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\begin{document}

\title{Supplemental Material for: Hierarchical Quantum Sensing with Floquet-Engineered Chaos and Exceptional Surfaces}

\author{Stella Rolande Mbokop Tchounda}
% \email{rolande.mbokop@facsciences-uy1.cm}
\affiliation{Department of Physics, Faculty of Sciences, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon}

\author{Carolle Tchodimou}
\affiliation{Department of Physics, Faculty of Sciences, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon}

\author{Philippe Djorwe}
\affiliation{Department of Physics, Faculty of Sciences, University of Ngaoundéré, P.O. Box 454, Ngaoundéré, Cameroon}

\author{Sifeu Takougang Kingni}
\affiliation{Department of Mechanical, Petroleum and Gas Engineering, National Advanced School of Mines and Petroleum Industries, University of Maroua, P.O. BOX 46, Maroua, Cameroon}

\author{Serge Guy Nana Engo}
\email{serge.nana-engo@facsciences-uy1.cm}
\affiliation{Department of Physics, Faculty of Sciences, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon}

\date{\today}

\maketitle

\section*{Contents}
\begin{itemize}
    \item \textbf{Section S1}: System Model and Derivations (Floquet-Langevin)
    \item \textbf{Section S2}: Stability Analysis (Floquet vs Routh-Hurwitz)
    \item \textbf{Section S3}: Lyapunov Methods for Chaos Characterization
    \item \textbf{Section S4}: Petermann Factor and EPs
    \item \textbf{Section S5}: Additional Figures
    \item \textbf{Section S6}: Non-Gaussianity Indicators
    \item \textbf{Section S7}: Extended Sensing Analysis (SNR vs Time)
    \item \textbf{Section S8}: Quantum Validation (Mini-Hilbert Benchmark)
\end{itemize}

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\bibliography{Mbokop_Manuscript}

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