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A .DS_Store A Presentations/.DS_Store A Presentations/20251215-Emerson-Pres/.DS_Store A Presentations/20251215-Emerson-Pres/ERLM_SABO_DRAFT_PRES.pdf A Presentations/20251215-Emerson-Pres/ERLM_SABO_FINAL_PRES.pdf A Presentations/20251215-Emerson-Pres/actual-presentation-outline.md A Presentations/20251215-Emerson-Pres/bouncing_ball_hybrid.py A Presentations/20251215-Emerson-Pres/images/.DS_Store
2025-12-13 22:34:13 -05:00 · 2025-12-13 22:34:13 -05:00 · 1f3afde500
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--- a/Presentations/.DS_Store
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--- a/Presentations/20251215-Emerson-Pres/.DS_Store
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--- a/Presentations/20251215-Emerson-Pres/ERLM_SABO_DRAFT_PRES.pdf
+++ b/Presentations/20251215-Emerson-Pres/ERLM_SABO_DRAFT_PRES.pdf
--- a/Presentations/20251215-Emerson-Pres/ERLM_SABO_FINAL_PRES.pdf
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--- a/Presentations/20251215-Emerson-Pres/actual-presentation-outline.md
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@ -0,0 +1,273 @@
+# Presentation Outline: ERLM Presentation
+
+Audience:
+- Engineering PhD students 
+- Dr. Cole,
+- Potentially other faculty members.
+
+Presentation Style:
+Proposal, Assertion Evidence
+
+## SLIDE 1: HOOK
+
+### Message
+**THE UNITED STATES STANDS ON THE PRECIPICE OF A SEVERE
+ENERGY CRISIS** 
+
+1. We're looking down the barrel of a severe energy shortage
+   with the introduction of data centers for AI buildout
+2. The cheapest way to build new power right now is natural
+   gas combined cycle power plants
+3. We also have a climate crisis, which nat gas definitely
+   will not help with
+4. The only baseload power solution we have to meet this
+   demand is nuclear power
+
+*BUT NUCLEAR POWER IS VERY EXPENSIVE TO OPERATE* 
+
+1. Nuclear power is actually really cheap when it comes to
+   fuel
+2. What makes nuclear power expensive is capital and
+   operating costs.
+3. Capital costs are being solved by new modular reactors
+4. Labor costs today actually get worse figuring modular
+   reactors. Reason being same staff required for different
+MWh
+5. This is the challenge we're going to take on. By making
+   autonomous systems that are safe, we can eliminate
+reliance on human operators
+
+### Presentation Strategy
+
+1. First, present a graph on energy consumption estimates in
+   US in a graph.
+2. Then, show the LCOE of different forms of energy
+   production. Highlight the relative cost of labor and
+operating costs.
+3. LCOE costs expect large nuclear reactors. Modular
+   reactors on usually a third of the power, so labor costs
+are a big deal.
+4. Bullet ending, we need to reduce labor costs of advanced
+   nuclear power
+
+## SLIDE 2: STATE OF THE ART
+
+### Message
+**Modern nuclear reactor operation is highly prescriptive
+and labor intensive**
+
+1. We've been talking about labor, who's in the reactor
+   room? Usually a senior reactor operator, and 2-3 reactor
+operators. Usually there's a chemist floating around too. 
+2. It's this staffing, 24/7/365
+3. Reactor operators are extensively trained individuals.
+   They have to train for multiple years and pass extensive
+and recurrent examinations.
+4. Reactor operator jobs aren't always super attractive
+   jobs. The work is somewhat monotonous, and requires
+individuals to usually live in very rural locations.
+5. What is the work? Well, it's extremely prescriptive
+   operations manuals. Nuclear reactors are so highly
+regulated and capital intensive that procedures and their
+creation happen in the design stage, before reactors are
+built. Safety is ensured at the design stage.
+6. Thus, we're using humans basically as controllers for
+   highly prescriptive tasks.
+7. What are humans really good at? Well for the most part,
+   general intelligence. Humans can use judgement and adapt
+   to situations.
+
+*But, human operators in nuclear reactor operating rooms are
+trained and instructed to follow strict procedural
+guidelines.* 
+
+8. There's also evidence that humans are actually not very
+   good at being controllers.
+9. Humans have very limited baud rates. We can only perceive
+   so much information at a time, and the probability of
+human error increases dramatically when we perceive an
+emergency and are overwhelmed. 
+10. Enter, the whole damn field of human factors
+    engineering. We bend over backwards to design control
+rooms and operating procedures to minimize the possibility
+of human error. This takes a lot of time and is expensive to
+implement.
+
+### Presentation Strategy
+
+1. First, show a picture of a reactor operating room, and
+   explain who the people are inside.
+2. Explain how these operators are trained, the
+   qualifications necesssary
+3. What are they actually doing in here?
+4. Split screen with reactor design photo. Show that there's
+   a wall between them.
+5. introduce point and details afterwards
+6. Talk about how designing these procedures, building these
+   control rooms, and training these people is extremely
+expensive
+
+## SLIDE 3: LIMITATIONS
+
+### Message
+These are going to just be a summary of the limits.
+
+### Presentation strategy
+Basically just a bulleted list of the limits.
+
+## SLIDE 4: RESEARCH APPROACH
+
+### Message
+**We will create high assurance autonomous control systems
+by breaking down the problem into smaller steps** 
+
+1. One does not go from zero to hero easily with these
+   systems.
+2. Instead, we're going to create a *chain of proof* that
+   our system is high assurance
+2.1. We're ACTUALLY going to start by explaining we'll use
+hybrid control systems
+    What is a hybrid system? well it's a system with both
+continuous dynamics and discrete dynamics. This is a system
+that both flows and jumps!.
+3. We'll start with the procedures. We'll take the natural
+   language and turn them into FRETish requirements
+4. We can do realizability checks at this point
+5. We take the requirements from FRET as temporal logical
+   statements, and move to the next step
+6. We take our temporal logic statements, and use reactive
+   synthesis tools to break them down into discrete automata
+7. These are our switching behvaior between continuous
+   modes
+8. Then, once we have this automata, we have two things:
+    1. We have the switching behavior with the boundary
+       conditions
+    2. We have a map of how one mode goes to another mode.
+9. At this point, we will build individual controllers for
+   each of the discrete modes
+10. To ensure the continuous dynamics actually satisfy
+    boundaries between states, we will use a couple of
+techniques from formal methods.
+    1. Reachability. Reachability will ensure that our input
+       and output conditions only satisfy the discrete
+    transition boundaries that we define.
+    2. Barrier Certificates. These will ensure that on the
+       interfaces, we won't develop zeno behavior
+
+*Each of these links together is what will allow us to prove
+that the whole system satisfies requirements.* 
+
+### Presentation Strategy
+This isn't really going to be one slide. Instead, I'll
+present an arrow from left to right about what the steps
+are, and dive into each subpiece for a slide, then jump back
+out to the original slide.
+
+The arrow should be from current operational procedure to
+autonomous hybrid control system. The steps should be
+- requirement synthesis in FRET
+- Reactive synthesis in STRIX or similar
+- building individual control modes
+- badda bing we're there.
+
+## SLIDE 5: METRICS OF SUCCESS
+
+### Message
+**In order to evaluate the progress of this research, we
+need to have a way to measure progress**
+
+1. This work is trying to make a real impact on building
+   autonomous control systems in nuclear power. Because of
+this, the relevancy to industry partners is what's most
+critical.
+
+*To measure success, we're going to use technology readiness
+levels*
+
+1. We're shooting for TRL 5.
+2. TRL 3 is critical function and proof of concept. This is
+   individual components working in isolation. If we can
+bumble through each of these steps in a hacky way, I'll call
+that TRL 3. This isn't necesarily a flushed out control
+system.
+3. TRL 4 is Laboratory Testing of Integrated Components.
+   This is a bench top simulation of a complete hybrid
+autonomous control system. This includes a start up and
+shutdown procedure, and load following with checks for xenon
+poisoning and an ability to handle component failures.
+4. TRL 5 is Laboratory testing in Relevant Environment. This
+   is TRL 4, plus putting it on the Ovation control system
+instead of a purely code (MATLAB / PYTHON) simulation.
+
+### Presentation Strategy
+
+Show a TRL timeline, With TRL 3, 4, 5 arrows. Insert
+Pictures along each step talking about what is what
+
+## SLIDE 6: RISKS AND CONTINGENCIES
+
+### Message
+**Possible challenges will be identified early and have
+planned mitigations** 
+
+1. Computational tractability
+    - It might be really hard to generate these automata and
+      do reacability
+    - Exponential scaling with specification complexity
+    - Early indicators are synthesis times >24 hours, very
+    large automata, etc.
+    - Contingency is we can reduce scope to just a startup
+    sequence
+    - We can exploit time / scale separation of reactor
+    dynamics too, and also use the high performance compute
+    at CRC
+
+2. Boolean guard conditions may not map cleanly to
+   continuous guard conditions
+   - early indicator: Continuous modes can't be built ot
+   reach transition boundaries, and safety regions can't be
+   expressed as polytopes.
+   - contingency: Restrict to polytopic invariants where
+   certain states are conservatively ignored. Sucks and
+   requires manipulation but could get the job done.
+
+3. Procedure Formalization is not within reach yet.
+    - early indicator is we have a really hard time forming
+      complete specifications in FRET from written
+    procedures or synthesizing automata
+    - contingency is we document the taxonomy and figure out
+      what's missing to get us there. What is missing from
+    the written procedures? This becomes a research
+    contribution.
+
+### Presentation Strategy
+
+Basically just top and bottom comparison of risk, and what
+the contingencies are
+
+
+## SLIDE 7: BROADER IMPACTS
+
+### Message
+**Automating nuclear reactor control is a
+billion-dollar-a-year problem**
+
+1. We need a lot of energy
+2. The only clean baseload option is nuclear power
+3. If we build advanced nuclear to meet this need, operating
+   costs are expensive
+
+*But automating control can reduce operator burden, and
+significantly reduce operating costs.* 
+
+### Presentation Strategy
+Basically copy over the one slider I made from earlier for
+the emerson CEO visit.
+
+## SLIDE 8: MONEY SLIDE
+
+### Message
+
+### Presentation Strategy
+
+
--- a/Presentations/20251215-Emerson-Pres/bouncing_ball_hybrid.py
+++ b/Presentations/20251215-Emerson-Pres/bouncing_ball_hybrid.py
@ -0,0 +1,332 @@
+"""
+Hybrid Dynamical System: Bouncing Ball in 1-D
+
+This model demonstrates a hybrid system with:
+- Flow State 1: Free fall (when ball center of mass is above radius r)
+- Flow State 2: Spring-mass-damper (when ball is in contact with ground)
+- Discrete transitions between these states
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.integrate import solve_ivp
+
+
+class HybridBouncingBall:
+    def __init__(self, m=0.1, r=0.1, g=9.81, k=5000.0, c=10.0):
+        """
+        Parameters:
+        -----------
+        m : float
+            Mass of the ball (kg)
+        r : float
+            Radius of the ball (m)
+        g : float
+            Gravitational acceleration (m/s^2)
+        k : float
+            Spring constant when in contact with ground (N/m)
+        c : float
+            Damping coefficient when in contact with ground (N·s/m)
+        """
+        self.m = m
+        self.r = r
+        self.g = g
+        self.k = k
+        self.c = c
+
+        # For tracking state transitions
+        self.state_history = []
+        self.transition_times = []
+
+    def free_fall_dynamics(self, t, y):
+        """
+        Flow dynamics for free fall state.
+        State: y = [position, velocity]
+        """
+        pos, vel = y
+        dpos = vel
+        dvel = -self.g
+        return [dpos, dvel]
+
+    def spring_damper_dynamics(self, t, y):
+        """
+        Flow dynamics for spring-mass-damper state.
+        State: y = [position, velocity]
+
+        When ball is compressed against ground:
+        F = -k*(r - pos) - c*vel - m*g
+        """
+        pos, vel = y
+        dpos = vel
+        # Spring force kicks in when position < r
+        # Compression is (r - pos)
+        compression = self.r - pos
+        spring_force = self.k * compression
+        damping_force = self.c * vel
+
+        dvel = (spring_force - damping_force - self.m * self.g) / self.m
+        return [dpos, dvel]
+
+    def event_contact_ground(self, t, y):
+        """Event: Ball contacts ground (transition to spring-damper)"""
+        pos, vel = y
+        return pos - self.r
+
+    def event_leave_ground(self, t, y):
+        """Event: Ball leaves ground (transition to free fall)"""
+        pos, vel = y
+        # Leave ground when position > r AND velocity > 0
+        if pos > self.r and vel > 0:
+            return 0
+        return 1
+
+    # Make events terminal to stop integration
+    event_contact_ground.terminal = True
+    event_leave_ground.terminal = True
+
+    def simulate(self, y0, t_span, max_transitions=20):
+        """
+        Simulate the hybrid system.
