diff --git a/Jauslin_2023.tex b/Jauslin_2023.tex
index c813122..e2a31b0 100644
--- a/Jauslin_2023.tex
+++ b/Jauslin_2023.tex
@@ -80,6 +80,7 @@ The {\it condensate fraction} is defined as the proportion of particles in the c
 The momentum distribution is an extension of the condensate fraction to a more general family of states.
 In particular, computing $\mathcal M(k)$ for $k\neq 0$ amounts to counting particles that are {\it not} in the condensate.
 This quantity has been used in the recent proof\-~\cite{FS20,FS22} of the energy asymptotics of the Bose gas at low density.
+A numerical computation of the prediction of the Simplified approach for $\mathcal M(k)$ have been published in\-~\cite{Ja23b}.
 \bigskip
 
 \indent
@@ -1690,6 +1691,12 @@ so by\-~(\ref{erho}),
 This, together with\-~(\ref{final1}), implies\-~(\ref{Msimpleqbog}).
 \qed
 
+\bigskip
+\bigskip
+
+\hfil{\bf Acknowledgements}\par
+The author thanks Elliott H. Lieb, Eric A. Carlen and Markus Holzmann for many valuable discussions.
+The author acknowledges support from the Simons Foundation, Grant Number\-~825876.
 
 \vfill
 \eject
diff --git a/bibliography/bibliography.tex b/bibliography/bibliography.tex
index 2419e95..ca6105f 100644
--- a/bibliography/bibliography.tex
+++ b/bibliography/bibliography.tex
@@ -51,6 +51,9 @@ arxiv:{\tt\color{blue}\href{https://arxiv.org/abs/2203.03440}{2203.03440}}.\par\
 \bibitem[Ja22]{Ja22}I. Jauslin - {\it Review of a Simplified Approach to study the Bose gas at all densities}, The Physics and Mathematics of Elliott Lieb, The\-~90th Anniversary Volume I, chapter\-~25, pages\-~609-635, ed. Rupert L. Frank, Ari Laptev, Mathieu Lewin, Robert Seiringer, EMS Press, 2022,\par\penalty10000
 doi:{\tt\color{blue}\href{http://dx.doi.org/10.4171/90-1/25}{10.4171/90-1/25}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2202.07637}{2202.07637}}.\par\medskip
  
+\bibitem[Ja23]{Ja23b}I.\-~Jauslin - {\it Evidence of a liquid phase in interacting Bosons at intermediate densities}, arXiv preprint, 2023\par\penalty10000
+arxiv:{\tt\color{blue}\href{https://arxiv.org/abs/2302.13449}{2302.13449}}.\par\medskip
+ 
 \bibitem[LHY57]{LHY57}T.D. Lee, K. Huang, C.N. Yang - {\it Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties}, Physical Review, volume\-~106, issue\-~6, pages\-~1135-1145, 1957,\par\penalty10000
 doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.106.1135}{10.1103/PhysRev.106.1135}}.\par\medskip