diff --git a/Cargo.lock b/Cargo.lock
index 9316238..ed31b82 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -134,8 +134,8 @@ dependencies = [
 
 [[package]]
 name = "p3-air"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "p3-field",
  "p3-matrix",
@@ -143,11 +143,12 @@ dependencies = [
 
 [[package]]
 name = "p3-challenger"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "p3-field",
  "p3-maybe-rayon",
+ "p3-monty-31",
  "p3-symmetric",
  "p3-util",
  "tracing",
@@ -155,8 +156,8 @@ dependencies = [
 
 [[package]]
 name = "p3-commit"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "itertools",
  "p3-challenger",
@@ -169,8 +170,8 @@ dependencies = [
 
 [[package]]
 name = "p3-dft"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "itertools",
  "p3-field",
@@ -183,8 +184,8 @@ dependencies = [
 
 [[package]]
 name = "p3-field"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "itertools",
  "num-bigint",
@@ -198,8 +199,8 @@ dependencies = [
 
 [[package]]
 name = "p3-fri"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "itertools",
  "p3-challenger",
@@ -212,15 +213,17 @@ dependencies = [
  "p3-util",
  "rand",
  "serde",
+ "thiserror",
  "tracing",
 ]
 
 [[package]]
 name = "p3-goldilocks"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "num-bigint",
+ "p3-challenger",
  "p3-dft",
  "p3-field",
  "p3-mds",
@@ -234,8 +237,8 @@ dependencies = [
 
 [[package]]
 name = "p3-interpolation"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "p3-field",
  "p3-matrix",
@@ -245,8 +248,8 @@ dependencies = [
 
 [[package]]
 name = "p3-keccak"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "p3-field",
  "p3-symmetric",
@@ -256,8 +259,8 @@ dependencies = [
 
 [[package]]
 name = "p3-matrix"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "itertools",
  "p3-field",
@@ -271,16 +274,16 @@ dependencies = [
 
 [[package]]
 name = "p3-maybe-rayon"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "rayon",
 ]
 
 [[package]]
 name = "p3-mds"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "p3-dft",
  "p3-field",
@@ -291,8 +294,8 @@ dependencies = [
 
 [[package]]
 name = "p3-merkle-tree"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "itertools",
  "p3-commit",
@@ -303,13 +306,37 @@ dependencies = [
  "p3-util",
  "rand",
  "serde",
+ "thiserror",
+ "tracing",
+]
+
+[[package]]
+name = "p3-monty-31"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
+dependencies = [
+ "itertools",
+ "num-bigint",
+ "p3-dft",
+ "p3-field",
+ "p3-matrix",
+ "p3-maybe-rayon",
+ "p3-mds",
+ "p3-poseidon2",
+ "p3-symmetric",
+ "p3-util",
+ "paste",
+ "rand",
+ "serde",
+ "spin",
  "tracing",
+ "transpose",
 ]
 
 [[package]]
 name = "p3-poseidon2"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "p3-field",
  "p3-mds",
@@ -320,8 +347,8 @@ dependencies = [
 
 [[package]]
 name = "p3-symmetric"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "itertools",
  "p3-field",
@@ -330,8 +357,8 @@ dependencies = [
 
 [[package]]
 name = "p3-util"
-version = "0.3.0"
-source = "git+https://github.com/Plonky3/Plonky3?rev=658115aae28312e97cd3ef38d1ab046839f734a8#658115aae28312e97cd3ef38d1ab046839f734a8"
+version = "0.4.2"
+source = "git+https://github.com/Plonky3/Plonky3?rev=0835481398d2b481bef0c6d0e8188b484ab9a636#0835481398d2b481bef0c6d0e8188b484ab9a636"
 dependencies = [
  "serde",
 ]
@@ -350,18 +377,18 @@ checksum = "3b3cff922bd51709b605d9ead9aa71031d81447142d828eb4a6eba76fe619f9b"
 
 [[package]]
 name = "proc-macro2"
-version = "1.0.103"
+version = "1.0.104"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "5ee95bc4ef87b8d5ba32e8b7714ccc834865276eab0aed5c9958d00ec45f49e8"
+checksum = "9695f8df41bb4f3d222c95a67532365f569318332d03d5f3f67f37b20e6ebdf0"
 dependencies = [
  "unicode-ident",
 ]
 
 [[package]]
 name = "quote"
-version = "1.0.41"
+version = "1.0.42"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ce25767e7b499d1b604768e7cde645d14cc8584231ea6b295e9c9eb22c02e1d1"
+checksum = "a338cc41d27e6cc6dce6cefc13a0729dfbb81c262b1f519331575dd80ef3067f"
 dependencies = [
  "proc-macro2",
 ]
@@ -454,15 +481,35 @@ checksum = "fe895eb47f22e2ddd4dabc02bce419d2e643c8e3b585c78158b349195bc24d82"
 
