From 6eb2ab4f4644627a41d6f85c7b700a8677cd790f Mon Sep 17 00:00:00 2001
From: Cofson <dimitrijevic.filip92@gmail.com>
Date: Tue, 23 Dec 2025 10:10:22 +0100
Subject: [PATCH] Fix mathematical variable definitions consistency

Standardize LaTeX notation for subscripts and superscripts:
- Use consistent braces for subscripts: K^{n}_{i} instead of K^{n}_i
- Fix malformed proof notation: pi^{K^{n}_{i}}_{Q}
- Use braces around mathbf arguments: \mathbf{K} instead of \mathbf K
- Add missing semicolons before "it also contains"
---
 nomos/raw/nomos-message-formatting.md | 36 +++++++++++++--------------
 1 file changed, 18 insertions(+), 18 deletions(-)

diff --git a/nomos/raw/nomos-message-formatting.md b/nomos/raw/nomos-message-formatting.md
index 2e5eb7c..b7fe9b3 100644
--- a/nomos/raw/nomos-message-formatting.md
+++ b/nomos/raw/nomos-message-formatting.md
@@ -90,16 +90,16 @@ class PublicHeader:
 **Fields:**
 
 - version=0x01 is version of the protocol.
-- public_key is $K^{n}_i$,
-  a public key from the set $\mathbf K^n_h$
+- public_key is $K^{n}_{i}$,
+  a public key from the set $\mathbf{K}^{n}_{h}$
   as defined in the Message Encapsulation spec.
-- proof_of_quota is $\pi^{K^{n}i}{Q}$,
-  a corresponding proof of quota for the key $K^{n}_i$ from the $\mathbf K^n_h$
+- proof_of_quota is $\pi^{K^{n}_{i}}_{Q}$,
+  a corresponding proof of quota for the key $K^{n}_{i}$ from the $\mathbf{K}^{n}_{h}$;
   it also contains the key nullifier.
-- signature is $\sigma_{K^{n}_{i}}(\mathbf {h|P}i)$,
+- signature is $\sigma_{K^{n}_{i}}(\mathbf{h|P}_{i})$,
   a signature of the concatenation of the $i$-th encapsulation
-  of the payload $\mathbf P$ and the private header $\mathbf h$,
-  that can be verified by the public key $K^{n}{i}$.
+  of the payload $\mathbf{P}$ and the private header $\mathbf{h}$,
+  that can be verified by the public key $K^{n}_{i}$.
 
 #### Private Header
 
@@ -107,7 +107,7 @@ The private_header must be generated as the outcome of
 the Message Encapsulation Mechanism.
 
 The private header contains a set of encrypted blending headers
-$\mathbf h = (\mathbf b_1,...,\mathbf b_{h_{max}})$.
+$\mathbf{h} = (\mathbf{b}_{1},...,\mathbf{b}_{h_{max}})$.
 
 ```python
 private_header: list[BlendingHeader]
@@ -118,7 +118,7 @@ as defined in the Global Parameters.
 
 **Blending Header:**
 
-The BlendingHeader ($\mathbf b_l$) is defined as follows:
+The BlendingHeader ($\mathbf{b}_{l}$) is defined as follows:
 
 ```python
 class BlendingHeader:
@@ -132,17 +132,17 @@ class BlendingHeader:
 **Fields:**
 
 - public_key is $K^{n}_{l}$,
-  a public key from the set $\mathbf K^n_h$.
-- proof_of_quota is $\pi^{K^{n}l}{Q}$,
-  a corresponding proof of quota for the key $K^{n}_l$ from the $\mathbf K^n_h$
+  a public key from the set $\mathbf{K}^{n}_{h}$.
+- proof_of_quota is $\pi^{K^{n}_{l}}_{Q}$,
+  a corresponding proof of quota for the key $K^{n}_{l}$ from the $\mathbf{K}^{n}_{h}$;
   it also contains the key nullifier.
-- signature is $\sigma_{K^{n}_{l}}(\mathbf {h|P}l)$,
+- signature is $\sigma_{K^{n}_{l}}(\mathbf{h|P}_{l})$,
   a signature of the concatenation of $l$-th encapsulation
-  of the payload $\mathbf P$ and the private header $\mathbf h$,
-  that can be verified by public key $K^{n}{l}$.
-- proof_of_selection is $\pi^{K^{n}{l+1},m{l+1}}{S}$,
-  a proof of selection of the node index $m{l+1}$
-  assuming valid proof of quota $\pi^{K^{n}{l}}{Q}$.
+  of the payload $\mathbf{P}$ and the private header $\mathbf{h}$,
+  that can be verified by public key $K^{n}_{l}$.
+- proof_of_selection is $\pi^{K^{n}_{l+1},m_{l+1}}_{S}$,
+  a proof of selection of the node index $m_{l+1}$
+  assuming valid proof of quota $\pi^{K^{n}_{l}}_{Q}$.
 - is_last is $\Omega$,
   a flag that indicates that this is the last encapsulation.