+
+        Parameters:
+        -----------
+        y0 : list
+            Initial state [position, velocity]
+        t_span : tuple
+            Time span (t_start, t_end)
+        max_transitions : int
+            Maximum number of state transitions to simulate
+
+        Returns:
+        --------
+        t_all : array
+            Time points
+        y_all : array
+            State trajectory
+        states : list
+            State labels ('free_fall' or 'spring_damper')
+        """
+        t_all = []
+        y_all = []
+        states = []
+
+        current_state = "free_fall" if y0[0] > self.r else "spring_damper"
+        current_y = y0
+        current_t = t_span[0]
+        t_end = t_span[1]
+
+        transitions = 0
+
+        while current_t < t_end and transitions < max_transitions:
+            if current_state == "free_fall":
+                # Integrate free fall until contact with ground
+                sol = solve_ivp(
+                    self.free_fall_dynamics,
+                    [current_t, t_end],
+                    current_y,
+                    events=self.event_contact_ground,
+                    dense_output=True,
+                    max_step=0.01,
+                )
+
+                # Store results
+                t_all.append(sol.t)
+                y_all.append(sol.y.T)
+                states.extend(["free_fall"] * len(sol.t))
+
+                # Check if event occurred
+                if sol.t_events[0].size > 0:
+                    # Transition to spring-damper
+                    current_state = "spring_damper"
+                    current_t = sol.t[-1]
+                    current_y = sol.y[:, -1]
+                    self.transition_times.append(current_t)
+                    transitions += 1
+                else:
+                    break
+
+            else:  # spring_damper
+                # Integrate spring-damper until leaving ground
+                sol = solve_ivp(
+                    self.spring_damper_dynamics,
+                    [current_t, t_end],
+                    current_y,
+                    events=self.event_leave_ground,
+                    dense_output=True,
+                    max_step=0.01,
+                )
+
+                # Store results
+                t_all.append(sol.t)
+                y_all.append(sol.y.T)
+                states.extend(["spring_damper"] * len(sol.t))
+
+                # Check if event occurred
+                if sol.t_events[0].size > 0:
+                    # Transition to free fall
+                    current_state = "free_fall"
+                    current_t = sol.t[-1]
+                    current_y = sol.y[:, -1]
+                    self.transition_times.append(current_t)
+                    transitions += 1
+                else:
+                    break
+
+        # Concatenate all results
+        t_all = np.concatenate(t_all)
+        y_all = np.vstack(y_all)
+
+        return t_all, y_all, states
+
+
+def plot_simulation(t, y, states, ball, show_phase=True):
+    """
+    Plot the simulation results.
+
+    Parameters:
+    -----------
+    t : array
+        Time points
+    y : array
+        State trajectory
+    states : list
+        State labels
+    ball : HybridBouncingBall
+        Ball object
+    show_phase : bool
+        Whether to show phase portrait
+    """
+    # Convert states to numeric for coloring
+    state_numeric = np.array([1 if s == "free_fall" else 2 for s in states])
+
+    if show_phase:
+        fig, axes = plt.subplots(2, 1, figsize=(8, 10))
+    else:
+        fig, axes = plt.subplots(2, 1, figsize=(12, 8))
+        axes = axes.reshape(-1, 1)
+
+    # Plot 1: Position vs Time
+    ax1 = axes[0] if show_phase else axes[0]
+    scatter = ax1.scatter(t, y[:, 0], c=state_numeric, s=1, cmap="coolwarm", alpha=0.6)
+    ax1.axhline(
+        y=ball.r,
+        color="k",
+        linestyle="--",
+        label=f"Ground contact (h={ball.r}m)",
+        linewidth=1,
+    )
+    ax1.axhline(
+        y=0, color="gray", linestyle="-", label="Ground level", linewidth=1, alpha=0.5
+    )
+
+    # Mark transitions
+    for t_trans in ball.transition_times:
+        ax1.axvline(x=t_trans, color="green", linestyle=":", alpha=0.3, linewidth=1)
+
+    ax1.set_xlabel("Time (s)", fontsize=11)
+    ax1.set_ylabel("Position (m)", fontsize=11)
+    ax1.set_title("Ball Position vs Time", fontsize=12, fontweight="bold")
+    ax1.grid(True, alpha=0.3)
+    ax1.legend(fontsize=9)
+
+    if show_phase:
+        # Plot 2: Vector Field / Phase Portrait
+        ax2 = axes[1]
+
+        # Create vector field grid
+        pos_range = np.linspace(0, max(y[:, 0]) * 1.1, 15)
+        vel_range = np.linspace(min(y[:, 1]) * 1.1, max(y[:, 1]) * 1.1, 15)
+        Pos, Vel = np.meshgrid(pos_range, vel_range)
+
+        # Calculate vector field
+        dPos = np.zeros_like(Pos)
+        dVel = np.zeros_like(Vel)
+
+        for i in range(Pos.shape[0]):
+            for j in range(Pos.shape[1]):
+                pos_val = Pos[i, j]
+                vel_val = Vel[i, j]
+
+                # Determine which dynamics to use
+                if pos_val > ball.r:
+                    # Free fall dynamics
+                    dPos[i, j] = vel_val
+                    dVel[i, j] = -ball.g
+                else:
+                    # Spring-damper dynamics
+                    dPos[i, j] = vel_val
+                    compression = ball.r - pos_val
+                    spring_force = ball.k * compression
+                    damping_force = ball.c * vel_val
+                    dVel[i, j] = (spring_force - damping_force - ball.m * ball.g) / ball.m
+
+        # Plot vector field with much smaller scale
+        ax2.quiver(Pos, Vel, dPos, dVel, alpha=0.3, color='gray', scale=300, width=0.003)
+
+        # Plot trajectory
+        scatter2 = ax2.scatter(
+            y[:, 0], y[:, 1], c=state_numeric, s=2, cmap="coolwarm", alpha=0.7
+        )
+        ax2.axvline(
+            x=ball.r, color="k", linestyle="--", label=f"Contact threshold", linewidth=1.5
+        )
+        ax2.axhline(y=0, color="gray", linestyle="-", linewidth=1, alpha=0.5)
+        ax2.set_xlabel("Position (m)", fontsize=11)
+        ax2.set_ylabel("Velocity (m/s)", fontsize=11)
+        ax2.set_title("Vector Field & Phase Portrait", fontsize=12, fontweight="bold")
+        ax2.grid(True, alpha=0.3)
+        ax2.legend(fontsize=9)
+
+    plt.tight_layout()
+    return fig
+
+
+if __name__ == "__main__":
+    # Create ball with specific parameters
+    ball = HybridBouncingBall(
+        m=0.10,  # 1 kg mass
+        r=0.1,  # 10 cm radius
+        g=9.81,  # Earth gravity
+        k=500.0,  # Spring constant
+        c=0.89,  # Damping coefficient
+    )
+
+    # Initial conditions: drop from 2 meters with zero velocity
+    y0 = [1.0, 0.0]  # [position (m), velocity (m/s)]
+
+    # Simulate for 5 seconds
+    t_span = (0, 5.0)
+
+    print("Simulating hybrid bouncing ball system...")
+    print(f"Initial conditions: h0 = {y0[0]} m, v0 = {y0[1]} m/s")
+    print(
+        f"Ball parameters: m={ball.m} kg, r={ball.r} m, k={ball.k} N/m, c={ball.c} N·s/m"
+    )
+    print()
+
+    t, y, states = ball.simulate(y0, t_span, max_transitions=30)
+
+    print(f"Simulation complete!")
+    print(f"Total time simulated: {t[-1]:.3f} s")
+    print(f"Number of state transitions: {len(ball.transition_times)}")
+    print(f"Transition times: {[f'{tt:.3f}' for tt in ball.transition_times[:10]]}")
+    print()
+
+    # Count time in each state
+    free_fall_count = states.count("free_fall")
+    spring_damper_count = states.count("spring_damper")
+    total_points = len(states)
+
+    print(f"Time distribution:")
+    print(f"  Free fall: {free_fall_count/total_points*100:.1f}%")
+    print(f"  Spring-damper: {spring_damper_count/total_points*100:.1f}%")
+
+    # Plot results
+    fig = plot_simulation(t, y, states, ball, show_phase=True)
+    plt.savefig(
+        "/home/danesabo/Documents/Dane's Vault/Presentations/ERLM/bouncing_ball_hybrid.png",
+        dpi=300,
+        bbox_inches="tight",
+    )
+    print(f"\nPlot saved to: bouncing_ball_hybrid.png")
+    plt.show()
--- a/Presentations/20251215-Emerson-Pres/images/.DS_Store
+++ b/Presentations/20251215-Emerson-Pres/images/.DS_Store
--- a/Presentations/20251215-Emerson-Pres/images/1_hook/energy-demand-graph-small.png
+++ b/Presentations/20251215-Emerson-Pres/images/1_hook/energy-demand-graph-small.png
--- a/Presentations/20251215-Emerson-Pres/images/1_hook/foreman.png
+++ b/Presentations/20251215-Emerson-Pres/images/1_hook/foreman.png
--- a/Presentations/20251215-Emerson-Pres/images/1_hook/nuclear-plant.png
+++ b/Presentations/20251215-Emerson-Pres/images/1_hook/nuclear-plant.png
--- a/Presentations/20251215-Emerson-Pres/images/1_hook/worker.png
+++ b/Presentations/20251215-Emerson-Pres/images/1_hook/worker.png
--- a/Presentations/20251215-Emerson-Pres/images/2_state_of_the_art/control_room.jpg
+++ b/Presentations/20251215-Emerson-Pres/images/2_state_of_the_art/control_room.jpg
--- a/Presentations/20251215-Emerson-Pres/images/2_state_of_the_art/foreman.png
+++ b/Presentations/20251215-Emerson-Pres/images/2_state_of_the_art/foreman.png
--- a/Presentations/20251215-Emerson-Pres/images/2_state_of_the_art/nuclear-plant.png
+++ b/Presentations/20251215-Emerson-Pres/images/2_state_of_the_art/nuclear-plant.png
--- a/Presentations/20251215-Emerson-Pres/images/2_state_of_the_art/worker.png
+++ b/Presentations/20251215-Emerson-Pres/images/2_state_of_the_art/worker.png
--- a/Presentations/20251215-Emerson-Pres/images/3_limitations/computer.png
+++ b/Presentations/20251215-Emerson-Pres/images/3_limitations/computer.png
--- a/Presentations/20251215-Emerson-Pres/images/3_limitations/foreman.png
+++ b/Presentations/20251215-Emerson-Pres/images/3_limitations/foreman.png
--- a/Presentations/20251215-Emerson-Pres/images/3_limitations/nuclear.png
+++ b/Presentations/20251215-Emerson-Pres/images/3_limitations/nuclear.png
--- a/Presentations/20251215-Emerson-Pres/images/3_limitations/test.png
+++ b/Presentations/20251215-Emerson-Pres/images/3_limitations/test.png
--- a/Presentations/20251215-Emerson-Pres/images/3_limitations/worker.png
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--- a/Presentations/20251215-Emerson-Pres/main.out
+++ b/Presentations/20251215-Emerson-Pres/main.out
--- a/Presentations/20251215-Emerson-Pres/main.pdf
+++ b/Presentations/20251215-Emerson-Pres/main.pdf
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+% !TEX program = lualatex
+% Formally Verified Autonomous Hybrid Control for Nuclear Reactors
+% A presentation arguing for formally assured autonomous control
+
+\documentclass[14pt]{beamer}
+\usepackage[T1]{fontenc}
+\usepackage{booktabs}
+\usepackage{colortbl}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{tikz}
+% TikZ libraries
+\usetikzlibrary{shapes,arrows,positioning,fit,backgrounds,calc}
+\usepackage{caption}
+\captionsetup[figure]{font=scriptsize}
+
+\title{Formally Verified Autonomous Hybrid Control}
+\subtitle{Enabling Economic Viability of Next-Generation Nuclear Power}
+\date{\today}
+\author[Dane A. Sabo]{%
+  \texorpdfstring{\textbf{Dane A. Sabo}}{Dane A. Sabo}%
+  \texorpdfstring{\\}{ }%
+  \texorpdfstring{\small{dane.sabo@pitt.edu}}{dane.sabo@pitt.edu}%
+  \texorpdfstring{\\}{ }%
+  \texorpdfstring{\vspace{0.25cm}}{}%
+  \texorpdfstring{\textbf{Dr. Daniel G. Cole}}{Dr. Daniel G. Cole}%
+  \texorpdfstring{\\}{ }%
+  \texorpdfstring{\small{dgcole@pitt.edu}}{dgcole@pitt.edu}%
+}
+
+\institute{University of Pittsburgh}
+
+% Fix hyperref PDF metadata warnings
+\hypersetup{
+  pdfauthor={Dane A. Sabo},
+  pdftitle={Formally Verified Autonomous Hybrid Control: Enabling Economic Viability of Next-Generation Nuclear Power}
+}
+
+%DEFINE TOGGLES!