 [[package]]
 name = "syn"
-version = "2.0.108"
+version = "2.0.113"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "da58917d35242480a05c2897064da0a80589a2a0476c9a3f2fdc83b53502e917"
+checksum = "678faa00651c9eb72dd2020cbdf275d92eccb2400d568e419efdd64838145cb4"
 dependencies = [
  "proc-macro2",
  "quote",
  "unicode-ident",
 ]
 
+[[package]]
+name = "thiserror"
+version = "2.0.17"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f63587ca0f12b72a0600bcba1d40081f830876000bb46dd2337a3051618f4fc8"
+dependencies = [
+ "thiserror-impl",
+]
+
+[[package]]
+name = "thiserror-impl"
+version = "2.0.17"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "3ff15c8ecd7de3849db632e14d18d2571fa09dfc5ed93479bc4485c7a517c913"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
 [[package]]
 name = "tiny-keccak"
 version = "2.0.2"
@@ -474,9 +521,9 @@ dependencies = [
 
 [[package]]
 name = "tracing"
-version = "0.1.41"
+version = "0.1.44"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "784e0ac535deb450455cbfa28a6f0df145ea1bb7ae51b821cf5e7927fdcfbdd0"
+checksum = "63e71662fa4b2a2c3a26f570f037eb95bb1f85397f3cd8076caed2f026a6d100"
 dependencies = [
  "pin-project-lite",
  "tracing-attributes",
@@ -485,9 +532,9 @@ dependencies = [
 
 [[package]]
 name = "tracing-attributes"
-version = "0.1.30"
+version = "0.1.31"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "81383ab64e72a7a8b8e13130c49e3dab29def6d0c7d76a03087b3cf71c5c6903"
+checksum = "7490cfa5ec963746568740651ac6781f701c9c5ea257c58e057f3ba8cf69e8da"
 dependencies = [
  "proc-macro2",
  "quote",
@@ -496,9 +543,9 @@ dependencies = [
 
 [[package]]
 name = "tracing-core"
-version = "0.1.34"
+version = "0.1.36"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b9d12581f227e93f094d3af2ae690a574abb8a2b9b7a96e7cfe9647b2b617678"
+checksum = "db97caf9d906fbde555dd62fa95ddba9eecfd14cb388e4f491a66d74cd5fb79a"
 
 [[package]]
 name = "transpose"
@@ -512,9 +559,9 @@ dependencies = [
 
 [[package]]
 name = "unicode-ident"
-version = "1.0.20"
+version = "1.0.22"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "462eeb75aeb73aea900253ce739c8e18a67423fadf006037cd3ff27e82748a06"
+checksum = "9312f7c4f6ff9069b165498234ce8be658059c6728633667c526e27dc2cf1df5"
 
 [[package]]
 name = "unty"
diff --git a/Cargo.toml b/Cargo.toml
index 6938de5..793fc08 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -11,19 +11,19 @@ rust-version = "1.88"
 [dependencies]
 serde = { version = "1", features = ["derive"] }
 bincode = { version = "2", features = ["serde"] }
-p3-air = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
-p3-goldilocks = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
-p3-challenger = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
-p3-commit = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
-p3-dft = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
-p3-field = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
-p3-fri = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
-p3-keccak = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
-p3-matrix = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
-p3-maybe-rayon = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
-p3-merkle-tree = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
-p3-symmetric = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
-p3-util = { git = "https://github.com/Plonky3/Plonky3", rev = "658115aae28312e97cd3ef38d1ab046839f734a8" }
+p3-air = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
+p3-goldilocks = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
+p3-challenger = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
+p3-commit = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
+p3-dft = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
+p3-field = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
+p3-fri = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
+p3-keccak = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
+p3-matrix = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
+p3-maybe-rayon = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
+p3-merkle-tree = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
+p3-symmetric = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
+p3-util = { git = "https://github.com/Plonky3/Plonky3", rev = "0835481398d2b481bef0c6d0e8188b484ab9a636" }
 
