diff --git a/air/src/options.rs b/air/src/options.rs
index 4466737fd..e0cd7062c 100644
--- a/air/src/options.rs
+++ b/air/src/options.rs
@@ -289,8 +289,9 @@ impl ProofOptions {
 }
 
 impl<E: StarkField> ToElements<E> for ProofOptions {
+    /// Encodes these proof options into 3 field elements.
     fn to_elements(&self) -> Vec<E> {
-        // encode field extension and FRI parameters into a single field element
+        // encode field extension, FRI parameters, and blowup factor into a single field element
         let mut buf = self.field_extension as u32;
         buf = (buf << 8) | self.fri_folding_factor as u32;
         buf = (buf << 8) | self.fri_remainder_max_degree as u32;
@@ -592,7 +593,7 @@ mod tests {
             fri_folding_factor as usize,
             fri_remainder_max_degree as usize,
             BatchingMethod::Linear,
-            BatchingMethod::Linear,
+            BatchingMethod::Algebraic,
         );
 
         let options_serialized = options.to_bytes();
diff --git a/air/src/proof/context.rs b/air/src/proof/context.rs
index f9c55f2c5..0b8bc6de6 100644
--- a/air/src/proof/context.rs
+++ b/air/src/proof/context.rs
@@ -106,12 +106,16 @@ impl<E: StarkField> ToElements<E> for Context {
     /// Converts this [Context] into a vector of field elements.
     ///
     /// The elements are laid out as follows:
-    /// - trace info [2 or more elements].
+    /// - trace info:
+    ///   - trace segment widths and the number of aux random values [1 element].
+    ///   - trace length [1 element].
+    ///   - trace metadata [0 or more elements].
     /// - field modulus bytes [2 field elements].
-    /// - field extension and FRI parameters [1 element].
-    /// - grinding factor [1 element].
-    /// - blowup factor [1 element].
-    /// - number of queries [1 element].
+    /// - number of constraints (1 element).
+    /// - proof options:
+    ///   - field extension, FRI parameters, and grinding factor [1 element].
+    ///   - blowup factor [1 element].
+    ///   - number of queries [1 element].
     fn to_elements(&self) -> Vec<E> {
         // convert trace layout
         let mut result = self.trace_info.to_elements();
diff --git a/air/src/proof/mod.rs b/air/src/proof/mod.rs
index 593c7e675..967fe4fde 100644
--- a/air/src/proof/mod.rs
+++ b/air/src/proof/mod.rs
@@ -115,14 +115,14 @@ impl Proof {
         // polynomials.
         let num_trace_polys = self.context.trace_info().width();
         let num_constraint_composition_polys = self.options().blowup_factor();
-        let num_polys = num_trace_polys + num_constraint_composition_polys;
+        let num_committed_polys = num_trace_polys + num_constraint_composition_polys;
         ProvenSecurity::compute(
             self.context.options(),
             self.context.num_modulus_bits(),
             self.trace_info().length(),
             H::COLLISION_RESISTANCE,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         )
     }
 