+\def\darkmode{1}
+\def\notemode{0}
+\def\gridmode{0}
+%
+
+% Add theme folder to search path
+\makeatletter
+\def\input@path{{theme/}}
+\makeatother
+
+\usetheme{dane_native}
+
+\begin{document}
+
+\begin{frame}
+  \titlepage
+\end{frame}
+
+\input{slides/1_Hook_v2}
+\input{slides/2_State_of_the_Art_v2}
+\input{slides/3_Limitations_v2}
+\input{slides/4_Research_Approach_v2}
+\input{slides/5_Metrics_of_Success_v2}
+\input{slides/7_Broader_Impacts_v3}
+\input{slides/8_Money_Slide_v2}
+
+%Supplemenatry
+% \input{slides/6_Risks_and_Contingencies_v2}
+
+\end{document}
--- a/Presentations/20251215-Emerson-Pres/main.toc
+++ b/Presentations/20251215-Emerson-Pres/main.toc
--- a/Presentations/20251215-Emerson-Pres/phase_portrait_sg1.png
+++ b/Presentations/20251215-Emerson-Pres/phase_portrait_sg1.png
--- a/Presentations/20251215-Emerson-Pres/presentation-outline.md
+++ b/Presentations/20251215-Emerson-Pres/presentation-outline.md
@ -0,0 +1,370 @@
+# Presentation Outline: Formally Verified Autonomous Hybrid Control for Nuclear Reactors
+
+**Audience:** Engineering PhDs (not necessarily control, nuclear, or formal methods experts)
+
+**Presentation Style:** Assertion-Evidence
+
+---
+
+## 0. Title Slide
+**Assertion:** Autonomous Hybrid Control with Formal Safety Guarantees Enables Economic Viability of Next-Generation Nuclear Power
+
+**Content:**
+- Your name, affiliation
+- Brief subtitle about bridging formal methods and control theory
+
+---
+
+## 2. The Economic Challenge
+**Assertion:** Small modular reactors face an unsustainable staffing cost problem that threatens their economic viability
+
+**Evidence:**
+- Comparison chart: staffing costs per MW for conventional vs SMR
+- Current requirement: 2+ ROs + 1 SRO per reactor
+- Training timeline: up to 6 years to become a reactor operator
+- Cost breakdown showing O&M as 23-30% of levelized cost
+- Projected datacenter demand reaching 1,050 TWh by 2030 = $21-28B annually in O&M
+
+**Key Message:** Automation is not optional—it's economically essential
+
+---
+
+## 3. The Safety Imperative
+**Assertion:** Human operators are the root cause of 70-80% of nuclear incidents despite decades of training improvements
+
+**Evidence:**
+- Bar chart: 70-80% human error vs 20% equipment failure
+- IAEA statement: "Human error was the root cause of all severe accidents"
+- TMI case study visualization:
+  - 100+ simultaneous alarms
+  - 44% core meltdown
+  - 500-fold underestimation of risk
+- Human Error Probability table showing degradation under stress:
+  - Optimal: 0.001-0.01
+  - Under accident conditions: 0.1-1.0 (essentially guaranteed failure)
+
+**Key Message:** Training alone cannot overcome fundamental cognitive limitations
+
+---
+
+## 4. The Paradox
+**Assertion:** Nuclear control faces a fundamental tension—human operators are both essential for flexibility and the primary source of failure
+
+**Evidence:**
+- Two-column comparison:
+  - LEFT: "Why we need humans" (judgment, adaptability, procedure interpretation)
+  - RIGHT: "Why humans fail" (cognitive limits, stress, 7±2 working memory, response time: seconds vs milliseconds)
+- Current division of labor diagram:
+  - Automated: Emergency protection (trip systems, ECCS)
+  - Manual: Strategic operations (startup, mode transitions, power changes)
+- Quote from TMI Commission about "ambiguity in responsibility"
+
+**Key Message:** We need the reliability of automation with the sophistication of human decision-making
+
+---
+
+## 5. What Are Hybrid Control Systems?
+**Assertion:** Hybrid systems combine continuous dynamics with discrete mode switching—exactly how nuclear plants operate
+
+**Evidence:**
+- Simple equations showing hybrid dynamics:
+  - Continuous: ẋ(t) = f(x(t), q(t), u(t))
+  - Discrete: q(k+1) = ν(x(k), q(k), u(k))
+- Intuitive example diagram: Nuclear reactor startup
+  - Mode 1 (Cold Shutdown): Temperature control
+  - Transition condition: T > 400°F
+  - Mode 2 (Heatup): Ramp rate control
+  - Transition condition: Approach criticality
+  - Mode 3 (Low Power): Neutron flux control
+- Contrast with pure continuous (traditional control) and pure discrete (software)
+
+**Key Message:** Nuclear operations are inherently hybrid—continuous physics with discrete strategic decisions
+
+---
+
+## 6. The Gap in Current Approaches
+**Assertion:** Existing methods can handle either continuous dynamics or discrete logic, but not both with formal guarantees
+
+**Evidence:**
+- Venn diagram showing the gap:
+  - Circle 1: Formal Methods (HARDENS) → Discrete logic verification ✓, Continuous dynamics ✗
+  - Circle 2: Control Theory → Continuous stability ✓, Discrete transitions ✗
+  - Gap in middle: Hybrid system verification
+- HARDENS achievement summary:
+  - Complete RTS verification in 9 months
+  - Requirements → verified binaries
+  - BUT: No continuous dynamics, no closed-loop verification
+  - TRL 3-4, no experimental validation
+
+**Key Message:** We can verify half the system with existing tools—we need to bridge the gap
+
+---
+
+## 7. Our Three-Thrust Approach
+**Assertion:** Unifying discrete synthesis and continuous verification enables end-to-end correctness guarantees for hybrid systems
+
+**Evidence:**
+- Pipeline diagram with three stages:
+
+  **Thrust 1:** Procedures → Temporal Logic (FRET)
+  - Input: Written procedures
+  - Tool: NASA FRET (FRETish language)
+  - Output: LTL specifications
+  - Key feature: Realizability checking
+
+  **Thrust 2:** Temporal Logic → Discrete Automaton (Reactive Synthesis)
+  - Input: LTL specifications
+  - Tool: Strix (reactive synthesis)
+  - Output: Discrete state machine
+  - Key feature: Correct by construction
+
+  **Thrust 3:** Continuous Controllers + Verification
+  - Input: Discrete automaton + plant model
+  - Tools: Reachability analysis, barrier certificates
+  - Output: Verified continuous modes
+  - Key feature: Compositional verification
+
+**Key Message:** Each piece uses state-of-the-art tools; innovation is in the integration
+
+---
+
+## 8. Thrust 1: From Procedures to Logic
+**Assertion:** NASA's FRET tool systematically translates written procedures into unambiguous temporal logic specifications
+
+**Evidence:**
+- Side-by-side example:
+  - LEFT: Natural language: "If a high temperature alarm triggers, control rods must immediately insert and remain inserted until operator reset"
+  - RIGHT: Temporal logic: G(HighTemp → X(RodsInserted ∧ (¬RodsWithdrawn U OperatorReset)))
+- FRETish structure diagram showing 6 required components:
+  - Scope | Condition | Component | Shall | Timing | Response
+- Realizability checking benefits:
+  - Detects conflicting requirements
+  - Identifies undefined behaviors
+  - Finds "bugs" in procedures before implementation
+
+**Key Message:** FRET bridges human-readable procedures and machine-verifiable specifications
+
+---
+
+## 9. Thrust 2: Synthesizing Discrete Controllers
+**Assertion:** Reactive synthesis automatically generates provably correct discrete switching logic from temporal specifications
+
+**Evidence:**
+- What is reactive synthesis? Simple explanation:
+  - Input: Temporal logic formula (what should happen)
+  - Output: State machine (how to make it happen)
+  - Guarantee: If a solution exists, it is correct by construction
+- Example automaton visualization for reactor mode transitions
+  - Nodes: Cold Shutdown, Heatup, Low Power, Full Power, SCRAM
+  - Edges: Transition conditions
+  - Highlight: This is the "operator's decision-making" automated
+- Strix tool performance (SYNTCOMP winner)
+
+**Key Message:** The discrete controller is mathematically guaranteed to follow procedures—no switching errors possible
+
+---
+
+## 10. Thrust 3: Continuous Mode Verification
+**Assertion:** Continuous controllers are verified using three complementary techniques that avoid global trajectory analysis
+
+**Evidence:**
+- Three types of continuous modes based on transition objectives:
+  - **Stabilizing:** Stay in current mode (e.g., full-power operation)
+  - **Transitory:** Drive toward next mode (e.g., startup heatup)
+  - **Expulsory:** Force to safe mode (e.g., SCRAM)
+- Three verification techniques:
+
+  1. **Reachability Analysis:**
+     - Computes reachable state sets
+     - Verifies boundary conditions are met
+     - Recent advances: Neural Hamilton-Jacobi for high dimensions
+
+  2. **Assume-Guarantee Contracts:**
+     - Each mode verified with input/output bounds
+     - Compositional: local verification, global guarantees
+
+  3. **Barrier Certificates:**
+     - Proves safe set forward invariance
+     - Guarantees transitions occur correctly
+     - Ensures stability across mode switches
+
+**Key Message:** Local verification of each mode is tractable; composition ensures global correctness
+
+---
+
+## 11. Why This Works: The Key Insight
+**Assertion:** Designing continuous controllers after synthesizing the discrete automaton enables local verification instead of intractable global analysis
+
+**Evidence:**
+- Problem with traditional approach:
+  - Design everything at once
+  - Verify entire trajectory through all modes
+  - Computationally intractable for complex systems
+- Our approach:
+  - Discrete automaton defines transition boundaries
+  - Design each continuous mode to satisfy its local transitions
+  - Use assume-guarantee to chain modes together
+  - Barrier certificates prove transitions are safe
+- Diagram showing modular verification:
+  - Each mode verified independently
+  - Interface contracts guarantee composition
+  - Total system correctness follows from local proofs
+
+**Key Message:** Decomposition is the key to tractable verification
+
+---
+
+## 12. Demonstration: SmAHTR Startup
+**Assertion:** Autonomous startup of a Small Modular Advanced High Temperature Reactor provides a rigorous test case spanning multiple coordinated modes
+
+**Evidence:**
+- Why SmAHTR?
+  - Well-documented startup procedures
+  - Multiple distinct operational modes
+  - Complex thermal-hydraulics + neutron kinetics
+  - Representative of next-gen reactor designs
+- Startup sequence complexity:
+  - Cold conditions → Controlled heating → Approach criticality → Low-power physics → Full power
+  - Multiple coordinated subsystems
+  - Strict timing and temperature constraints
+- Implementation platform:
+  - High-fidelity Simulink model (thermal-hydraulics + neutron kinetics)
+  - Emerson Ovation control hardware (industry standard)
+  - ARCADE integration (hardware-in-the-loop)
+  - Real-time performance validation
+
+**Key Message:** This is not a toy problem—it's representative of actual deployment challenges
+
+---
+
+## 13. Expected Outcomes
+**Assertion:** Success will be measured by progression to TRL 5, demonstrating practical feasibility beyond theoretical proof
+
+**Evidence:**
+- TRL progression chart:
+  - Starting point: TRL 2-3 (basic concepts, HARDENS as precedent)
+  - Target: TRL 5 (validated prototype in relevant environment)
+  - Gap: Experimental validation with continuous dynamics
+- Three concrete deliverables:
+
+  **Outcome 1:** Procedure translation methodology
+  - Engineers can generate verified controllers from regulatory procedures
+  - No formal methods expertise required
+
+  **Outcome 2:** Continuous verification framework
+  - Standard control design + iterative verification
+  - Proof of safe mode transitions
+
+  **Outcome 3:** SmAHTR demonstration
+  - Autonomous startup on industrial hardware
+  - Hardware-in-the-loop validation
+  - Path to deployment
+
+**Key Message:** TRL 5 proves both theoretical validity and practical implementability
+
+---
+
+## 14. Broader Impact: Beyond Nuclear
+**Assertion:** This methodology generalizes to any safety-critical hybrid system with documented operational procedures
+
+**Evidence:**
+- Common pattern across domains:
+  - Written procedures exist
+  - Continuous dynamics + discrete decisions
+  - Safety is paramount
+  - Autonomy has economic benefits
+- Application domains table:
+  - Chemical process control (batch processes, safety interlocks)
+  - Aerospace (flight phases, emergency procedures)
+  - Autonomous transportation (driving modes, emergency maneuvers)
+  - Medical devices (therapy modes, patient monitoring)
+- Economic multiplier:
+  - Nuclear O&M: $21-28B annually (projected datacenter demand alone)
+  - Broader safety-critical infrastructure: Much larger
+- Regulatory pathway:
+  - Proving concept in nuclear (highest safety bar)
+  - Establishes precedent for other industries
+  - Mathematical proof as regulatory evidence
+
+**Key Message:** Nuclear is the proving ground; impact extends far beyond
+
+---
+
+## 15. Innovation Summary
+**Assertion:** The innovation is not in individual techniques but in their systematic integration to bridge a fundamental gap in cyber-physical systems
+
+**Evidence:**
+- What's NOT new (but state-of-the-art):
+  - Temporal logic and reactive synthesis (computer science)
+  - Reachability analysis and barrier certificates (control theory)
+  - Hardware-in-the-loop validation (industry practice)
+- What IS new:
+  - **Integration:** Unifying discrete and continuous verification
+  - **Methodology:** Systematic tool-supported workflow from procedures to verified controller
+  - **Decomposition:** Local verification with compositional guarantees
+  - **Practical:** Targets existing industrial hardware (Emerson Ovation)
+- Comparison to HARDENS:
+  - HARDENS: Discrete only, TRL 3-4, no continuous dynamics
+  - This work: Full hybrid system, TRL 5, hardware-in-the-loop
+- Key enabling insight:
+  - Automaton-first design enables tractable continuous verification
+
+**Key Message:** Standing on the shoulders of giants to solve a previously intractable problem
+
+---
+
+## 16. Timeline and Feasibility
+**Assertion:** This research is feasible within a PhD timeline given existing tools, models, and infrastructure access
+
+**Evidence:**
+- Existing infrastructure:
+  - University of Pittsburgh Cyber Energy Center
+  - Emerson control hardware access
+  - SmAHTR Simulink model already developed
+  - ARCADE platform operational
+  - Industry collaboration channels
+- Tool maturity:
+  - FRET: Production-ready (NASA JPL)
+  - Strix: Competition-winning synthesis tool
+  - Reachability tools: Recent advances make high-dimensional systems tractable
+- Risk mitigation:
+  - Start with simpler mode sequences, add complexity incrementally
+  - Extensive simulation before hardware-in-the-loop
+  - Fallback: Manual continuous controller design if synthesis proves intractable
+- Precedent: HARDENS achieved similar scope in 9 months
+
+**Key Message:** Ambitious but achievable with existing resources and tools
+
+---
+
+## 17. Conclusion: The Path Forward
+**Assertion:** Formally verified autonomous hybrid control is essential for next-generation nuclear power and provides a template for broader safety-critical autonomy
+
+**Evidence:**
+- Three converging imperatives:
+  1. **Economic:** SMRs need autonomy to be viable ($21-28B annual O&M for datacenter demand)
+  2. **Safety:** Human error causes 70-80% of incidents; training can't fix cognitive limits
+  3. **Technical:** Tools now exist to verify hybrid systems; HARDENS proved discrete is feasible
+- This research closes the gap:
+  - HARDENS + Continuous Verification = Complete Hybrid System
+  - Theory + Hardware-in-the-Loop = TRL 5
+  - Nuclear Demonstration = Pathway for broader adoption
+- Vision: Control engineers generate high-assurance autonomous controllers from procedures
+  - No formal methods PhD required
+  - Mathematical proof of correctness included
+  - Deployable on existing industrial hardware
+
+**Key Message:** The pieces exist; we're putting them together at the right time for the right application
+
+---
+
+## 18. Questions
+**Assertion:** (Keep a few backup slides here for common questions)
+
+Potential backup slides:
+- Detailed FRET example
+- Reactive synthesis algorithm overview
+- Reachability analysis visualization
+- Comparison with other autonomy approaches (ML, MPC, etc.)
