doc/book: fix nullifier derivation N = H(x, C)

doc/src/arch/anonymous_assets.md

@@ -43,13 +43,11 @@ Reveal $C$ and $V$ commitments. Add $C$ to the Merkle tree.
 When we spend the coin, we must ensure that the value of the coin
 cannot be double spent. We call this the *Burn* phase. The process
 relies on a $N$ nullifier, which we create  using the secret key $x$
-for the public key $P$ and the secret serial $\rho$. Nullifiers are unique per coin and prevent
+for the public key $P$ and the coin itself $C$. Nullifiers are unique per coin and prevent
 double spending. $R$ is the Merkle root. $v$ is the coin's value.
 
 Generate a random number $r_V$.
 
-$$ N = H(x, \rho) $$
-
 Check that the secret key corresponds to a public key:
 
 $$ P = xG $$
@@ -60,6 +58,10 @@ tree $R$:
 $$ C = H(P, v, \rho, r_C) $$
 $$ C \in R $$
 
+Derive the nullifier:
+
+$$ N = H(x, C) $$
+
 Check that the value commitment is constructed correctly:
 
 $$ v > 0 $$
@@ -92,4 +94,4 @@ blinding factor for the amounts.
 
 ![](diagram-dkzk.png)
 
-*Note: In the diagram $s$ correspond to the $\rho$*
+*Note: In the diagram $s$ correspond to the $\rho$*

doc/src/arch/services.md

@@ -133,7 +133,7 @@ impl Parent {
             // ...
         });
 
-        self_.child.p2p.init(self_.clone());
+        self_.child.parent.init(self_.clone());
         // ...
         self_
     }