 [features]
 parallel = ["p3-maybe-rayon/parallel"]
diff --git a/src/chips/blake3_circuit.rs b/src/chips/blake3_circuit.rs
index cfb4b24..fbc0d46 100644
--- a/src/chips/blake3_circuit.rs
+++ b/src/chips/blake3_circuit.rs
@@ -1990,7 +1990,8 @@ mod tests {
         let fri_parameters = FriParameters {
             log_final_poly_len: 0,
             num_queries: 64,
-            proof_of_work_bits: 0,
+            commit_proof_of_work_bits: 0,
+            query_proof_of_work_bits: 0,
         };
 
         let proof =
@@ -2160,7 +2161,8 @@ mod tests {
             let fri_parameters = FriParameters {
                 log_final_poly_len: 0,
                 num_queries: 64,
-                proof_of_work_bits: 0,
+                commit_proof_of_work_bits: 0,
+                query_proof_of_work_bits: 0,
             };
 
             let proof =
diff --git a/src/chips/byte_operations.rs b/src/chips/byte_operations.rs
index 64eeeb0..cd0daeb 100644
--- a/src/chips/byte_operations.rs
+++ b/src/chips/byte_operations.rs
@@ -145,7 +145,8 @@ mod tests {
         let fri_parameters = FriParameters {
             log_final_poly_len: 0,
             num_queries: 64,
-            proof_of_work_bits: 0,
+            commit_proof_of_work_bits: 0,
+            query_proof_of_work_bits: 0,
         };
         let proof = system.prove_multiple_claims(fri_parameters, &key, claims, witness);
         system
diff --git a/src/chips/u32_add.rs b/src/chips/u32_add.rs
index ecd24d8..a72dfc0 100644
--- a/src/chips/u32_add.rs
+++ b/src/chips/u32_add.rs
@@ -198,7 +198,8 @@ mod tests {
         let fri_parameters = FriParameters {
             log_final_poly_len: 0,
             num_queries: 64,
-            proof_of_work_bits: 0,
+            commit_proof_of_work_bits: 0,
+            query_proof_of_work_bits: 0,
         };
         let proof = system.prove_multiple_claims(fri_parameters, &key, claims, witness);
         system
diff --git a/src/lookup.rs b/src/lookup.rs
index cd73ffa..fecd998 100644
--- a/src/lookup.rs
+++ b/src/lookup.rs
@@ -424,7 +424,8 @@ mod tests {
         let fri_parameters = FriParameters {
             log_final_poly_len: 0,
             num_queries: 64,
-            proof_of_work_bits: 0,
+            commit_proof_of_work_bits: 0,
+            query_proof_of_work_bits: 0,
         };
         let proof = system.prove(fri_parameters, &key, claim, witness);
         system.verify(fri_parameters, claim, &proof).unwrap();
diff --git a/src/types.rs b/src/types.rs
index 274d85d..a15926c 100644
--- a/src/types.rs
+++ b/src/types.rs
@@ -65,7 +65,8 @@ impl Committer {
         let dummy_parameters = FriParameters {
             log_final_poly_len: 0,
             num_queries: 0,
-            proof_of_work_bits: 0,
+            commit_proof_of_work_bits: 0,
+            query_proof_of_work_bits: 0,
         };
         let pcs = new_pcs(commitment_parameters, dummy_parameters);
         Self { pcs }
@@ -92,7 +93,10 @@ pub struct CommitmentParameters {
 pub struct FriParameters {
     pub log_final_poly_len: usize,
     pub num_queries: usize,
-    pub proof_of_work_bits: usize,
+    /// Number of bits for the PoW phase before sampling _each_ batching challenge.
+    pub commit_proof_of_work_bits: usize,
+    /// Number of bits for the PoW phase before sampling the queries.
+    pub query_proof_of_work_bits: usize,
 }
 
 type KeccakCompressionFunction =
@@ -113,7 +117,8 @@ fn new_pcs(commitment_parameters: CommitmentParameters, fri_parameters: FriParam
         log_blowup: commitment_parameters.log_blowup,
         log_final_poly_len: fri_parameters.log_final_poly_len,
         num_queries: fri_parameters.num_queries,
-        proof_of_work_bits: fri_parameters.proof_of_work_bits,
+        commit_proof_of_work_bits: fri_parameters.commit_proof_of_work_bits,
+        query_proof_of_work_bits: fri_parameters.query_proof_of_work_bits,
         mmcs,
     };
     let dft = Dft::default();
diff --git a/src/verifier.rs b/src/verifier.rs
index d1e25aa..ef63a21 100644
--- a/src/verifier.rs
+++ b/src/verifier.rs
@@ -491,7 +491,8 @@ mod tests {
         let fri_parameters = FriParameters {
             log_final_poly_len: 0,
             num_queries: 64,
-            proof_of_work_bits: 0,
+            commit_proof_of_work_bits: 0,
+            query_proof_of_work_bits: 0,
         };
         let no_claims = &[];
         let proof = system.prove_multiple_claims(fri_parameters, &key, no_claims, witness);
@@ -525,7 +526,8 @@ mod tests {
         let fri_parameters = FriParameters {
             log_final_poly_len: 0,
             num_queries: 100,
-            proof_of_work_bits: 20,
+            commit_proof_of_work_bits: 10,
+            query_proof_of_work_bits: 10,
         };
         let no_claims = &[];
         let proof = benchmark!(