+- Regulatory acceptance pathway
+- Scalability to larger systems
--- a/Presentations/20251215-Emerson-Pres/sections/01_title.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/01_title.tex
@ -0,0 +1,39 @@
+% Title slide
+\begin{frame}
+  \titlepage
+\end{frame}
+
+% Roadmap slide
+\begin{frame}{Roadmap}
+  \textbf{Central Thesis:} Formally verified autonomous hybrid control is both \emph{necessary} and \emph{achievable} for next-generation nuclear power.
+
+  \vspace{0.5cm}
+
+  \begin{enumerate}
+    \item \textbf{The Problem:} Why we need autonomous control
+    \begin{itemize}
+      \item Economic challenge of small modular reactors
+      \item Fundamental human reliability limits
+    \end{itemize}
+
+    \vspace{0.3cm}
+
+    \item \textbf{The Technical Challenge:} What's missing
+    \begin{itemize}
+      \item Hybrid systems: continuous + discrete
+      \item Existing methods address only half the problem
+    \end{itemize}
+
+    \vspace{0.3cm}
+
+    \item \textbf{The Solution:} How we'll solve it
+    \begin{itemize}
+      \item Three-thrust approach with formal guarantees
+      \item Hardware-in-the-loop demonstration
+    \end{itemize}
+
+    \vspace{0.3cm}
+
+    \item \textbf{The Impact:} Why it matters beyond nuclear
+  \end{enumerate}
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/02_economic_challenge.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/02_economic_challenge.tex
@ -0,0 +1,32 @@
+% Economic Challenge
+\begin{frame}{Small modular reactors face an unsustainable staffing cost problem}
+
+  \begin{center}
+    \begin{tikzpicture}
+      \draw[thick, fill=gray!20] (0,0) rectangle (12,6);
+      \node[align=center, text width=10cm] at (6,3) {
+        \textbf{FIGURE: Staffing Cost Comparison}\\[0.3cm]
+        Bar chart showing:\\
+        - Conventional reactor: lower \$/MW staffing\\
+        - SMR: higher \$/MW staffing\\[0.3cm]
+        Highlight: Same overhead, less output\\
+        \$21--28B annual market opportunity
+      };
+    \end{tikzpicture}
+  \end{center}
+
+\end{frame}
+
+% SPEAKER NOTES:
+% The Economic Reality:
+%   - Current requirement: 2+ ROs + 1+ SRO per unit
+%   - Training: up to 6 years
+%   - SMRs have same overhead but lower output
+%   - Result: Higher $/MW O&M costs threaten viability
+%
+% The Market Opportunity:
+%   - Datacenter demand: 1,050 TWh annually by 2030
+%   - Nuclear O&M: 23-30% of levelized cost ($88.24/MWh)
+%   - Annual O&M for datacenter demand alone: $21-28 billion
+%
+% Key message: Automation is not optional---it's economically essential
--- a/Presentations/20251215-Emerson-Pres/sections/03_safety_imperative.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/03_safety_imperative.tex
@ -0,0 +1,43 @@
+% Safety Imperative
+\begin{frame}{Human operators are the root cause of 70--80\% of nuclear incidents}
+
+  \begin{center}
+    \begin{tikzpicture}
+      \draw[thick, fill=gray!20] (0,0) rectangle (12,7);
+      \node[align=center, text width=10cm] at (6,3.5) {
+        \textbf{FIGURE: Human Error Statistics}\\[0.3cm]
+        Top: Pie chart showing 70--80\% human error\\
+        vs 20\% equipment failure\\[0.3cm]
+        Middle: TMI timeline visualization\\
+        100+ alarms $\rightarrow$ operator confusion $\rightarrow$ 44\% meltdown\\[0.3cm]
+        Bottom: Human Error Probability chart\\
+        HEP: 0.001 (optimal) $\rightarrow$ 1.0 (accident conditions)\\
+        Stress factors multiply error rates 10-50x
+      };
+    \end{tikzpicture}
+  \end{center}
+
+  %SPEAKER NOTES: See comments below
+%
+    \textbf{The Human Error Problem:}
+    \begin{itemize}
+      \item 70--80\% of events attributed to human error (multiple independent analyses)
+      \item IAEA: ``Human error was the root cause of ALL severe accidents'' (TMI, Chernobyl, Fukushima)
+    \end{itemize}
+
+    \textbf{Three Mile Island (1979):}
+    \begin{itemize}
+      \item 100+ simultaneous alarms overwhelmed operators
+      \item Operators shut down emergency cooling based on incorrect assessment
+      \item Result: 44\% of fuel melted
+      \item Risk assessment was off by 500-fold (5\% actual vs 0.01\% predicted)
+    \end{itemize}
+
+    \textbf{Fundamental Cognitive Limitations:}
+    \begin{itemize}
+      \item Working memory: 7±2 items (Miller, 1956)
+      \item HEP: 0.001--0.01 optimal $\rightarrow$ 0.1--1.0 under accident conditions
+      \item Four decades of training improvements haven't changed the 70--80\% ratio
+    \end{itemize}
+% (End of speaker notes)
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/04_the_paradox.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/04_the_paradox.tex
@ -0,0 +1,37 @@
+% The Paradox
+\begin{frame}{Nuclear control faces a fundamental tension}
+
+  \begin{center}
+    \begin{tikzpicture}
+      \draw[thick, fill=gray!20] (0,0) rectangle (12,7);
+      \node[align=center, text width=10cm] at (6,3.5) {
+        \textbf{FIGURE: The Human Paradox}\\[0.3cm]
+        Split diagram:\\[0.2cm]
+        LEFT side (green): Why we need humans\\
+        (judgment, flexibility, novel situations)\\[0.2cm]
+        RIGHT side (red): Why humans fail\\
+        (7±2 memory, seconds vs ms, biases, stress)\\[0.3cm]
+        Bottom: Current division of labor\\
+        Automated = Terminal ops | Manual = Routine ops\\[0.2cm]
+        Arrow pointing to gap: \textbf{This is backwards!}
+      };
+    \end{tikzpicture}
+  \end{center}
+
+  %SPEAKER NOTES: See comments below
+%
+    \textbf{The Paradox:} Human operators are both essential for flexibility and the primary source of failure
+
+    \textbf{Why We Need Humans:}
+    Strategic decision-making, procedure interpretation, handling novel situations, adaptive judgment, legal authority (10 CFR 55)
+
+    \textbf{Why Humans Fail:}
+    Working memory: 7±2 items, response time: seconds vs milliseconds, cognitive biases (confirmation, anchoring), stress degrades performance 10-50x, error rates: 0.001 → 1.0 under accident conditions
+
+    \textbf{Current Division:}
+    Automated = Emergency protection (trip systems, ECCS) --- terminal operations;
+    Manual = Strategic operations (startup, mode transitions, power changes) --- routine operations
+
+    \textbf{Goal:} Reliability of automation with sophistication of human decision-making
+% (End of speaker notes)
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/05_hybrid_systems.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/05_hybrid_systems.tex
@ -0,0 +1,35 @@
+% Hybrid Systems
+\begin{frame}{Hybrid systems combine continuous dynamics with discrete mode switching}
+
+  \begin{center}
+    \begin{tikzpicture}
+      \draw[thick, fill=gray!20] (0,0) rectangle (12,7);
+      \node[align=center, text width=10cm] at (6,3.5) {
+        \textbf{FIGURE: Hybrid System Visualization}\\[0.3cm]
+        Top: Split diagram\\
+        LEFT: Continuous (temp, flux, pressure curves)\\
+        Equation: $\dot{x}(t) = f(x(t), q(t), u(t))$\\[0.2cm]
+        RIGHT: Discrete (state machine diagram)\\
+        Equation: $q(k+1) = \nu(x(k), q(k), u(k))$\\[0.3cm]
+        Bottom: Reactor startup state machine\\
+        Cold $\xrightarrow{T>400°F}$ Heatup $\xrightarrow{\text{near crit}}$ Crit $\rightarrow$ Power\\
+        Each box shows continuous dynamics within
+      };
+    \end{tikzpicture}
+  \end{center}
+
+  %SPEAKER NOTES: See comments below
+%
+    \textbf{Nuclear plants are inherently hybrid systems}
+
+    \textbf{Continuous Dynamics:} Reactor temperature, neutron flux, pressure, flow rates, heat transfer.
+    Governed by differential equations: $\dot{x}(t) = f(x(t), q(t), u(t))$
+
+    \textbf{Discrete Decisions:} Mode transitions, control strategy changes, safety system actuation, procedure steps.
+    Governed by logic: $q(k+1) = \nu(x(k), q(k), u(k))$
+
+    \textbf{Example:} Reactor startup: Cold Shutdown → Heatup → Approach Criticality → Low Power
+    Each mode has continuous dynamics; transitions are discrete strategic decisions.
+    This is exactly what human operators do today.
+% (End of speaker notes)
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/06_current_gaps.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/06_current_gaps.tex
@ -0,0 +1,50 @@
+% Current Gaps
+\begin{frame}{Existing methods can handle either continuous or discrete, but not both}
+
+  \begin{center}
+    \begin{tikzpicture}[scale=0.9, transform shape]
+      % Formal Methods circle
+      \draw[thick, fill=red!20, opacity=0.7] (-2,0) circle (2.5cm);
+      \node at (-2, 2) {\textbf{Formal Methods}};
+      \node at (-2, 1.2) {\small (HARDENS)};
+      \node[align=center, font=\small] at (-2, 0.3) {
+        Discrete \checkmark
+      };
+      \node[align=center, font=\small, text=red] at (-2, -0.5) {
+        Continuous \textbf{$\times$}
+      };
+
+      % Control Theory circle
+      \draw[thick, fill=blue!20, opacity=0.7] (2,0) circle (2.5cm);
+      \node at (2, 2) {\textbf{Control Theory}};
+      \node[align=center, font=\small] at (2, 0.3) {
+        Continuous \checkmark
+      };
+      \node[align=center, font=\small, text=red] at (2, -0.5) {
+        Discrete \textbf{$\times$}
+      };
+
+      % The Gap
+      \node[align=center, font=\Large, text=orange] at (0, -3) {
+        \textbf{THE GAP}
+      };
+    \end{tikzpicture}
+  \end{center}
+
+  %SPEAKER NOTES: See comments below
+%
+    \textbf{Formal Methods (HARDENS):}
+    Can verify discrete logic (requirements → verified binaries). Achieved in 9 months, low cost.
+    But: Cannot handle continuous dynamics.
+
+    \textbf{Control Theory:}
+    Can verify continuous stability (Lyapunov, LQR, robust control).
+    But: Cannot verify discrete transitions or mode switching.
+
+    \textbf{THE GAP:} Hybrid system verification with formal guarantees spanning both continuous and discrete.
+
+    \textbf{HARDENS Achievement:} Complete RTS verification (discrete only), TRL 3-4, no experimental validation.
