\begin{thebibliography}{99} \bibitem{BLLT} N.~Benjamin, K.~Langhoff, W.~Li and J.~Thaler, \emph{Constraining the spectral gap of 2d CFTs just above $c=1$}, \href{https://arxiv.org/abs/2611.07011}{arXiv:2611.07011}. \bibitem{EL} L.~Eberhardt and N.~Levine, \emph{Classification of $c=1$ CFTs}, \href{https://arxiv.org/abs/2609.16111}{arXiv:2609.16111}. \bibitem{Hellerman} S.~Hellerman, \emph{A universal inequality for CFT and quantum gravity}, J. High Energy Phys. \textbf{08} (2011) 130, \href{https://arxiv.org/abs/0902.2790}{arXiv:0902.2790}. \bibitem{FriedanKeller} D.~Friedan and C.~A.~Keller, \emph{Constraints on 2d CFT partition functions}, J. High Energy Phys. \textbf{10} (2013) 180, \href{https://arxiv.org/abs/1307.6562}{arXiv:1307.6562}. \bibitem{CLY} S.~Collier, Y.-H.~Lin and X.~Yin, \emph{Modular bootstrap revisited}, J. High Energy Phys. \textbf{09} (2018) 061, \href{https://arxiv.org/abs/1608.06241}{arXiv:1608.06241}. \bibitem{HMR} T.~Hartman, D.~Maz\'a\v{c} and L.~Rastelli, \emph{Sphere packing and quantum gravity}, J. High Energy Phys. \textbf{12} (2019) 048, \href{https://arxiv.org/abs/1905.01319}{arXiv:1905.01319}. \bibitem{KaidiPerlmutter} J.~Kaidi and E.~Perlmutter, \emph{Discreteness and integrality in conformal field theory}, J. High Energy Phys. \textbf{02} (2021) 064, \href{https://arxiv.org/abs/2008.02190}{arXiv:2008.02190}. \bibitem{ACHT} N.~Afkhami-Jeddi, H.~Cohn, T.~Hartman and A.~Tajdini, \emph{Free partition functions and an averaged holographic duality}, J. High Energy Phys. \textbf{01} (2021) 130, \href{https://arxiv.org/abs/2006.04839}{arXiv:2006.04839}. \bibitem{Cohen} P.~J.~Cohen, \emph{On a conjecture of Littlewood and idempotent measures}, Amer. J. Math. \textbf{82} (1960), 191--212. \end{thebibliography}