diff --git a/doc/src/spec/payment/burn.md b/doc/src/spec/payment/burn.md
index d3b6cdad4..2ca3a5f86 100644
--- a/doc/src/spec/payment/burn.md
+++ b/doc/src/spec/payment/burn.md
@@ -2,14 +2,14 @@
 
 $$ X = (nullifier, cm^{value}_x, cm^{value}_y, cm^{token}, root, data, spendHook, signature^{public}_x, signature^{public}_y) $$
 
-$$ W = (value, token, blind^{value}, blind^{token}, sn, spendHook, data, blind^{data}, sk, pos^{leaf}, path, signature^{secret}) $$
+$$ W = (value, token, blind^{value}, blind^{token}, sn, spendHook, data, blind^{data}, sk, pos, path, signature^{secret}) $$
 
 $$ \mathcal{L} = \{X:W\in \mathcal{R}\} $$
 
 
 | Public Input         | Description                                             |
 |----------------------|---------------------------------------------------------|
-| nullifier            | hash of (secretKey||serial)                             |
+| nullifier            | hash of (sk||sn)                                        |
 | $cm^{value}_x$       | x coordinate of value point commitment                  |
 | $cm^{value}_y$       | y coordinate of value point commitment                  |
 | $cm^{token}$         | commitment of tokenId as field element                  |
@@ -31,6 +31,6 @@ $$ \mathcal{L} = \{X:W\in \mathcal{R}\} $$
 | data                 | data read during spendHook execution                |
 | $blind^{data}$       | blinding term for data commitment                   |
 | sk                   | coin private key                                    |
-| $pos^{leaf}$         | coin commitment leaf position in the merkle tree    |
+| pos                  | coin commitment leaf position in the merkle tree    |
 | path                 | coin commitment merkle tree path                    |
 | $signature^{secret}$ | signature secret key                                |
diff --git a/doc/src/spec/payment/token_mint.md b/doc/src/spec/payment/token_mint.md
index 66bbedc64..907f21272 100644
--- a/doc/src/spec/payment/token_mint.md
+++ b/doc/src/spec/payment/token_mint.md
@@ -4,7 +4,7 @@ mint new tokens with arbitrary supply to given recipient.
 
 # new token mint
 
-$$ X = (authority^{public}_x, authority^{public}_y, token, cm^{coin}, cm^{value}_x, cm^{value}_y), cm^{token} $$
+$$ X = (authority^{public}_x, authority^{public}_y, token, cm^{coin}, cm^{value}_x, cm^{value}_y, cm^{token}) $$
 
 $$ W = (authority^{secret}, value, rcpt_x, rcpt_y, sn, spendHook, data, blind^{value}, blind^{token}) $$
 
@@ -22,7 +22,7 @@ $$ \mathcal{L}= \{X:W\in \mathcal{R}\} $$
 
 | witnesses            | Description                                         |
 |----------------------|-----------------------------------------------------|
-| $authority^{secret}  | minting authority secret key                        |
+| $authority^{secret}$ | minting authority secret key                        |
 | value                | token minted supply value                           |
 | $rcpt_x$             | token recipient public key x coordinate             |
 | $rcpt_y$             | token recipient public key y coordinate             |