+
+    \textbf{We need to bridge this gap.}
+% (End of speaker notes)
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/07_approach_overview.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/07_approach_overview.tex
@ -0,0 +1,60 @@
+% Approach Overview
+\begin{frame}{Unifying discrete synthesis and continuous verification enables end-to-end guarantees}
+
+  \begin{center}
+    \begin{tikzpicture}[node distance=1.5cm, auto, scale=0.85, transform shape]
+      \tikzstyle{box} = [rectangle, rounded corners, minimum width=3.5cm, minimum height=1.2cm, text centered, draw=black, fill=blue!20, font=\small]
+      \tikzstyle{arrow} = [->, >=stealth, very thick]
+      \tikzstyle{tool} = [font=\tiny, text=green!50!black]
+
+      % Thrust 1
+      \node[box] (proc) {Procedures};
+      \node[box, right=of proc] (ltl) {Temporal\\Logic};
+      \draw[arrow] (proc) -- node[above] {\textbf{Thrust 1}} (ltl);
+      \node[tool, below=0.1cm of ltl] {FRET};
+
+      % Thrust 2
+      \node[box, right=of ltl] (auto) {Discrete\\Automaton};
+      \draw[arrow] (ltl) -- node[above] {\textbf{Thrust 2}} (auto);
+      \node[tool, below=0.1cm of auto] {Synthesis};
+
+      % Thrust 3
+      \node[box, right=of auto] (cont) {Continuous\\Modes};
+      \draw[arrow] (auto) -- node[above] {\textbf{Thrust 3}} (cont);
+      \node[tool, below=0.1cm of cont] {Reachability};
+    \end{tikzpicture}
+  \end{center}
+
+  \vspace{0.5cm}
+
+  \begin{center}
+    \begin{tikzpicture}
+      \draw[thick, fill=gray!20] (0,0) rectangle (12,3);
+      \node[align=center, text width=10cm] at (6,1.5) {
+        \textbf{FIGURE: Detailed Pipeline Diagram}\\[0.2cm]
+        Show example flowing through all three thrusts\\
+        with visual representations of transformations
+      };
+    \end{tikzpicture}
+  \end{center}
+
+  %SPEAKER NOTES: See comments below
+%
+    \textbf{Three-Thrust Integrated Approach:}
+
+    \textbf{Thrust 1 (Procedures → Temporal Logic):}
+    Use NASA FRET to translate written procedures to formal specifications.
+    Example: ``If high temp, insert rods until reset'' becomes $G(T_{high} \rightarrow X(\text{rods} \wedge \ldots))$
+    Realizability checking catches errors in procedures before implementation.
+
+    \textbf{Thrust 2 (Temporal Logic → Discrete Automaton):}
+    Reactive synthesis generates correct-by-construction state machine.
+    Discrete controller is mathematically guaranteed to follow specifications.
+
+    \textbf{Thrust 3 (Continuous Controllers):}
+    Use reachability analysis and barrier certificates.
+    Compositional verification: local proofs, global guarantees.
+
+    \textbf{Innovation:} Each piece uses state-of-the-art tools; innovation is in the integration.
+% (End of speaker notes)
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/08_thrust1_procedures.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/08_thrust1_procedures.tex
@ -0,0 +1,40 @@
+% Thrust 1: Procedures to Logic
+\begin{frame}{Thrust 1: NASA's FRET tool translates procedures into unambiguous logic}
+
+  \begin{center}
+    \begin{tikzpicture}[node distance=2cm, auto]
+      \tikzstyle{box} = [rectangle, rounded corners, minimum width=7cm, minimum height=1.2cm, text centered, draw=black, font=\small]
+
+      \node[box, fill=yellow!20] (nl) {
+        Natural Language (Procedure)
+      };
+
+      \node[box, fill=green!20, below=of nl] (tl) {
+        Temporal Logic Formula
+      };
+
+      \draw[->, >=stealth, very thick] (nl) -- node[right] {FRET} (tl);
+    \end{tikzpicture}
+  \end{center}
+
+  \vspace{0.5cm}
+
+  \begin{center}
+    \begin{tikzpicture}
+      \draw[thick, fill=gray!20] (0,0) rectangle (12,3.5);
+      \node[align=center, text width=10cm] at (6,1.75) {
+        \textbf{FIGURE: FRET Interface Screenshot/Mockup}\\[0.2cm]
+        Show FRETish structured input:\\
+        [Scope] [Condition] [Component] SHALL [Timing] [Response]\\[0.2cm]
+        Example with actual SCRAM requirement\\
+        Show realizability checking finding conflicts
+      };
+    \end{tikzpicture}
+  \end{center}
+
+  \note[item]{The Challenge: Natural language is ambiguous; machines need precise specifications}
+  \note[item]{Example Translation: Natural language procedure becomes temporal logic formula}
+  \note[item]{FRETish Structure: 6 components eliminate ambiguity}
+  \note[item]{Realizability Checking catches errors before implementation}
+  \note[item]{Output: Unambiguous temporal logic ready for synthesis}
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/09_thrust2_synthesis.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/09_thrust2_synthesis.tex
@ -0,0 +1,53 @@
+% Thrust 2: Reactive Synthesis
+\begin{frame}{Thrust 2: Reactive synthesis generates provably correct discrete controllers}
+
+  \begin{center}
+    \textbf{Temporal Logic} $\xrightarrow{\text{Strix}}$ \textbf{Automaton}
+  \end{center}
+
+  \vspace{0.5cm}
+
+  \begin{center}
+    \begin{tikzpicture}[node distance=2.8cm, auto, scale=0.75, transform shape]
+      \tikzstyle{state} = [circle, minimum width=1.5cm, text centered, draw=black, fill=blue!20, font=\small]
+      \tikzstyle{arrow} = [->, >=stealth, thick]
+
+      \node[state] (cold) {Cold\\Shutdown};
+      \node[state, right of=cold] (heat) {Heatup};
+      \node[state, right of=heat] (power) {Full\\Power};
+      \node[state, below of=heat, fill=red!30] (scram) {SCRAM};
+
+      \draw[arrow] (cold) -- node[above, font=\tiny] {$T > 400°F$} (heat);
+      \draw[arrow] (heat) -- node[above, font=\tiny] {Stable} (power);
+      \draw[arrow] (heat) to[bend left=45] node[right, font=\tiny] {Fault} (scram);
+      \draw[arrow] (power) to[bend right=45] node[left, font=\tiny] {Fault} (scram);
+      \draw[arrow] (scram) to[loop below] node[below, font=\tiny] {Stay safe} (scram);
+    \end{tikzpicture}
+  \end{center}
+
+  \vspace{0.5cm}
+
+  \begin{center}
+    \Large \textbf{Correct by Construction}\\
+    \normalsize No switching errors possible
+  \end{center}
+
+  %SPEAKER NOTES: See comments below
+%
+    \textbf{What is Reactive Synthesis?}
+    Input: Temporal logic formula (what should happen)
+    Output: Finite state machine (how to make it happen)
+    Guarantee: If a solution exists, it is correct by construction
+
+    \textbf{Example: Simplified Reactor Automaton}
+    Nodes = discrete modes (what control strategy to use)
+    Edges = transition conditions (when to switch)
+    No switching errors possible---the automaton is mathematically guaranteed to satisfy specifications
+
+    \textbf{This is the ``Operator's Decision-Making'' Automated}
+
+    Tool: Strix (SYNTCOMP competition winner)
+
+    Output: Discrete controller with formal correctness guarantee
+% (End of speaker notes)
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/10_thrust3_continuous.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/10_thrust3_continuous.tex
@ -0,0 +1,39 @@
+% Thrust 3: Continuous Verification
+\begin{frame}{Thrust 3: Continuous controllers verified using three complementary techniques}
+
+  \begin{center}
+    \begin{tikzpicture}
+      \draw[thick, fill=gray!20] (0,0) rectangle (12,7);
+      \node[align=center, text width=10cm] at (6,3.5) {
+        \textbf{FIGURE: Continuous Verification Visualization}\\[0.3cm]
+        Top: Three mode types with phase portraits\\
+        \textbf{Stabilizing} (attractor) | \textbf{Transitory} (flow) | \textbf{Expulsory} (escape)\\[0.3cm]
+        Middle: State space diagram showing\\
+        reachable sets at boundaries\\[0.3cm]
+        Bottom: Barrier certificate illustration\\
+        Safe set with vector field showing\\
+        all trajectories stay inside or exit correctly
+      };
+    \end{tikzpicture}
+  \end{center}
+
+  %SPEAKER NOTES: See comments below
+%
+    \textbf{Three Types of Continuous Modes:}
+    1. Stabilizing: Stay in current mode (e.g., full-power operation)
+    2. Transitory: Drive toward next mode (e.g., startup heatup)
+    3. Expulsory: Force to safe mode (e.g., SCRAM)
+
+    \textbf{Three Verification Techniques:}
+    1. Reachability Analysis: Compute reachable state sets, verify boundary conditions met
+    2. Assume-Guarantee: Local verification, global guarantees. Each mode verified independently
+    3. Barrier Certificates: Prove safe set forward invariance, guarantee transitions occur correctly
+
+    \textbf{Key Innovation:} Design continuous controllers after synthesizing automaton
+    - Automaton defines transition boundaries
+    - Design each mode to satisfy its local transitions
+    - Compositional verification avoids intractable global analysis
+
+    Output: Verified continuous modes + discrete automaton = Complete hybrid controller
+% (End of speaker notes)
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/11_key_insight.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/11_key_insight.tex
@ -0,0 +1,38 @@
+% Key Insight
+\begin{frame}{Key Insight: Automaton-first design makes verification tractable}
+
+  \begin{center}
+    \begin{tikzpicture}
+      \draw[thick, fill=gray!20] (0,0) rectangle (12,7);
+      \node[align=center, text width=10cm] at (6,3.5) {
+        \textbf{FIGURE: Traditional vs Our Approach}\\[0.3cm]
+        LEFT (red X): Traditional approach\\
+        Tangled spaghetti diagram showing\\
+        monolithic verification problem\\
+        Label: ``Intractable''\\[0.3cm]
+        RIGHT (green check): Our approach\\
+        Clean modular diagram:\\
+        Automaton $\rightarrow$ Local modes $\rightarrow$ Compose\\
+        Each module verified independently\\
+        Label: ``Tractable''
+      };
+    \end{tikzpicture}
+  \end{center}
+
+  %SPEAKER NOTES: See comments below
+%
+    \textbf{Traditional Approach (Intractable):}
+    - Design everything at once
+    - Verify entire trajectory through all modes
+    - Computationally intractable for complex systems
+
+    \textbf{Our Approach (Tractable):}
+    1. Synthesize Discrete Automaton (tells us what boundaries to verify)
+    2. Define Transition Boundaries (from automaton structure)
+    3. Design Continuous Modes Locally (each controller designed for its specific job)
+    4. Verify Each Mode Independently (local verification is tractable)
+    5. Compose via Assume-Guarantee (interface contracts guarantee composition)
+
+    \textbf{Key Message:} Decomposition is the key to tractable verification
+% (End of speaker notes)
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/12_demonstration.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/12_demonstration.tex
@ -0,0 +1,40 @@
+% Demonstration
+\begin{frame}{Demonstration: SmAHTR autonomous startup provides a rigorous test case}
+
+  \begin{center}
+    \begin{tikzpicture}
+      \draw[thick, fill=gray!20] (0,0) rectangle (12,7);
+      \node[align=center, text width=10cm] at (6,3.5) {
+        \textbf{FIGURE: SmAHTR Hardware-in-Loop Setup}\\[0.3cm]
+        Top: SmAHTR reactor diagram\\
+        (liquid-salt cooled, representative SMR)\\[0.3cm]
+        Middle: Hardware-in-loop architecture\\
+        Simulink Model $\leftrightarrow$ ARCADE $\leftrightarrow$ Emerson Ovation\\[0.3cm]
+        Bottom: Startup sequence state machine\\
+        Cold $\rightarrow$ Heat $\rightarrow$ Criticality $\rightarrow$ Low Power $\rightarrow$ Full Power\\
+        Show continuous trajectories within each state
+      };
+    \end{tikzpicture}
+  \end{center}
+
+  %SPEAKER NOTES: See comments below
+%
+    \textbf{Small Modular Advanced High Temperature Reactor (SmAHTR):}
+    - Liquid-salt cooled reactor design
+    - Well-documented startup procedures
+    - Representative of next-generation SMR designs
+
+    \textbf{Startup Sequence:} Cold → Controlled Heating → Approach Criticality → Low-Power Physics → Full Power
+    Each mode has different control objective (temp control, ramp rate, reactivity, neutron flux, load following)
+
+    \textbf{Implementation Platform:}
+    - Simulation: High-fidelity Simulink model (thermal-hydraulics + neutron kinetics)
+    - Hardware: Emerson Ovation control system (industry standard)
+    - Integration: ARCADE platform (hardware-in-the-loop)
+    - Validation: Real-time performance on actual control equipment
+
+    \textbf{Why This Matters:}
+    Multiple coordinated subsystems, strict timing/temperature constraints, complex nonlinear dynamics.
+    This is not a toy problem---it's representative of deployment challenges.
