Improve set_v1.zk comments

proof/set_v1.zk

@@ -1,7 +1,15 @@
+# Intro:
+# 
+# This is the source of ZK circuit. 
+# It has 3 sections: constant, witness and circuit.
+# constant and witness describe the data the ZK statements are constraining.
+
 # 2 ** k is the maximum nubmer of rows in the circuit.
-k = 13;
+k = 11;
 
 # Section to declare constants used in the circuit.
+# "Set_V1" is the namepsace of circuit. 
+# It is the namespace for storing verifying key onchain.
 constant "Set_V1" {} 
 
 # Witness is the inputs to the circuit, both public and private.
@@ -49,13 +57,18 @@ circuit "Set_V1" {
 # # Prove
 # 
 # The prove API is essentially: prove(proving_key, witness) -> proof
-# The proving key, essentially, is the same across different witnesses and proofs
-# but unique per circuit.
+# 
+# The prover provides the circuit, and generates the proving key. The proving key essentially
+# encodes the circuit but does not include information for the witness, so it is
+# the same across different witnesses (and therefore proofs) but unique per circuit.
 # 
 # # Verify
 # 
 # The verifying API is essentially: verify(verifying_key, proof, public_inputs) -> {T, F}
-# The verifying key is the same across different proofs but unique per circuit.
-#
-# For more info, you can try this zk intro to get a mental model:
+# 
+# The verifier provides the circuit, and generates the verifying key. The verifying key similarly
+# encodes only the circuit, and not the public inputs or the proof. The verifying key is the same
+# across different proofs but unique per circuit.
+# 
+# For more info, you can try this zk intro:
 # https:#learn.0xparc.org/materials/circom/learning-group-1/circom-1