirProvingContext, CommittedTraceData},
     },
-    AirRef, Chip,
+    Chip,
 };
 use rustc_hash::FxHashMap;
 
 use self::{connector::VmConnectorAir, program::ProgramAir, public_values::PublicValuesAir};
 use crate::{
     arch::{
-        vm_poseidon2_config, AirInventory, AirInventoryError, BusIndexManager, ChipInventory,
-        ChipInventoryError, DenseRecordArena, ExecutionBridge, ExecutionBus, ExecutionState,
-        ExecutorInventory, ExecutorInventoryError, MatrixRecordArena, PhantomSubExecutor,
-        RowMajorMatrixArena, SystemConfig, VmAirWrapper, VmBuilder, VmChipComplex, VmChipWrapper,
-        VmCircuitConfig, VmExecutionConfig, CONNECTOR_AIR_ID, PROGRAM_AIR_ID, PUBLIC_VALUES_AIR_ID,
+        vm_poseidon2_config, AirInventory, AirInventoryError, AirRefWithColumnNames,
+        BusIndexManager, ChipInventory, ChipInventoryError, DenseRecordArena, ExecutionBridge,
+        ExecutionBus, ExecutionState, ExecutorInventory, ExecutorInventoryError, MatrixRecordArena,
+        PhantomSubExecutor, RowMajorMatrixArena, SystemConfig, VmAirWrapper, VmBuilder,
+        VmChipComplex, VmChipWrapper, VmCircuitConfig, VmExecutionConfig, CONNECTOR_AIR_ID,
+        PROGRAM_AIR_ID, PUBLIC_VALUES_AIR_ID,
     },
     system::{
         connector::VmConnectorChip,
@@ -224,8 +225,8 @@ impl<SC: StarkGenericConfig> SystemAirInventory<SC> {
         }
     }
 
-    pub fn into_airs(self) -> Vec<AirRef<SC>> {
-        let mut airs: Vec<AirRef<SC>> = Vec::new();
+    pub fn into_airs(self) -> Vec<AirRefWithColumnNames<SC>> {
+        let mut airs: Vec<AirRefWithColumnNames<SC>> = Vec::new();
         airs.push(Arc::new(self.program));
         airs.push(Arc::new(self.connector));
         if let Some(public_values) = self.public_values {
diff --git a/crates/vm/src/system/poseidon2/mod.rs b/crates/vm/src/system/poseidon2/mod.rs
index 608e5e5d02..ea1e0c5564 100644
--- a/crates/vm/src/system/poseidon2/mod.rs
+++ b/crates/vm/src/system/poseidon2/mod.rs
@@ -16,7 +16,7 @@ use openvm_stark_backend::{
     config::{StarkGenericConfig, Val},
     interaction::{BusIndex, LookupBus},
     p3_field::{Field, PrimeField32},
-    AirRef, ChipUsageGetter,
+    ChipUsageGetter,
 };
 
 #[cfg(test)]
@@ -27,7 +27,10 @@ mod chip;
 pub use chip::*;
 
 use crate::{
-    arch::hasher::{Hasher, HasherChip},
+    arch::{
+        hasher::{Hasher, HasherChip},
+        AirRefWithColumnNames,
+    },
     system::poseidon2::air::Poseidon2PeripheryAir,
 };
 pub mod columns;
@@ -60,7 +63,7 @@ pub fn new_poseidon2_periphery_air<SC: StarkGenericConfig>(
     poseidon2_config: Poseidon2Config<Val<SC>>,
     direct_bus: LookupBus,
     max_constraint_degree: usize,
-) -> AirRef<SC> {
+) -> AirRefWithColumnNames<SC> {
     if max_constraint_degree >= 7 {
         Arc::new(Poseidon2PeripheryAir::<Val<SC>, 0>::new(
             Arc::new(Poseidon2SubAir::new(poseidon2_config.constants.into())),