changed 'e' subscript to uppercase

text/auditing.tex

@@ -63,7 +63,7 @@ \subsection{Selection of Reports}
 
 Formally, for each tranche $n$ we ensure the announcement statement is published and distributed to all other validators along with our validator index $v$, evidence $s_n$ and all signed data. Validator's announcement statements must be in the set $S$:
 \begin{align}
-  S &\equiv \sig{\kappa'[v]_e}{\mathsf{X}_I \doubleplus n \concat \mathbf{x}_n \concat \mathcal{H}(\mathbf{H})} \\
+  S &\equiv \sig{\kappa'[v]_E}{\mathsf{X}_I \doubleplus n \concat \mathbf{x}_n \concat \mathcal{H}(\mathbf{H})} \\
   \where \mathbf{x}_n &= \se([\se_2(c) \frown \mathcal{H}(w) \mid \tup{c, w} \in \mathbf{a}_n])\\
   \mathsf{X}_I &= \token{\$jam\_announce}
 \end{align}
@@ -118,7 +118,7 @@ \subsection{Selection of Reports}
 
 From this mapping the validator issues a set of judgments $\mathbf{j}_n$:
 \begin{align}
-  \mathbf{j}_n &= \{ \mathcal{S}_{\kappa'[v]_e}(\mathsf{X}_{e(w)} \concat \mathcal{H}(w)) \mid (c, w) \in \mathbf{a}_n \}
+  \mathbf{j}_n &= \{ \mathcal{S}_{\kappa'[v]_E}(\mathsf{X}_{e(w)} \concat \mathcal{H}(w)) \mid (c, w) \in \mathbf{a}_n \}
 \end{align}
 
 %We denote the guarantors of a work-package $w$ as $\mathbf{G}(w)$ from a particular chain head, and this may be derived from the guarantees extrinsic $\xtguarantees$ of the ancestor block which introduced the work-report. Our restrictions on the guarantees extrinsic (described in section \ref{sec:accumulation}) ensures that this is unique.

text/judgments.tex

@@ -41,7 +41,7 @@ \subsection{Extrinsic}
 The signatures of all judgments must be valid in terms of one of the two allowed validator key-sets, identified by the verdict's second term which must be either the epoch index of the prior state or one less. Formally:
 \begin{align}
   &\begin{aligned}
-    &\forall (r, a, \mathbf{j}) \in \xtverdicts, \forall (v, i, s) \in \mathbf{j} : s \in \sig{\mathbf{k}[i]_e}{\mathsf{X}_v \concat r}\\
+    &\forall (r, a, \mathbf{j}) \in \xtverdicts, \forall (v, i, s) \in \mathbf{j} : s \in \sig{\mathbf{k}[i]_E}{\mathsf{X}_v \concat r}\\
     &\quad\where \mathbf{k} = \begin{cases}
       \kappa &\when a = \displaystyle \ffrac{\tau}{\mathsf{E}}\\
       \lambda &\otherwise\\
@@ -63,7 +63,7 @@ \subsection{Extrinsic}
     &k \in \mathbf{k} \,,\\
     &s \in \sig{k}{\mathsf{X}_v \concat r}\\
   \end{aligned}\right.\\
-  \nonumber\where \mathbf{k} &= \{k_e \mid k \in \lambda \cup \kappa\} \setminus \offenders
+  \nonumber\where \mathbf{k} &= \{k_E \mid k \in \lambda \cup \kappa\} \setminus \offenders
 \end{align}
 
 Verdicts $\xtverdicts$ must be ordered by report hash. Offender signatures $\xtculprits$ and $\xtfaults$ must each be ordered by the validator's Ed25519 key. There may be no duplicate report hashes within the extrinsic, nor amongst any past reported hashes. Formally:

text/reporting_assurance.tex

@@ -112,7 +112,7 @@ \subsubsection{The Assurances Extrinsic}
 
 The signature must be one whose public key is that of the validator assuring and whose message is the serialization of the parent hash $\mathbf{H}_p$ and the aforementioned bitstring:
 \begin{align}
-  &\forall a \in \xtassurances : a_s \in \sig{\kappa'[a_v]_e}{\mathsf{X}_A\frown \mathcal{H}(\se(\mathbf{H}_p, a_f))} \\
+  &\forall a \in \xtassurances : a_s \in \sig{\kappa'[a_v]_E}{\mathsf{X}_A\frown \mathcal{H}(\se(\mathbf{H}_p, a_f))} \\
   &\mathsf{X}_A \equiv \token{\$jam\_available}
 \end{align}
 

text/safrole.tex

@@ -83,11 +83,11 @@ \subsection{Key Rotation}\label{sec:keyrotation}
 
 We must introduce $\mathbb{K}$, the set of validator key tuples. This is a combination of a set of cryptographic public keys and metadata which is an opaque octet sequence, but utilized to specify practical identifiers for the validator, not least a hardware address.
 
-The set of validator keys itself is equivalent to the set of 336-octet sequences. However, for clarity, we divide the sequence into four easily denoted components. For any validator key $k$, the Bandersnatch key is denoted $k_b$, and is equivalent to the first 32-octets; the Ed25519 key, $k_e$, is the second 32 octets; the \textsc{bls} key denoted $k_{BLS}$ is equivalent to the following 144 octets, and finally the metadata $k_m$ is the last 128 octets. Formally:
+The set of validator keys itself is equivalent to the set of 336-octet sequences. However, for clarity, we divide the sequence into four easily denoted components. For any validator key $k$, the Bandersnatch key is denoted $k_b$, and is equivalent to the first 32-octets; the Ed25519 key, $k_E$, is the second 32 octets; the \textsc{bls} key denoted $k_{BLS}$ is equivalent to the following 144 octets, and finally the metadata $k_m$ is the last 128 octets. Formally:
 \begin{align}
   \mathbb{K} &\equiv \mathbb{Y}_{336} \\
   \forall k \in \mathbb{K} : k_b \in \H_B &\equiv k_{0\dots+32} \\
-  \forall k \in \mathbb{K} : k_e \in \H_E &\equiv k_{32\dots+32} \\
+  \forall k \in \mathbb{K} : k_E \in \H_E &\equiv k_{32\dots+32} \\
   \forall k \in \mathbb{K} : k_{BLS} \in \Y_{BLS} &\equiv k_{64\dots+144} \\
   \forall k \in \mathbb{K} : k_m \in \Y_{128} &\equiv k_{208\dots+128}
 \end{align}
@@ -99,7 +99,7 @@ \subsection{Key Rotation}\label{sec:keyrotation}
   \end{cases} \\
   \nonumber \where z &= \mathcal{O}([k_b \mid k \orderedin \gamma'_\mathbf{k}]) \\
   \label{eq:blacklistfilter} \Phi(\mathbf{k}) &\equiv \sq{
-    \begin{rcases}[0, 0, \dots] &\when k_e \in \offenders' \\ k &\otherwise \end{rcases}
+    \begin{rcases}[0, 0, \dots] &\when k_E \in \offenders' \\ k &\otherwise \end{rcases}
     \,\middle\mid\, k \orderedin \mathbf{k}
   }
 \end{align}