diff --git a/doc/src/architecture/consensus/burn.md b/doc/src/architecture/consensus/burn.md
index 043513801..7a29504c9 100644
--- a/doc/src/architecture/consensus/burn.md
+++ b/doc/src/architecture/consensus/burn.md
@@ -2,8 +2,8 @@
 
 proof of burn of staked coin.
 
-$$ X = <sn, ep, pk_x, pk_y, root, cm_x^{value}, cm_y^{value}> $$
-$$ W = <value, ep, nonce, value_{blind}, sk, \tau ,path> $$
+$$ X = (sn, ep, pk_x, pk_y, root, cm_x^{value}, cm_y^{value}) $$
+$$ W = (value, ep, nonce, value_{blind}, sk, \tau ,path) $$
 $$ \mathcal{L}= \{X:W\in \mathcal{R}\} $$
 
 | Public Input | Description                                                |
diff --git a/doc/src/architecture/consensus/mint.md b/doc/src/architecture/consensus/mint.md
index b5d524308..da746cf25 100644
--- a/doc/src/architecture/consensus/mint.md
+++ b/doc/src/architecture/consensus/mint.md
@@ -1,7 +1,7 @@
 # leadership mint proof
 
-$$ X = <ep, C, cm_x^{value}, cm_y^{value}> $$
-$$ W = <pk_x, pk_y, value, ep, nonce, value_{blind}> $$
+$$ X = (ep, C, cm_x^{value}, cm_y^{value}) $$
+$$ W = (pk_x, pk_y, value, ep, nonce, value_{blind}) $$
 $$ \mathcal{L}= \{X:W\in \mathcal{R}\} $$
 
 | Public Input | Description                                                |
diff --git a/doc/src/architecture/consensus/proposal.md b/doc/src/architecture/consensus/proposal.md
index 5398a1670..82ac2057e 100644
--- a/doc/src/architecture/consensus/proposal.md
+++ b/doc/src/architecture/consensus/proposal.md
@@ -19,8 +19,8 @@ a new coin that includes the block reward and is eligible to compete
 in upcoming future slots.
 
 
-$$ X = <sn, ep, pk_x, pk_y, root, cm_x^{value}, cm_y^{value}, reward, cm_x^{value^{out}}, cm_y^{value^{out}}, C, \mu_y, y, \mu_{\rho}, \rho,\sigma_1, \sigma_2, headstart> $$
-$$ W = <sk, nonce, value, ep, reward, value_{blind}, \tau, path, value_{blind}^{out}, \mu_y, \mu_{\rho}, \sigma1, \sigma2, headstart> $$
+$$ X = (sn, ep, pk_x, pk_y, root, cm_x^{value}, cm_y^{value}, reward, cm_x^{value^{out}}, cm_y^{value^{out}}, C, \mu_y, y, \mu_{\rho}, \rho,\sigma_1, \sigma_2, headstart) $$
+$$ W = (sk, nonce, value, ep, reward, value_{blind}, \tau, path, value_{blind}^{out}, \mu_y, \mu_{\rho}, \sigma1, \sigma2, headstart) $$
 $$ \mathcal{L}= \{X:W\in \mathcal{R}\} $$