diff --git a/Manuscript/FarDFT.tex b/Manuscript/FarDFT.tex
index d6474a0..a9e4bde 100644
--- a/Manuscript/FarDFT.tex
+++ b/Manuscript/FarDFT.tex
@@ -238,12 +238,14 @@ Unless otherwise stated, atomic units are used throughout.
 \section{Theory}
 \label{sec:theo}
 
-Let us consider a GOK ensemble of $\nEns$ electronic states with individual energies $\E{}{(0)} \le \ldots \le \E{}{(\nEns-1)}$, and (normalised) monotonically decreasing weights $\bw = (\ew{1},\ldots,\ew{M-1})$, \ie, $\ew{0}=1-\sum_{I=1}^{\nEns-1} \ew{I}$, and $\ew{0} \ge \ldots \ge \ew{\nEns-1}$.
+Let us consider a GOK ensemble of $\nEns$ electronic states with
+individual energies $\E{}{(0)} \le \ldots \le \E{}{(\nEns-1)}$, and
+(normalised) monotonically decreasing weights $\bw \equiv (\ew{1},\ldots,\ew{M-1})$, \ie, $\ew{0}=1-\sum_{I=1}^{\nEns-1} \ew{I}$, and $\ew{0} \ge \ldots \ge \ew{\nEns-1}$.
 The corresponding ensemble energy
 \begin{equation}
 	\E{}{\bw} = \sum_{I=0}^{\nEns-1} \ew{I} \E{}{(I)}
 \end{equation}
-can be obtained from the variational principle
+can be obtained from the GOK variational principle
 as follows\cite{Gross_1988a}
 \begin{eqnarray}\label{eq:ens_energy}
 	\E{}{\bw}  = \min_{\hGam{\bw}} \Tr[\hGam{\bw} \hH],
@@ -259,20 +261,21 @@ where $\lbrace \overline{\Psi}^{(I)} \rbrace_{0 \le I \le \nEns-1}$ is a set of
 The lower bound of Eq.~\eqref{eq:ens_energy} is reached when the set of wave functions correspond to the exact eigenstates of $\hH$, \ie, $\lbrace \overline{\Psi}^{(I)} \rbrace_{0 \le I \le \nEns-1} = \lbrace \Psi^{(I)} \rbrace_{0 \le I \le \nEns-1}$.
 Multiplet degeneracies can be easily handled by assigning the same
 weight to the degenerate states. \cite{Gross_1988b}
-One of the key feature of the GOK ensemble is that individual excitation
-energies can be extracted from the ensemble energy via differentiation with respect to individual weights:
+One of the key feature of the GOK ensemble is that \trashEF{individual} excitation
+energies can be extracted from the ensemble energy via differentiation
+with respect to the individual \manu{excited-state} weights \manu{$\ew{I}$ ($I>0$)}:
 \begin{equation}\label{eq:diff_Ew}
 	\pdv{\E{}{\bw}}{\ew{I}} = \E{}{(I)} - \E{}{(0)} = \Ex{}{(I)}.
 \end{equation}
 
-Turning to GOK-DFT, the extension of the Hohenberg--Kohn theorem to ensembles allows to rewrite the exact variational expression for the ensemble energy as\cite{Gross_1988a}
+Turning to GOK-DFT, the extension of the Hohenberg--Kohn theorem to ensembles allows to rewrite the exact variational expression for the ensemble energy as\cite{Gross_1988b}
 \begin{equation}
 \label{eq:Ew-GOK}
 	\E{}{\bw} = \min_{\n{}{}} \qty{ \F{}{\bw}[\n{}{}] + \int \vne(\br{}) \n{}{}(\br{}) d\br{} },
 \end{equation}
 where $\vne(\br{})$ is the external potential and $\F{}{\bw}[\n{}{}]$ is the universal ensemble functional
 (the weight-dependent analog of the Hohenberg--Kohn universal functional for ensembles).
-In the KS formulation, this functional can be decomposed as
+In the KS formulation, this functional is decomposed as
 \begin{equation}\label{eq:FGOK_decomp}
       \F{}{\bw}[\n{}{}] 
       = \Tr{ \hgamdens{\bw} \hT }+ \E{\Ha}{}[\n{}{}]+\E{\xc}{\bw}[\n{}{}],