\begin{thebibliography}{99} \bibitem{CKM16} H.~Cohn, A.~Kumar and G.~Minton, \emph{Optimal simplices and codes in projective spaces}, Geom. Topol. \textbf{20} (2016), no.~3, 1289--1357, \href{https://doi.org/10.2140/gt.2016.20.1289}{doi:10.2140/gt.2016.20.1289}; \href{https://arxiv.org/abs/1308.3188v4}{arXiv:1308.3188v4}. Section, theorem and equation numbers agree in both versions; page numbers cited here are those of arXiv v4. \bibitem{Hoggar84} S.~G.~Hoggar, \emph{Parameters of $t$-designs in $\mathbb{F}P^{d-1}$}, European J. Combin. \textbf{5} (1984), no.~1, 29--36, \href{https://doi.org/10.1016/S0195-6698(84)80015-3}{doi:10.1016/S0195-6698(84)80015-3}. \bibitem{CK07} H.~Cohn and A.~Kumar, \emph{Universally optimal distribution of points on spheres}, J. Amer. Math. Soc. \textbf{20} (2007), no.~1, 99--148, \href{https://doi.org/10.1090/S0894-0347-06-00546-7}{doi:10.1090/S0894-0347-06-00546-7}. \bibitem{Baez02} J.~C.~Baez, \emph{The octonions}, Bull. Amer. Math. Soc. (N.S.) \textbf{39} (2002), no.~2, 145--205, \href{https://doi.org/10.1090/S0273-0979-01-00934-X}{doi:10.1090/S0273-0979-01-00934-X}; \href{https://arxiv.org/abs/math/0105155v4}{arXiv:math/0105155v4}. \bibitem{CJKT11} H.~Cohn, Y.~Jiao, A.~Kumar and S.~Torquato, \emph{Rigidity of spherical codes}, Geom. Topol. \textbf{15} (2011), no.~4, 2235--2273, \href{https://doi.org/10.2140/gt.2011.15.2235}{doi:10.2140/gt.2011.15.2235}; \href{https://arxiv.org/abs/1102.5060v2}{arXiv:1102.5060v2}. \bibitem{TZ08} W.~Tadej and K.~\.Zyczkowski, \emph{Defect of a unitary matrix}, Linear Algebra Appl. \textbf{429} (2008), no.~2--3, 447--481, \href{https://doi.org/10.1016/j.laa.2008.02.036}{doi:10.1016/j.laa.2008.02.036}; \href{https://arxiv.org/abs/math/0702510v2}{arXiv:math/0702510v2}. \bibitem{BSB13} N.~Barros e S\'a and I.~Bengtsson, \emph{Families of complex Hadamard matrices}, Linear Algebra Appl. \textbf{438} (2013), no.~7, 2929--2957, \href{https://doi.org/10.1016/j.laa.2012.10.029}{doi:10.1016/j.laa.2012.10.029}; \href{https://arxiv.org/abs/1202.1181v2}{arXiv:1202.1181v2}. Page numbers cited refer to the arXiv version. \bibitem{CW96} R.~Connelly and W.~Whiteley, \emph{Second-order rigidity and prestress stability for tensegrity frameworks}, SIAM J. Discrete Math. \textbf{9} (1996), no.~3, 453--491, \href{https://doi.org/10.1137/S0895480192229236}{doi:10.1137/S0895480192229236}. \bibitem{Lojasiewicz59} S.~\L{}ojasiewicz, \emph{Sur le probl\`eme de la division}, Studia Math. \textbf{18} (1959), no.~1, 87--136, \href{https://doi.org/10.4064/sm-18-1-87-136}{doi:10.4064/sm-18-1-87-136}. \bibitem{AAA91} E.~R.~Avakov, A.~A.~Agrachev and A.~V.~Arutyunov, \emph{The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping}, Mat. Sb. \textbf{182} (1991), no.~8, 1091--1104 (Russian); English transl., Math. USSR-Sb. \textbf{73} (1992), no.~2, 455--466, \href{https://doi.org/10.1070/SM1992v073n02ABEH002555}{doi:10.1070/SM1992v073n02ABEH002555}. \bibitem{IS01} A.