+% (End of speaker notes)
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/13_outcomes.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/13_outcomes.tex
@ -0,0 +1,60 @@
+% Expected Outcomes
+\begin{frame}{Success measured by progression to TRL 5---practical feasibility beyond theory}
+
+  \begin{center}
+    \begin{tikzpicture}[scale=0.9, transform shape]
+      \draw[->, >=stealth, very thick] (0,0) -- (11,0) node[right] {TRL};
+
+      % TRL markers
+      \foreach \x/\label in {1/1, 3/2-3, 5.5/4, 8/5, 10/6} {
+        \draw[thick] (\x,0.1) -- (\x,-0.1);
+        \node[below] at (\x,-0.2) {\small\label};
+      }
+
+      % Starting point
+      \node[circle, fill=red, minimum size=0.3cm, label=above:{\small Current}] at (3,0) {};
+      \node[below=1cm of {(3,0)}, align=center, font=\tiny] {HARDENS\\TRL 3-4};
+
+      % Target
+      \node[circle, fill=green, minimum size=0.3cm, label=above:{\small\textbf{Target}}] at (8,0) {};
+      \node[below=1cm of {(8,0)}, align=center, font=\tiny, text width=2.5cm] {Hardware-in-loop\\validated};
+
+      % Arrow
+      \draw[->, >=stealth, very thick, blue] (3.5,0.5) -- (7.5,0.5) node[midway, above] {\textbf{This Work}};
+    \end{tikzpicture}
+  \end{center}
+
+  \vspace{0.5cm}
+
+  \textbf{Three Deliverables:}
+
+  \begin{enumerate}
+    \item Procedure translation methodology
+    \item Continuous verification framework
+    \item SmAHTR demonstration on Emerson Ovation
+  \end{enumerate}
+
+  %SPEAKER NOTES: See comments below
+%
+    \textbf{Technology Readiness Level Progression:}
+    Current: TRL 2-3 (basic concepts, HARDENS precedent)
+    Target: TRL 5 (validated prototype in relevant environment)
+
+    \textbf{Three Concrete Deliverables:}
+
+    1. Procedure Translation Methodology
+       - Engineers generate verified controllers from regulatory procedures
+       - No formal methods expertise required
+
+    2. Continuous Verification Framework
+       - Standard control design + iterative verification
+       - Mathematical proof of safe mode transitions
+
+    3. SmAHTR Hardware-in-the-Loop Demonstration
+       - Autonomous startup on industrial control hardware
+       - Real-time performance validation
+       - Clear path to deployment
+
+    \textbf{Key Message:} TRL 5 proves both theoretical validity and practical implementability
+% (End of speaker notes)
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/14_broader_impact.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/14_broader_impact.tex
@ -0,0 +1,43 @@
+% Broader Impact
+\begin{frame}{This methodology generalizes to any safety-critical hybrid system}
+
+  \begin{center}
+    \begin{tikzpicture}
+      \draw[thick, fill=gray!20] (0,0) rectangle (12,6.5);
+      \node[align=center, text width=10cm] at (6,3.25) {
+        \textbf{FIGURE: Application Domains}\\[0.3cm]
+        Center: Nuclear reactor (this work)\\[0.2cm]
+        Radiating out to icons representing:\\
+        - Chemical plant (batch processes)\\
+        - Aircraft (flight phases)\\
+        - Autonomous vehicle (driving modes)\\
+        - Medical device (therapy modes)\\
+        - Power grid (generation modes)\\[0.3cm]
+        All connected with ``Common pattern:\\
+        procedures + hybrid dynamics + safety''
+      };
+    \end{tikzpicture}
+  \end{center}
+
+  %SPEAKER NOTES: See comments below
+%
+    \textbf{Common Pattern Across Domains:}
+    Written procedures exist, continuous dynamics + discrete decisions, safety is paramount, autonomy has economic benefits
+
+    \textbf{Application Domains:}
+    Chemical Process: Batch processes, safety interlocks
+    Aerospace: Flight phases, emergency procedures
+    Autonomous Transport: Driving modes, emergency maneuvers
+    Medical Devices: Therapy modes, patient monitoring
+    Power Grid: Generation modes, fault response
+
+    \textbf{Economic Multiplier:}
+    Nuclear O\&M (datacenter demand): \$21--28B annually
+    Broader safety-critical infrastructure: Much larger
+
+    \textbf{Regulatory Pathway:}
+    Proving concept in nuclear (highest safety bar) establishes precedent: mathematical proof as regulatory evidence. Easier adoption in other industries.
+
+    \textbf{Key Message:} Nuclear is the proving ground; impact extends far beyond
+% (End of speaker notes)
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/15_innovation.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/15_innovation.tex
@ -0,0 +1,52 @@
+% Innovation Summary
+\begin{frame}{The innovation is systematic integration to bridge a fundamental gap}
+
+  \begin{center}
+    \begin{tikzpicture}
+      \draw[thick, fill=gray!20] (0,0) rectangle (12,3.5);
+      \node[align=center, text width=10cm] at (6,1.75) {
+        \textbf{FIGURE: Innovation Visualization}\\[0.2cm]
+        Show existing tools (FRET, Strix, reachability)\\
+        as building blocks being assembled into\\
+        integrated methodology\\[0.1cm]
+        Highlight: Integration + Decomposition = Novel contribution
+      };
+    \end{tikzpicture}
+  \end{center}
+
+  \vspace{0.5cm}
+
+  \begin{center}
+    \small
+    \begin{tabular}{lcc}
+      \toprule
+      & \textbf{HARDENS} & \textbf{This Work} \\
+      \midrule
+      Discrete verification & \checkmark & \checkmark \\
+      Continuous verification & $\times$ & \checkmark \\
+      Hybrid verification & $\times$ & \checkmark \\
+      Hardware-in-loop & $\times$ & \checkmark \\
+      \bottomrule
+    \end{tabular}
+  \end{center}
+
+  %SPEAKER NOTES: See comments below
+%
+    \textbf{What's NOT New (but state-of-the-art):}
+    Temporal logic, reactive synthesis, reachability analysis, barrier certificates, hardware-in-the-loop.
+    These are mature techniques from computer science and control theory.
+
+    \textbf{What IS New:}
+    - Integration: Unifying discrete and continuous verification
+    - Methodology: Systematic tool-supported workflow
+    - Decomposition: Automaton-first design enables tractable verification
+    - Practical: Targets existing industrial hardware
+
+    \textbf{Comparison to HARDENS:}
+    HARDENS: Discrete only, TRL 3-4, no hardware-in-loop
+    This Work: Full hybrid system, TRL 5, hardware-in-loop
+
+    \textbf{Key Enabling Insight:}
+    Automaton-first design makes continuous verification tractable by decomposing the problem into local verifications with compositional guarantees
+% (End of speaker notes)
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/sections/16_conclusion.tex
+++ b/Presentations/20251215-Emerson-Pres/sections/16_conclusion.tex
@ -0,0 +1,88 @@
+% 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}
--- a/Presentations/20251215-Emerson-Pres/sg1_uncertainty.png
+++ b/Presentations/20251215-Emerson-Pres/sg1_uncertainty.png
--- a/Presentations/20251215-Emerson-Pres/slides/1_Hook.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/1_Hook.tex
@ -0,0 +1,75 @@
+\begin{frame}{The United States stands on the precipice of a severe
+  energy crisis}
+  
+  \begin{columns}
+    \begin{column}{0.5\textwidth}
+      \centering{
+
+      \begin{figure}
+        \begin{center}
+          \includegraphics[height=0.50\textheight]{images/1_hook/energy-demand-graph-small.png}
+        \end{center}
+        \caption*{Source: Pew Research Center, Data from IEA}
+      \end{figure}
+
+    %   \scriptsize{
+    %       \begin{tabular}{lcc}
+    %     \textbf{Source} (30yr LCOE) & \textbf{Total (\$/MWh)} & \textbf{O\&M (\$/MWh)} \\
+    %     \midrule Adv. Nuclear & 88.24 & \cellcolor{red!30!primary}\textbf{16.15} \\ 
+    %     Natural Gas & 39.94 & 1.68 \\
+    %     \bottomrule
+    %   \end{tabular}
+    % }
+    %
+    % \scriptsize Source: EIA Annual Energy Outlook 2022 
+    %
+    }
+    \end{column}
+
+    \begin{column}{0.5\textwidth}
+      \center
+
+      \textbf<1>{How much baseload power increase is this?}
+
+      \pause
+
+      \only<2>{% TikZ grid of nuclear plants
+      \begin{tikzpicture}
+        % Adjustable parameters
+        \def\iconsize{0.9cm}        % Size of each icon
+        \def\xspacing{1.2cm}        % Horizontal spacing between icons
+        \def\yspacing{1.0cm}        % Vertical spacing between icons
+
+        % Draw grid of icons
+        \foreach \row in {0,...,5} {
+          \foreach \col in {0,...,4} {
+            \node at (\col*\xspacing, -\row*\yspacing)
+              {\includegraphics[width=\iconsize]{images/1_hook/nuclear-plant.png}};
+          }
+        }
+      \end{tikzpicture}
+      }
+      
+      \only<3>{% TikZ grid of nuclear plants
+      \begin{tikzpicture}
+        % Adjustable parameters
+        \def\iconsize{0.44cm}        % Size of each icon
+        \def\xspacing{0.6cm}        % Horizontal spacing between icons
+        \def\yspacing{0.6cm}        % Vertical spacing between icons
+
+        % Draw grid of icons
+        \foreach \row in {0,...,9} {
+          \foreach \col in {0,...,9} {
+            \node at (\col*\xspacing, -\row*\yspacing)
+              {\includegraphics[width=\iconsize]{images/1_hook/nuclear-plant.png}};
+          }
+        }
+      \end{tikzpicture}
+      }
+
+      \textbf<2>{30 gigawatts!}
+
+    \end{column}
+  \end{columns}
+
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/1_Hook_v2.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/1_Hook_v2.tex
@ -0,0 +1,57 @@
+\begin{frame}{The United States stands on the precipice of a severe
+  energy crisis}
+  
+  \begin{columns}
+    \begin{column}{0.5\textwidth}
+      \centering{
+
+      \begin{figure}
+        \begin{center}
+          \includegraphics[height=0.50\textheight]{images/1_hook/energy-demand-graph-small.png}
+        \end{center}
+        \caption*{Source: Pew Research Center, Data from IEA}
+      \end{figure}
+
+    %   \scriptsize{
+    %       \begin{tabular}{lcc}
+    %     \textbf{Source} (30yr LCOE) & \textbf{Total (\$/MWh)} & \textbf{O\&M (\$/MWh)} \\
+    %     \midrule Adv. Nuclear & 88.24 & \cellcolor{red!30!primary}\textbf{16.15} \\ 
+    %     Natural Gas & 39.94 & 1.68 \\
+    %     \bottomrule
+    %   \end{tabular}
+    % }
+    %
+    % \scriptsize Source: EIA Annual Energy Outlook 2022 
+    %
+    }
+    \end{column}
+
+    \begin{column}{0.5\textwidth}
+      \center
+
+      \textbf<1>{How much baseload power increase is this?}
+
+      \only<2>{% TikZ grid of nuclear plants
+      \begin{tikzpicture}
+        % Adjustable parameters
+        \def\iconsize{0.44cm}        % Size of each icon
+        \def\xspacing{0.6cm}        % Horizontal spacing between icons
+        \def\yspacing{0.6cm}        % Vertical spacing between icons
+
+        % Draw grid of icons
+        \foreach \row in {0,...,9} {
+          \foreach \col in {0,...,9} {
+            \node at (\col*\xspacing, -\row*\yspacing)
+              {\includegraphics[width=\iconsize]{images/1_hook/nuclear-plant.png}};
+          }
+        }
+      \end{tikzpicture}
+      
+
+      \textbf<2>{30 gigawatts!}
+    }
+
+    \end{column}
+  \end{columns}
+
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/2_State_of_the_Art.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/2_State_of_the_Art.tex
@ -0,0 +1,110 @@
+\begin{frame}{Staffing these new reactors will be an incredible challenge}
+  \centering
+  \underline{How many reactor operators are required to staff this new fleet?}
+
+  \vspace{0.3cm}
+
+  \begin{columns}[c]
+    \begin{column}{0.3\textwidth}
+
+      \begin{figure}
+        \includegraphics[width=0.3\textwidth]{images/2_state_of_the_art/nuclear-plant.png}
+        \caption*{For one Small Modular Reactor (SMR)...}
+      \end{figure}
+
+    \end{column}
+
+    \begin{column}{0.7\textwidth}
+      \centering
+
+      % Onslide 1: One shift (2 SROs, 2 ROs)
+      \only<2>{
+        \textbf{One shift requires:}
+
+        \vspace{0.3cm}
+
+        \begin{tikzpicture}
+          % Adjustable parameters
+          \def\iconsize{0.8cm}
+          \def\spacing{1.0cm}
+
+          % 2 Senior Operators (foreman)
+          \foreach \i in {0,1} {
+            \node at (\i*\spacing, 0) {\includegraphics[width=\iconsize]{images/2_state_of_the_art/foreman.png}};
+          }
+
+          % 2 Reactor Operators (worker)
+          \foreach \i in {0,1} {
+            \node at (\i*\spacing, -1.2cm) {\includegraphics[width=\iconsize]{images/2_state_of_the_art/worker.png}};
+          }
+
+          % Labels
+          \node[right] at (2.2*\spacing, 0) {\small 2 Senior Reactor Operators};
+          \node[right] at (2.2*\spacing, -1.2cm) {\small 2 Reactor Operators};
+        \end{tikzpicture}
+      }
