% Conclusion
\begin{frame}{Formally verified autonomous hybrid control: necessary, achievable, timely}

  \begin{center}
    \Large \textbf{Three Converging Imperatives}
  \end{center}

  \vspace{0.3cm}

  \begin{center}
    \begin{tikzpicture}
      \draw[thick, fill=gray!20] (0,0) rectangle (12,4);
      \node[align=center, text width=10cm] at (6,2) {
        \textbf{FIGURE: Convergence Diagram}\\[0.2cm]
        Three arrows pointing to center:\\[0.1cm]
        1. Economic: \$21--28B annual O\&M\\
        2. Safety: 70--80\% human error\\
        3. Technical: Tools now exist\\[0.2cm]
        Center: ``NOW is the time''
      };
    \end{tikzpicture}
  \end{center}

  \vspace{0.5cm}

  \begin{center}
    \begin{tikzpicture}[node distance=1.2cm, scale=0.85, transform shape]
      \node[align=center] (h) {HARDENS\\(Discrete)};
      \node[right=of h] (plus) {+};
      \node[right=of plus, align=center] (c) {Continuous\\Verification};
      \node[right=of c] (eq) {=};
      \node[right=of eq, align=center, text=blue, font=\bfseries] (res) {Complete\\Hybrid System};

      \draw[->, >=stealth, very thick] (h) -- (plus);
      \draw[->, >=stealth, very thick] (plus) -- (c);
      \draw[->, >=stealth, very thick] (c) -- (eq);
      \draw[->, >=stealth, very thick] (eq) -- (res);
    \end{tikzpicture}
  \end{center}

  %SPEAKER NOTES: See comments below
%
    \textbf{Three Converging Imperatives:}

    1. Economic: SMRs need autonomy to be viable
       \$21--28B annual O\&M for datacenter demand alone
       Per-megawatt staffing costs threaten SMR economics

    2. Safety: Human error causes 70--80\% of incidents
       Training can't overcome fundamental cognitive limits
       Error probability: 0.001 → 1.0 under accident conditions

    3. Technical: Tools now exist to verify hybrid systems
       HARDENS proved discrete verification is feasible
       Control theory provides continuous verification tools
       We can now bridge the gap

    \textbf{This Research Closes the Gap:}
    HARDENS (Discrete) + Continuous Verification = Complete Hybrid System

    \textbf{Vision:} Control engineers generate high-assurance autonomous controllers from procedures.
    No formal methods PhD required. Mathematical proof included. Deployable on existing industrial hardware.
% (End of speaker notes)
\end{frame}

% Final slide
\begin{frame}{}
  \begin{center}
    \Huge \textbf{Questions?}

    \vspace{1cm}

    \Large Formally Verified Autonomous Hybrid Control

    \vspace{0.5cm}

    \normalsize
    Dane A. Sabo\\
    \texttt{dane.sabo@pitt.edu}\\[0.3cm]
    Dr. Dan G. Cole\\
    \texttt{dgcole@pitt.edu}

    \vspace{0.5cm}

    University of Pittsburgh\\
    Cyber Energy Center
  \end{center}
\end{frame}