diff --git a/documents/thesis/chapters/beacon_discipline.tex b/documents/thesis/chapters/beacon_discipline.tex
index e42a737..57980d7 100644
--- a/documents/thesis/chapters/beacon_discipline.tex
+++ b/documents/thesis/chapters/beacon_discipline.tex
@@ -169,7 +169,7 @@ The measured arrival term $\tMeasArriv$ in \eqref{eq:transmitter2antenna_t0} is
 	 = f\left( \frac{\pMeasArriv}{2\pi}\,T + kT \right)\\
 	,
 \end{equation}%>>>
-where $-\pi < \pMeasArriv < \pi$ is the phase of the beacon at time $\tMeasArriv$, $T$ the period of the beacon and $k \in \mathbb{Z}$ is an unknown period counter.
+where $-\pi < \pMeasArriv < \pi$ is the phase of the beacon $f(t)$ at time $\tMeasArriv$, $T$ the period of the beacon and $k \in \mathbb{Z}$ is an unknown period counter.
 Of course, this means that the clock defects $\tClock$ can only be resolved up to the beacon's period, changing \eqref{eq:synchro_mismatch_clocks} to
 \begin{equation}\label{eq:synchro_mismatch_clocks_periodic}%<<<
 	\begin{aligned}
@@ -193,11 +193,11 @@ The correct period $k$ alignment might be found in at least two ways.
 First, if the timescale of the beacon is much longer than the estimated accuracy of another timing mechanism (such as a \gls{GNSS}),
  one can be confident to have the correct period.
 In \gls{AERA} for example, multiple sine waves were used amounting to a total beacon period of $\sim 1 \us$\cite[Figure~2]{PierreAuger:2015aqe}.
-With an estimated timing accuracy of the \gls{GNSS} under $50 \ns$ the correct beacon period can be determined, resulting in a unique $\tTrueEmit$ transmit time.
+With an estimated timing accuracy of the \gls{GNSS} under $50 \ns$ the correct beacon period can be determined, resulting in a unique measured arrival time $\tMeasArriv$.
 \\
 % lifing period multiplicity -> short timescale counting +
-A second method consists of using an additional discrete signal to declare a unique $\tTrueEmit$.
-This relies on the ability of counting how many beacon periods have passed since the discrete signal has been recorded.
+A second method consists of using an additional (discrete) signal to declare a unique $\tMeasArriv$.
+This relies on the ability of counting how many beacon periods have passed since this extra signal has been recorded.
 Chapter~\ref{sec:single_sine_sync} shows a special case of this last scenario where the period counters are approximated from an extensive air shower.
 \\%>>>
 
@@ -214,7 +214,7 @@ The mismatch terms for any two pairs of antennas sharing one antenna $\{ (i,j),
 Taking one antenna as the reference antenna with $(\tClock)_r = 0$, the mismatches across the array can be determined by applying \eqref{eq:synchro_mismatch_clocks} over consecutive pairs of antennas and thus all relative clock deviations $(\Delta \tClock)_{ir}$.
 \\
 
-As discussed previously, the synchronisation problem is different for a continuous and an impulsive beacon due to the non-uniqueness (in the sine wave case) of the $\tTrueEmit$ of the transmitter.
+As discussed previously, the synchronisation problem is different for a continuous and an impulsive beacon due to the non-uniqueness (in the sine wave case) of the measured arrival time $\tMeasArriv$.
 This is illustrated in Figure~\ref{fig:dynamic-resolve} where a three-element array constrains the location of the transmitter using the true timing information of the antennas.
 It works by finding the minimum deviation between the putative and measured time differences ($\Delta t_{ij}(x)$, $\Delta t_{ij}$ respectively) per baseline $(i,j)$ for each location on a grid.
 \\