+
+      % Onslide 2: Full staffing (6 shifts)
+      \only<3->{
+        \vspace{0.3cm}
+        \textbf{24/7 operations require \(\sim\)6 shifts:}
+
+        \vspace{0.1cm}
+
+        \begin{tikzpicture}
+          % Adjustable parameters
+          \def\iconsize{0.6cm}
+          \def\xspacing{0.8cm}
+          \def\yspacing{0.9cm}
+
+          % 12 Senior Operators (2 per shift <20> 6 shifts)
+          \foreach \row in {0,1} {
+            \foreach \col in {0,...,5} {
+              \node at (\col*\xspacing, -\row*\yspacing)
+                {\includegraphics[width=\iconsize]{images/2_state_of_the_art/foreman.png}};
+            }
+          }
+
+          % 12 Reactor Operators (2 per shift <20> 6 shifts)
+          \foreach \row in {2,3} {
+            \foreach \col in {0,...,5} {
+              \node at (\col*\xspacing, -\row*\yspacing)
+                {\includegraphics[width=\iconsize]{images/2_state_of_the_art/worker.png}};
+            }
+          }
+
+          % Labels
+          \node[right] at (6*\xspacing, -0.5*\yspacing) {\small 12 SROs};
+          \node[right] at (6*\xspacing, -2.5*\yspacing) {\small 12 ROs};
+        \end{tikzpicture}
+
+        \vspace{0.1cm}
+        \textbf{24 licensed operators per reactor}
+      }
+
+      % Onslide 3: Total for 100 reactors
+      \only<4->{
+        \vspace{0.3cm}
+      }
+
+    \end{column}
+
+  \end{columns}
+
+\onslide<4->{ \large{ \textbf{To meet demand we require 2,400 new licensed
+operators!} } }
+
+
+\onslide<5>{
+  \alert{
+    \textit{We currently have only 3,600 licensed operators total...}
+  }
+}
+
+\end{frame}
+
+\begin{frame}{Nuclear reactors are operated with prescriptive handbooks and
+  legacy control technologies}
+  \centering
+  \includegraphics[width=\textwidth,height=0.75\textheight,keepaspectratio]{images/2_state_of_the_art/control_room.jpg}
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/2_State_of_the_Art_v2.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/2_State_of_the_Art_v2.tex
@ -0,0 +1,82 @@
+\begin{frame}{Nuclear reactors are operated with prescriptive handbooks and
+  legacy control technologies}
+  \centering
+  \includegraphics[width=\textwidth,height=0.75\textheight,keepaspectratio]{images/2_state_of_the_art/control_room.jpg}
+\end{frame}
+
+% \begin{frame}{Building a fleet of new reactors with current requirements 
+%     will be an incredible staffing challenge
+%   }
+%   \centering
+%   \underline{How many reactor operators are required to staff this new fleet?}
+%
+%   \vspace{0.3cm}
+%
+%   \begin{columns}[c]
+%     \begin{column}{0.3\textwidth}
+%
+%       \begin{figure}
+%         \includegraphics[width=0.3\textwidth]{images/2_state_of_the_art/nuclear-plant.png}
+%         \caption*{For one Small Modular Reactor (SMR)...}
+%       \end{figure}
+%
+%     \end{column}
+%
+%     \begin{column}{0.7\textwidth}
+%       \centering
+%       \only<2->{
+%         \vspace{0.3cm}
+%         \textbf{24/7 operations require \(\sim\)6 shifts:}
+%
+%         \vspace{0.1cm}
+%
+%         \begin{tikzpicture}
+%           % Adjustable parameters
+%           \def\iconsize{0.6cm}
+%           \def\xspacing{0.8cm}
+%           \def\yspacing{0.9cm}
+%
+%           % 12 Senior Operators (2 per shift <20> 6 shifts)
+%           \foreach \row in {0,1} {
+%             \foreach \col in {0,...,5} {
+%               \node at (\col*\xspacing, -\row*\yspacing)
+%                 {\includegraphics[width=\iconsize]{images/2_state_of_the_art/foreman.png}};
+%             }
+%           }
+%
+%           % 12 Reactor Operators (2 per shift <20> 6 shifts)
+%           \foreach \row in {2,3} {
+%             \foreach \col in {0,...,5} {
+%               \node at (\col*\xspacing, -\row*\yspacing)
+%                 {\includegraphics[width=\iconsize]{images/2_state_of_the_art/worker.png}};
+%             }
+%           }
+%
+%           % Labels
+%           \node[right] at (6*\xspacing, -0.5*\yspacing) {\small 12 SROs};
+%           \node[right] at (6*\xspacing, -2.5*\yspacing) {\small 12 ROs};
+%         \end{tikzpicture}
+%
+%         \vspace{0.1cm}
+%         \textbf{24 licensed operators per reactor}
+%       }
+%
+%     \end{column}
+%
+%   \end{columns}
+%
+%   \onslide<2->{\vspace{0.2cm} 
+%     \large{ 
+%       \textbf{To meet demand we require 2,400 new licensed operators!} 
+%   } 
+% }
+%
+%
+% \onslide<3>{
+%   \alert{
+%     \textit{We currently have only 3,600 licensed operators total...}
+%   }
+% }
+%
+% \end{frame}
+%
--- a/Presentations/20251215-Emerson-Pres/slides/3_Limitations.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/3_Limitations.tex
@ -0,0 +1,59 @@
+\begin{frame}{Human reactor operators have key limitations that limit nuclear
+  buildout}
+
+  \begin{columns}[t]
+    \begin{column}{0.33\textwidth}
+      \only<1>{
+        \begin{alertblock}{Humans cannot meet labor demand}
+
+        \centering
+
+        \includegraphics[width=2cm]{images/3_limitations/foreman.png}
+        \includegraphics[width=2cm]{images/3_limitations/worker.png}
+
+        \end{alertblock}
+      }
+      \only<2->{
+        \begin{block}{Humans cannot meet labor demand}
+
+        \centering
+
+        \includegraphics[width=2cm]{images/3_limitations/foreman.png}
+        \includegraphics[width=2cm]{images/3_limitations/worker.png}
+        \end{block}
+      }
+\end{column}
+    
+    \pause
+
+    \begin{column}{0.33\textwidth}
+      \only<2>{
+      \begin{alertblock}{Procedures are not exhaustively verified}
+        \centering 
+        \includegraphics[width=2cm]{images/3_limitations/computer.png}
+      \end{alertblock}
+      }
+
+      \only<3->{
+      \begin{block}{Procedures are not exhaustively verified}
+        \centering 
+        \includegraphics[width=2cm]{images/3_limitations/computer.png}
+      \end{block}
+
+      }
+    \end{column}
+
+    \pause
+
+    \begin{column}{0.33\textwidth}
+      \only<3>{
+      \begin{alertblock}{Human factors cannot be trained away}
+        \centering
+        \includegraphics[width=2cm]{images/3_limitations/test.png}
+      \end{alertblock}
+      }
+
+    \end{column}
+  \end{columns}
+
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/3_Limitations_v2.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/3_Limitations_v2.tex
@ -0,0 +1,59 @@
+\begin{frame}{Human reactor operators have key limitations that limit nuclear
+  buildout}
+
+  \begin{columns}[t]
+    \begin{column}{0.33\textwidth}
+      \only<1>{
+        \begin{alertblock}{Humans cannot meet labor demand}
+
+        \centering
+
+        \includegraphics[width=2cm]{images/3_limitations/foreman.png}
+        \includegraphics[width=2cm]{images/3_limitations/worker.png}
+
+        \end{alertblock}
+      }
+      \only<2->{
+        \begin{block}{Humans cannot meet labor demand}
+
+        \centering
+
+        \includegraphics[width=2cm]{images/3_limitations/foreman.png}
+        \includegraphics[width=2cm]{images/3_limitations/worker.png}
+        \end{block}
+      }
+\end{column}
+    
+    \pause
+
+    \begin{column}{0.33\textwidth}
+      \only<2>{
+      \begin{alertblock}{Procedures are not formally verified}
+        \centering 
+        \includegraphics[width=2cm]{images/3_limitations/computer.png}
+      \end{alertblock}
+      }
+
+      \only<3->{
+      \begin{block}{Procedures are not formally verified}
+        \centering 
+        \includegraphics[width=2cm]{images/3_limitations/computer.png}
+      \end{block}
+
+      }
+    \end{column}
+
+    \pause
+
+    \begin{column}{0.33\textwidth}
+      \only<3>{
+      \begin{alertblock}{Human factors cannot be trained away}
+        \centering
+        \includegraphics[width=2cm]{images/3_limitations/test.png}
+      \end{alertblock}
+      }
+
+    \end{column}
+  \end{columns}
+
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/4_Research_Approach.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/4_Research_Approach.tex
@ -0,0 +1,175 @@
+\begin{frame}{The goal of this research is to create verified autonomous control
+  systems}
+
+  \textbf{\underline{
+    If this research is successful, we will be able to do the following:
+  }}
+  \pause
+
+  \begin{enumerate}
+
+    \item \alert<2>{Translate written procedures into discrete control logic}
+      \pause
+
+    \item \alert<3>{Verify continuous control behavior across discrete mode
+      transitions}
+      \pause
+
+    \item \alert<4>{Demonstrate autonomous reactor startup with verifiable safety
+      guarantees}
+
+  \end{enumerate}
+\end{frame}
+
+\begin{frame}{First, we will formalize written procedures into logical
+  statements}
+
+  \begin{columns}
+    \begin{column}{0.33\textwidth}
+      \includegraphics[width=\textwidth]{images/4_research_approach/procedure.png}
+    \end{column}
+
+    \begin{column}{0.33\textwidth}
+      \only<2>{
+        \begin{alertblock}{FRET Specification}
+        \scriptsize
+        \texttt{INITIAL\_CONDITIONS shall satisfy:}
+        \begin{itemize}
+          \item[] \texttt{mode = MODE\_5}
+          \item[] \texttt{k\_eff < 0.99}
+          \item[] \texttt{power = 0}
+          \item[] \texttt{t\_avg < 200}
+          \item[] \texttt{...}
+        \end{itemize}
+      \end{alertblock}
+      }
+
+      \only<3->{
+        \begin{block}{FRET Specification}
+        \scriptsize
+        \texttt{INITIAL\_CONDITIONS shall satisfy:}
+        \begin{itemize}
+          \item[] \texttt{mode = MODE\_5}
+          \item[] \texttt{k\_eff < 0.99}
+          \item[] \texttt{power = 0}
+          \item[] \texttt{t\_avg < 200}
+          \item[] \texttt{...}
+        \end{itemize}
+      \end{block}
+      }
+    \end{column}
+
+    \begin{column}{0.33\textwidth}
+      \only<3>{
+        \begin{alertblock}{LTL Formula}
+          \scriptsize
+          \texttt{$\Box$ (initial $\rightarrow$ (}
+          \begin{itemize}
+            \item[] \texttt{mode\_5\_active $\land$}
+            \item[] \texttt{k\_eff\_subcritical $\land$}
+            \item[] \texttt{zero\_power $\land$}
+            \item[] \texttt{temp\_safe $\land$}
+            \item[] \texttt{...))}
+          \end{itemize}
+        \end{alertblock}
+      }
+    \end{column}
+  \end{columns}
+
+\end{frame}
+
+\begin{frame}{Second, we will use the logical formulae to generate discrete
+  automata}
+
+  \centering
+  \begin{tikzpicture}[node distance=2cm]
+    % Blocks
+    \node[draw, rectangle, minimum width=3cm, minimum height=1.5cm, align=center, fill=blue!20!primary] (ltl) {LTL\\Specification};
+    \node[draw, rectangle, minimum width=3cm, minimum height=1.5cm, align=center, fill=blue!20!primary, right=of ltl] (game) {Parity\\Game};
+    \node[draw, rectangle, minimum width=3cm, minimum height=1.5cm, align=center, fill=blue!20!primary, right=of game] (automata) {Discrete\\Automata};
+
+    % Arrows
+    \draw[->, thick] (ltl) -- (game);
+    \draw[->, thick] (game) -- (automata);
+
+    % Curly bracket
+    \draw[decorate, decoration={brace, amplitude=10pt, mirror}, thick]
+      ([yshift=-1cm]ltl.south west) -- ([yshift=-1cm]automata.south east)
+      node[midway, below=0.5cm] {\textbf{Reactive Synthesis}};
+  \end{tikzpicture}
+
+\end{frame}
+
+\begin{frame}{Finally, we will build continuous controllers to move between
+  discrete states}
+
+  \begin{columns}
+    \begin{column}{0.5\textwidth}
+      \includegraphics[height=0.7\textheight]{bouncing_ball_hybrid.png}
+
+    \end{column}
+
+    \begin{column}{0.5\textwidth}
+      \only<2>{
+        \begin{alertblock}{Key Challenge}
+          \small
+          Verify continuous control behavior across discrete mode transitions
+        \end{alertblock}
+      }
+      \only<3->{
+        \begin{block}{Key Challenge}
+          \small
+          Verify continuous control behavior across discrete mode transitions
+        \end{block}
+      }
+
+      \vspace{0.3cm}
+
+      \only<3>{
+        \begin{alertblock}{Reachable Set}
+          \small
+          $\mathcal{R}(t) = \{x(t) \mid x(0) \in X_0, \dot{x} = f(x)\}$
+        \end{alertblock}
+      }
+      \only<4->{
+        \begin{block}{Reachable Set}
+          \small
+          $\mathcal{R}(t) = \{x(t) \mid x(0) \in X_0, \dot{x} = f(x)\}$
+        \end{block}
+      }
+
+      \vspace{0.3cm}
+
+      \only<4>{
+        \begin{alertblock}{Barrier Certificate}
+          \small
+          $B(x) > 0 \land \nabla B \cdot f(x) \leq 0 \implies x \in \text{Safe}$
+        \end{alertblock}
+      }
+    \end{column}
+  \end{columns}
+
+\end{frame}
+
+\begin{frame}{Verified autonomous controllers can be created by building this
