\newcommand{\eu}{\mathrm{e}} \newcommand{\im}{\mathrm{i}} \newcommand{\degree}{\,^{\circ}} \newcommand{\transpose}[1]{{#1}^{\mathsf{T}}} \newcommand{\Int}{\int\limits_{-\infty}^{\infty}} \newcommand{\rint}[2]{\int{#1}\dd{#2}} \newcommand{\Rint}[4]{\int\limits_{#1}^{#2}{#3}\dd{#4}} \newcommand{\HH}{\mathbb{H}} \DeclareMathOperator{\ot}{ot} \DeclareMathOperator{\cof}{cof} \DeclareMathOperator{\TC}{TC} \newcommand{\ORD}{\text{ORD}} \makeatletter \newcommand*\bigcdot{\mathpalette\bigcdot@{.5}} \newcommand*\bigcdot@[2]{\mathbin{\vcenter{\hbox{\scalebox{#2}{$\m@th#1\bullet$}}}}} \makeatother \newcommand{\Ham}{\hat{\mathcal{H}}} \renewcommand{\Tr}{\mathrm{Tr}} \newcommand{\christoffelsecond}[4]{\dfrac{1}{2}g^{#3 #4}(\partial_{#1} g_{#2 #4} + \partial_{#2} g_{#1 #4} - \partial_{#4} g_{#1 #2})} \newcommand{\riemanncurvature}[5]{\partial_{#3} \Gamma_{#4 #2}^{#1} - \partial_{#4} \Gamma_{#3 #2}^{#1} + \Gamma_{#3 #5}^{#1} \Gamma_{#4 #2}^{#5} - \Gamma_{#4 #5}^{#1} \Gamma_{#3 #2}^{#5}} \newcommand{\covariantriemanncurvature}[5]{g_{#1 #5} R^{#5}{}_{#2 #3 #4}} \newcommand{\riccitensor}[5]{g_{#1 #5} R^{#5}{}_{#2 #3 #4}} \renewcommand{\emptyset}{\varnothing} \DeclareMathOperator{\dom}{dom} \DeclareMathOperator{\imm}{imm} \newcommand{\rel}{\mathcal{R}} \newcommand{\FF}{\mathcal{F}} \newcommand{\bigtimes}{\varprod} \DeclareMathOperator{\Fun}{Fun} \DeclareMathOperator{\id}{id} \newcommand{\PP}{\mathbb{P}} \newcommand{\NN}{\mathbb{N}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\QQ}{\mathbb{Q}} \newcommand{\RR}{\mathbb{R}} \newcommand{\CC}{\mathbb{C}} \newcommand{\UU}{\mathbb{V}} \newcommand{\VV}{\mathbb{V}} \newcommand{\se}{\text{se }} \newcommand{\altrimenti}{\text{altrimenti}} \newcommand{\inv}{^{-1}} \newcommand{\AC}{$\mathsf{AC}$} \newcommand{\PA}{$\mathsf{PA}$} \newcommand{\cc}{\mathfrak{c}} \DeclareMathOperator{\Fin}{Fin} \newcommand{\PPFin}{\PP^{\mathsf{fin}}} \DeclareMathOperator{\FSeq}{FSeq} \DeclareMathOperator{\bige}{Big} \DeclareMathOperator{\Sym}{\mathfrak{S}} \newcommand{\OO}{\mathfrak{O}} \newcommand{\basis}{\mathcal{B}} \newcommand{\restr}[2]{ #1\arrowvert_{#2} }