diff --git a/groth16/files/export_json.nim b/groth16/files/export_json.nim
index ebb09a3..53b2828 100644
--- a/groth16/files/export_json.nim
+++ b/groth16/files/export_json.nim
@@ -33,6 +33,8 @@ proc exportPublicIO*( fpath: string, prf: Proof ) =
   let f = open(fpath, fmWrite)
   defer: f.close()
 
+  # note: we start from 1 because the 0th element is the constant 1 "variable", 
+  # which is automatically added by the tools
   for i in 1..<n:
     let str : string = toQuotedDecimalFr( prf.publicIO[i] )
     if i==1:
diff --git a/groth16/files/r1cs.nim b/groth16/files/r1cs.nim
index b31a4fb..cb65712 100644
--- a/groth16/files/r1cs.nim
+++ b/groth16/files/r1cs.nim
@@ -43,7 +43,7 @@
 #   ...
 #   ...
 #
-# 4: Custom gates application
+# 5: Custom gates application
 # ---------------------------
 #   ...
 #   ...
diff --git a/groth16/files/witness.nim b/groth16/files/witness.nim
index 7de8b23..f849eb3 100644
--- a/groth16/files/witness.nim
+++ b/groth16/files/witness.nim
@@ -11,9 +11,7 @@
 #
 #     nvars = 1 + pub + secret = 1 + npubout + npubin + nprivin + nsecret
 #
-# NOTE: Unlike the `.zkey` files, which encode field elements in the 
-# Montgomery representation, the `.wtns` file encode field elements in 
-# the standard representation!
+# Field elements are encoded in the standard representation.
 #
 
 import std/streams
diff --git a/groth16/files/zkey.nim b/groth16/files/zkey.nim
index ccb23a9..73ce1e5 100644
--- a/groth16/files/zkey.nim
+++ b/groth16/files/zkey.nim
@@ -31,7 +31,7 @@
 #   beta2   : G2        = [beta]_2
 #   gamma2  : G2        = [gamma]_2
 #   delta1  : G1        = [delta]_1
-#   delta2  : G2        = [delta_2]
+#   delta2  : G2        = [delta]_2
 #
 # 3: IC
 # -----