diff --git a/air/src/proof/security.rs b/air/src/proof/security.rs
index d280d88dc..c2c62176f 100644
--- a/air/src/proof/security.rs
+++ b/air/src/proof/security.rs
@@ -80,7 +80,7 @@ impl ProvenSecurity {
         trace_domain_size: usize,
         collision_resistance: u32,
         num_constraints: usize,
-        num_polys: usize,
+        num_committed_polys: usize,
     ) -> Self {
         let unique_decoding = cmp::min(
             proven_security_protocol_unique_decoding(
@@ -88,7 +88,7 @@ impl ProvenSecurity {
                 base_field_bits,
                 trace_domain_size,
                 num_constraints,
-                num_polys,
+                num_committed_polys,
             ),
             collision_resistance as u64,
         ) as u32;
@@ -106,7 +106,7 @@ impl ProvenSecurity {
                 trace_domain_size,
                 a as usize,
                 num_constraints,
-                num_polys,
+                num_committed_polys,
             )
         })
         .expect(
@@ -120,7 +120,7 @@ impl ProvenSecurity {
                 trace_domain_size,
                 m_optimal as usize,
                 num_constraints,
-                num_polys,
+                num_committed_polys,
             ),
             collision_resistance as u64,
         ) as u32;
@@ -153,7 +153,7 @@ fn proven_security_protocol_for_given_proximity_parameter(
     trace_domain_size: usize,
     m: usize,
     num_constraints: usize,
-    num_polys: usize,
+    num_committed_polys: usize,
 ) -> u64 {
     let extension_field_bits = (base_field_bits * options.field_extension().degree()) as f64;
     let num_fri_queries = options.num_queries() as f64;
@@ -199,7 +199,7 @@ fn proven_security_protocol_for_given_proximity_parameter(
     // comparison. N is the number of batched polynomials.
     let batching_factor = match options.deep_poly_batching_method() {
         BatchingMethod::Linear => 1.0,
-        BatchingMethod::Algebraic => num_polys as f64 - 1.0,
+        BatchingMethod::Algebraic => num_committed_polys as f64 - 1.0,
     };
     let epsilon_3_bits_neg = extension_field_bits
         - log2(
@@ -225,7 +225,7 @@ fn proven_security_protocol_unique_decoding(
     base_field_bits: u32,
     trace_domain_size: usize,
     num_constraints: usize,
-    num_polys: usize,
+    num_committed_polys: usize,
 ) -> u64 {
     let extension_field_bits = (base_field_bits * options.field_extension().degree()) as f64;
     let num_fri_queries = options.num_queries() as f64;
@@ -263,7 +263,7 @@ fn proven_security_protocol_unique_decoding(
     // being batched.
     let batching_factor = match options.deep_poly_batching_method() {
         BatchingMethod::Linear => 1.0,
-        BatchingMethod::Algebraic => num_polys as f64 - 1.0,
+        BatchingMethod::Algebraic => num_committed_polys as f64 - 1.0,
     };
     let epsilon_3_bits_neg = extension_field_bits - log2(lde_domain_size * batching_factor);
     epsilons_bits_neg.push(epsilon_3_bits_neg);
@@ -366,7 +366,7 @@ mod tests {
         let num_queries = 119;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(20);
-        let num_polys = 2;
+        let num_committed_polys = 2;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -385,7 +385,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(unique_decoding, 100);
@@ -410,7 +410,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(list_decoding, 69);
@@ -436,7 +436,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(list_decoding, 100);
@@ -453,7 +453,7 @@ mod tests {
         let num_queries = 123;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(8);
-        let num_polys = 2;
+        let num_committed_polys = 2;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -472,7 +472,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(unique_decoding, 116);
@@ -494,7 +494,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(unique_decoding, 115);
@@ -511,7 +511,7 @@ mod tests {
         let num_queries = 195;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(8);
-        let num_polys = 2;
+        let num_committed_polys = 2;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -530,7 +530,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(unique_decoding, 100);
@@ -559,7 +559,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(list_decoding, 100);
@@ -585,7 +585,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(unique_decoding, 100);
@@ -610,7 +610,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(list_decoding, 100);
@@ -627,7 +627,7 @@ mod tests {
         let num_queries = 80;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(18);
-        let num_polys = 2;
+        let num_committed_polys = 2;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -646,7 +646,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(list_decoding, 99);
@@ -671,7 +671,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(list_decoding, 99);
@@ -688,7 +688,7 @@ mod tests {
         let num_queries = 85;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(18);
-        let num_polys = 2;
+        let num_committed_polys = 2;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -707,7 +707,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(list_decoding, 128);
@@ -732,7 +732,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(list_decoding, 128);
@@ -749,7 +749,7 @@ mod tests {
         let num_queries = 85;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(18);
-        let num_polys = 2;
+        let num_committed_polys = 2;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -768,7 +768,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(list_decoding, 70);
@@ -793,7 +793,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(list_decoding, 128);
@@ -810,7 +810,7 @@ mod tests {
         let num_queries = 80;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(20);
-        let num_polys = 2;
+        let num_committed_polys = 2;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -832,7 +832,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         let trace_length = 2_usize.pow(16);
@@ -856,7 +856,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert!(security_1 < security_2);
@@ -873,7 +873,7 @@ mod tests {
         let num_queries = 60;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(20);
-        let num_polys = 2;
+        let num_committed_polys = 2;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -895,7 +895,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         let num_queries = 80;
@@ -919,7 +919,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert!(security_1 < security_2);
@@ -936,7 +936,7 @@ mod tests {
         let num_queries = 30;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(20);
-        let num_polys = 2;
+        let num_committed_polys = 2;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -958,7 +958,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         let blowup_factor = 16;
@@ -982,7 +982,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert!(security_1 < security_2);
@@ -999,7 +999,7 @@ mod tests {
         let num_queries = 120;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(16);
-        let num_polys = 1 << 1;
+        let num_committed_polys = 1 << 1;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -1021,7 +1021,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_1, 106);
@@ -1029,7 +1029,7 @@ mod tests {
         // when the FRI batching error is not largest when compared to the other soundness error
         // terms, increasing the number of committed polynomials might not lead to a degradation
         // in the round-by-round soundness of the protocol
-        let num_polys = 1 << 2;
+        let num_committed_polys = 1 << 2;
         options = ProofOptions::new(
             num_queries,
             blowup_factor,
@@ -1049,13 +1049,13 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_2, 106);
 