~F.~Izmailov and M.~V.~Solodov, \emph{Error bounds for $2$-regular mappings with Lipschitzian derivatives and their applications}, Math. Program. \textbf{89} (2001), no.~3, 413--435, \href{https://doi.org/10.1007/PL00011406}{doi:10.1007/PL00011406}. \bibitem{VW00} K.~G.~H.~Vollbrecht and R.~F.~Werner, \emph{Why two qubits are special}, J. Math. Phys. \textbf{41} (2000), no.~10, 6772--6782, \href{https://doi.org/10.1063/1.1286032}{doi:10.1063/1.1286032}; \href{https://arxiv.org/abs/quant-ph/9910064v1}{arXiv:quant-ph/9910064v1}. \bibitem{Hoggar83} S.~G.~Hoggar, \emph{Parameters of association schemes}, Ars Combin. \textbf{16-B} (1983), 325--339. \bibitem{BBRV02} S.~Bandyopadhyay, P.~O.~Boykin, V.~Roychowdhury and F.~Vatan, \emph{A new proof for the existence of mutually unbiased bases}, Algorithmica \textbf{34} (2002), no.~4, 512--528, \href{https://doi.org/10.1007/s00453-002-0980-7}{doi:10.1007/s00453-002-0980-7}; \href{https://arxiv.org/abs/quant-ph/0103162v3}{arXiv:quant-ph/0103162v3}. \bibitem{Yokota09} I.~Yokota, \emph{Exceptional Lie groups}, \href{https://arxiv.org/abs/0902.0431v1}{arXiv:0902.0431v1}, 2009. \bibitem{Knill96} E.~Knill, \emph{Group representations, error bases and quantum codes}, Los Alamos National Laboratory report, 1996, \href{https://doi.org/10.2172/378680}{doi:10.2172/378680}; \href{https://arxiv.org/abs/quant-ph/9608049v1}{arXiv:quant-ph/9608049v1}. \bibitem{SPGP26} E.~Svegborn, J.~Pauwels, N.~Gisin and A.~Pozas-Kerstjens, \emph{Uncountably many inequivalent maximally entangled measurements for two qutrits}, \href{https://arxiv.org/abs/2607.16396v1}{arXiv:2607.16396v1}, 2026. \bibitem{dMU21} L.~de~Moura and S.~Ullrich, \emph{The Lean~4 theorem prover and programming language}, in: Automated Deduction -- CADE~28, Lecture Notes in Comput. Sci. \textbf{12699}, Springer, Cham, 2021, 625--635, \href{https://doi.org/10.1007/978-3-030-79876-5_37}{doi:10.1007/978-3-030-79876-5\_37}. \bibitem{Mathlib20} The mathlib Community, \emph{The Lean mathematical library}, in: Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP~'20), ACM, New York, 2020, 367--381, \href{https://doi.org/10.1145/3372885.3373824}{doi:10.1145/3372885.3373824}. \bibitem{Palomar} Palomar registry of machine-checked Lean formalizations, \url{https://palomar-registry.org/about}, entry \href{https://palomar-registry.org/entry?id=PALOMAR-2026-10-29-000034&version=1}{\texttt{PALOMAR-2026-10-29-000034}, version~1}. \bibitem{McCrimmon04} K.~McCrimmon, \emph{A Taste of Jordan Algebras}, Universitext, Springer, New York, 2004, \href{https://doi.org/10.1007/b97489}{doi:10.1007/b97489}. \bibitem{TZ06} W.~Tadej and K.~\.Zyczkowski, \emph{A concise guide to complex Hadamard matrices}, Open Syst. Inf. Dyn. \textbf{13} (2006), no.~2, 133--177, \href{https://doi.org/10.1007/s11080-006-8220-2}{doi:10.1007/s11080-006-8220-2}; \href{https://arxiv.org/abs/quant-ph/0512154v2}{arXiv:quant-ph/0512154v2}. \end{thebibliography}