         // but after a certain point, there will be a degradation
-        let num_polys = 1 << 5;
+        let num_committed_polys = 1 << 5;
         options = ProofOptions::new(
             num_queries,
             blowup_factor,
@@ -1075,14 +1075,14 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_2, 104);
 
         // and this degradation is on the order of log2(N - 1) where N is the number of
         // committed polynomials
-        let num_polys = num_polys << 3;
+        let num_committed_polys = num_committed_polys << 3;
         options = ProofOptions::new(
             num_queries,
             blowup_factor,
@@ -1102,7 +1102,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_2, 101);
@@ -1119,7 +1119,7 @@ mod tests {
         let num_queries = 120;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(22);
-        let num_polys = 1 << 1;
+        let num_committed_polys = 1 << 1;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -1141,7 +1141,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_1, 126);
@@ -1149,8 +1149,8 @@ mod tests {
         // increasing the number of committed polynomials might lead to a degradation
         // in the round-by-round soundness of the protocol on the order of log2(N - 1) where
         // N is the number of committed polynomials. This happens when the FRI batching error
-        // is the largest among all erros
-        let num_polys = 1 << 8;
+        // is the largest among all errors
+        let num_committed_polys = 1 << 8;
         options = ProofOptions::new(
             num_queries,
             blowup_factor,
@@ -1170,7 +1170,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_2, 118);
@@ -1187,7 +1187,7 @@ mod tests {
         let num_queries = 120;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(16);
-        let num_polys = 1 << 1;
+        let num_committed_polys = 1 << 1;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -1209,7 +1209,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_1, 108);
@@ -1237,7 +1237,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_2, 108);
@@ -1263,7 +1263,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_2, 107);
@@ -1290,7 +1290,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_2, 105);
@@ -1307,7 +1307,7 @@ mod tests {
         let num_queries = 120;
         let collision_resistance = 128;
         let trace_length = 2_usize.pow(22);
-        let num_polys = 1 << 1;
+        let num_committed_polys = 1 << 1;
         let num_constraints = 100;
 
         let mut options = ProofOptions::new(
@@ -1329,7 +1329,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_1, 126);
@@ -1357,7 +1357,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_2, 126);
@@ -1383,7 +1383,7 @@ mod tests {
             trace_length,
             collision_resistance,
             num_constraints,
-            num_polys,
+            num_committed_polys,
         );
 
         assert_eq!(security_3, 125);