+chain of proof of correctness}
+
+  \begin{enumerate}
+    \item<1-> \alert<1>{Formalize regulatory procedures into FRET specifications and translate to Linear Temporal Logic (LTL)}
+
+    \item<2-> \alert<2>{Synthesize discrete automata from LTL using reactive synthesis}
+
+    \item<3-> \alert<3>{Design continuous controllers for each discrete mode and verify safety across mode transitions using barrier certificates and reachability analysis}
+  \end{enumerate}
+
+  \vspace{1cm}
+ 
+  \onslide<4>{
+    \begin{center}
+      \large
+      \textbf{Result: Complete hybrid autonomous system\\
+      with correctness guarantees by construction}
+    \end{center}
+  }
+
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/4_Research_Approach_v2.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/4_Research_Approach_v2.tex
@ -0,0 +1,152 @@
+\begin{frame}{The goal of this research is to create verified autonomous control
+  systems}
+
+  \textbf{\underline{
+    If this research is successful, we will be able to do the following:
+  }}
+  \pause
+
+  \begin{enumerate}
+
+    \item \alert<2>{Translate written procedures into discrete control logic}
+      \pause
+
+    \item \alert<3>{Verify continuous control behavior across discrete mode
+      transitions}
+      \pause
+
+    \item \alert<4>{Demonstrate autonomous reactor startup with verifiable safety
+      guarantees}
+
+  \end{enumerate}
+\end{frame}
+
+\begin{frame}{First, we will formalize written procedures into logical
+  statements}
+
+  \begin{columns}[c]
+    \begin{column}{0.7\textwidth}
+      \includegraphics[
+        width=1.0\textwidth,
+        trim={1cm 22cm 1cm 0cm},
+        clip
+      ]
+      {images/4_research_approach/procedure.png}
+      \scriptsize{
+      Westinghouse Technology Systems Manual, Section 19.0 - Plant Operations
+    }
+    \end{column}
+
+    \begin{column}{0.3\textwidth}
+      \only<2>{
+        \begin{alertblock}{FRET Specification}
+        \scriptsize
+        \texttt{INITIAL\_CONDITIONS shall satisfy:}
+        \begin{itemize}
+          \item[] \texttt{mode = MODE\_5}
+          \item[] \texttt{k\_eff < 0.99}
+          \item[] \texttt{power = 0}
+          \item[] \texttt{t\_avg < 200}
+          \item[] \texttt{...}
+        \end{itemize}
+      \end{alertblock}
+      }
+
+      \only<3->{
+        \begin{block}{FRET Specification}
+        \scriptsize
+        \texttt{INITIAL\_CONDITIONS shall satisfy:}
+        \begin{itemize}
+          \item[] \texttt{mode = MODE\_5}
+          \item[] \texttt{k\_eff < 0.99}
+          \item[] \texttt{power = 0}
+          \item[] \texttt{t\_avg < 200}
+          \item[] \texttt{...}
+        \end{itemize}
+      \end{block}
+      }
+
+      \only<3>{
+        \begin{alertblock}{LTL Formula}
+          \scriptsize
+          \texttt{$\Box$ (initial $\rightarrow$ (}
+          \begin{itemize}
+            \item[] \texttt{mode\_5\_active $\land$}
+            \item[] \texttt{k\_eff\_subcritical $\land$}
+            \item[] \texttt{zero\_power $\land$}
+            \item[] \texttt{temp\_safe $\land$}
+            \item[] \texttt{...))}
+          \end{itemize}
+        \end{alertblock}
+      }
+    \end{column}
+
+  \end{columns}
+
+\end{frame}
+
+\begin{frame}{Second, we will use reactive synthesis to convert the logical formulae to generate discrete
+  automata}
+
+  \begin{columns}
+    \begin{column}{0.5\textwidth}
+      \begin{tikzpicture}
+        \node (chess) at (0cm,0cm){\includegraphics[width=0.4\textwidth]{images/4_research_approach/strategy.png}};
+        \node[draw=textcolor, fill=secondary, left=0.1cm of chess, yshift=-0.8cm] {Plant};
+        \node[draw=textcolor, fill=primary!30!red, right=0.1cm of chess, yshift=0.4cm] {Controller};
+      \end{tikzpicture}
+    \end{column}
+
+    \begin{column}{0.5\textwidth}
+      \begin{tikzpicture}[
+        state/.style={circle, draw=textcolor, fill=secondary, minimum size=1.2cm},
+        transition/.style={->, >=stealth, thick}
+      ]
+        
+        % States arranged vertically
+        \coordinate (start) at (0,1.5);
+        \node[state] (s0) at (0,0) {\scriptsize MODE 5};
+        \node[state] (s1) at (0,-2) {\scriptsize MODE 4};
+        \node[state] (s2) at (1,-4) {\scriptsize MODE 3};
+        \node[state] (s3) at (3,-5.) {\scriptsize MODE 2};
+        \node[state] (s4) at (5,-6) {\scriptsize MODE 1};
+        \node[state] (s5) at (3,-1.5) {\scriptsize SCRAM};
+
+        % Transitions
+      \draw[transition] (start) -- node[midway, right] {\scriptsize Start} (s0);
+        \draw[transition] (s0) -- (s1);
+        \draw[transition] (s1) -- (s2);
+        \draw[transition] (s2) -- (s3);
+        \draw[transition] (s3) -- (s4);
+        \draw[transition] (s2) to[bend right] (s5);
+        \draw[transition] (s1) to[bend right] (s5);
+        \draw[transition] (s3) to[bend right] (s5);
+        \draw[transition] (s4) to[bend right] (s5);
+
+        \draw[transition] (s0) to[loop left] (s0);
+        \draw[transition] (s1) to[loop left] (s1);
+        \draw[transition] (s2) to[loop left] (s2);
+        \draw[transition] (s3) to[loop below] (s3);
+        \draw[transition] (s4) to[loop below] (s4);
+
+      \end{tikzpicture}
+    \end{column}
+  \end{columns}
+  
+\end{frame}
+
+\begin{frame}{Finally, we will build continuous controllers with formal methods
+  to ensure transitions between modes}
+
+  \begin{columns}
+    \begin{column}{0.4\textwidth}
+      \includegraphics[height=0.9\textwidth]{images/4_research_approach/two_loop.png}
+    \end{column}
+    \begin{column}{0.6\textwidth}
+      \includegraphics[height=0.75\textheight]{images/4_research_approach/phase_portrait_sg1.png}
+    \end{column}
+  \end{columns}
+
+\end{frame}
+
+
--- a/Presentations/20251215-Emerson-Pres/slides/5_Metrics_of_Success.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/5_Metrics_of_Success.tex
@ -0,0 +1,53 @@
+\begin{frame}{Success will be measured through Technology Readiness Level advancement}
+
+  \begin{columns}
+    \begin{column}{0.3\textwidth}
+      \begin{block}{Why TRLs?}
+        \small
+        Bridge gap between proof-of-concept and deployment
+        \begin{itemize}
+          \item[] Measure both rigor and feasibility
+        \end{itemize}
+      \end{block}
+
+      \vspace{0.5cm}
+
+      \textbf{Current:} TRL 2-3\\
+      \textbf{Target:} TRL 5
+    \end{column}
+
+    \begin{column}{0.7\textwidth}
+      \begin{columns}
+        \begin{column}{0.33\textwidth}
+          \centering
+          \only<1->{\only<1>{\alert{\textbf{TRL 3}}}%
+          \only<2->{\textbf{TRL 3}}\\
+          \small Components\\
+          \vspace{0.2cm}
+          \includegraphics[width=0.8\textwidth]{images/5_metrics_of_success/puzzle.png}}
+        \end{column}
+
+        \begin{column}{0.33\textwidth}
+          \centering
+          \only<2->{\only<2>{\alert{\textbf{TRL 4}}}%
+          \only<3->{\textbf{TRL 4}}\\
+          \small Integration\\
+          \vspace{0.2cm}
+          \includegraphics[width=0.8\textwidth]{images/5_metrics_of_success/puzzle_complete.png}}
+        \end{column}
+
+        \begin{column}{0.33\textwidth}
+          \centering
+          \only<3->{\alert<3>{\textbf{TRL 5}}\\
+          \small Hardware\\
+          \vspace{0.2cm}
+          \begin{tikzpicture}
+            \node[anchor=south west,inner sep=0] (controller) at (0,0) {\includegraphics[width=0.8\columnwidth]{images/5_metrics_of_success/controller.png}};
+            \node[anchor=center,inner sep=2pt] at (2.48,1.88) {\includegraphics[width=0.3\columnwidth]{images/5_metrics_of_success/emerson_logo_only.png}};
+          \end{tikzpicture}}
+        \end{column}
+      \end{columns}
+    \end{column}
+  \end{columns}
+
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/5_Metrics_of_Success_v2.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/5_Metrics_of_Success_v2.tex
@ -0,0 +1,171 @@
+% Frame 1: Traditional approach - Engineer designs for nuclear plant, NRC rejects
+\begin{frame}{Validating this methodology is not possible using real nuclear
+  plants}
+
+  \begin{center}
+    \begin{tikzpicture}
+      % Define positions
+      \coordinate (engineer_pos) at (0,0);
+      \coordinate (plant_pos) at (6,0);
+      \coordinate (nrc_pos) at (3,0);
+
+      % Engineer icon
+      \node[anchor=center] (engineer) at (engineer_pos) {
+        \includegraphics[width=2cm]{images/5_metrics_of_success/engineer.png}
+      };
+      \node[below=0.1cm of engineer, text width=2cm, align=center] {\small Engineer};
+
+      % Nuclear plant icon
+      \only<1->{
+        \node[anchor=center] (plant) at (plant_pos) {
+          \includegraphics[width=2.5cm]{images/5_metrics_of_success/nuclear-plant.png}
+        };
+        \node[below=0.1cm of plant, text width=3cm, align=center] {\small Nuclear Plant};
+      }
+
+      % Bidirectional arrow with label
+      \only<1->{
+        \draw[->, >=stealth, very thick, draw=textcolor]
+          ([yshift=0.3cm]engineer.east) -- ([yshift=0.3cm]plant.west)
+          node[midway, above, text width=2.5cm, align=center] {\scriptsize Controller Design};
+        \draw[->, >=stealth, very thick, draw=textcolor]
+          ([yshift=-0.3cm]plant.west) -- ([yshift=-0.3cm]engineer.east)
+          node[midway, below, text width=2cm, align=center] {\scriptsize Validation};
+      }
+
+      % NRC appears with "no way" speech bubble
+      \only<2->{
+        \node[anchor=center] (nrc) at (nrc_pos) {
+          \includegraphics[width=2.5cm]{images/5_metrics_of_success/Seal_of_the_United_States_Nuclear_Regulatory_Commission.png}
+        };
+
+        % Speech bubble
+        \node[above=0.5cm of nrc,
+              draw=textcolor,
+              fill=secondary,
+              rounded corners,
+              thick,
+              text width=1.8cm,
+              align=center] (bubble) {\textbf{No way!}};
+
+        % Speech bubble pointer
+        \draw[draw=textcolor, thick, fill=secondary]
+          (bubble.south) -- +(-0.2,-0.3) -- +(0.2,-0.3) -- cycle;
+      }
+
+    \end{tikzpicture}
+  \end{center}
+
+\end{frame}
+
+% Frame 2: New approach - Digital twin enables validation
+\begin{frame}{Instead, digital twins will enable controller development and
+    validation before
+  implementation}
+
+  \begin{center}
+    \begin{tikzpicture}
+      % Define position
+      \coordinate (engineer_pos) at (0,0);
+      \coordinate (twin_pos) at (6,0);
+      \coordinate (nrc_pos) at (8.5,0);
+
+      % Engineer icon
+      \node[anchor=center] (engineer) at (engineer_pos) {
+        \includegraphics[width=2cm]{images/5_metrics_of_success/engineer.png}
+      };
+      \node[below=0.1cm of engineer, text width=2cm, align=center] {\small Engineer};
+
+      % Computer with nuclear plant overlay (digital twin concept)
+      \node[anchor=center] (computer) at (twin_pos) {
+        \includegraphics[width=2.8cm]{images/5_metrics_of_success/computer.png}
+      };
+
+      % Nuclear plant logo overlaid on computer
+      \node[anchor=center] at ([yshift=0.3cm, xshift=-0.3cm]computer.center) {
+        \includegraphics[width=1.0cm]{images/5_metrics_of_success/nuclear-plant.png}
+      };
+
+      \node[below=0.1cm of computer, text width=3cm, align=center] {\small Digital Twin};
+
+      % Bidirectional arrows
+      \draw[->, >=stealth, very thick, draw=textcolor]
+        ([yshift=0.3cm]engineer.east) -- ([yshift=0.3cm]computer.west)
+        node[midway, above, text width=2cm, align=center] {\scriptsize Design};
+      \draw[->, >=stealth, very thick, draw=textcolor]
+        ([yshift=-0.3cm]computer.west) -- ([yshift=-0.3cm]engineer.east)
+        node[midway, below, text width=2cm, align=center] {\scriptsize Validate};
+
+      % NRC logo with speech bubble
+      \node[anchor=center] (nrc) at (nrc_pos) {
+        \includegraphics[width=1.8cm]{images/5_metrics_of_success/Seal_of_the_United_States_Nuclear_Regulatory_Commission.png}
+      };
+
+      % Speech bubble
+      \node[above=0.3cm of nrc,
+            draw=textcolor,
+            fill=secondary,
+            rounded corners,
+            thick,
+            text width=1.5cm,
+            align=center] (bubble) {\scriptsize Now I see it!};
+
+      % Speech bubble pointer
+      \draw[draw=textcolor, thick, fill=secondary]
+        (bubble.south) -- +(-0.15,-0.25) -- +(0.15,-0.25) -- cycle;
+
+    \end{tikzpicture}
+  \end{center}
+
+\end{frame}
+
+\begin{frame}{Success will be measured through Technology Readiness Level (TRL) advancement}
+
+  \begin{columns}
+    \begin{column}{0.3\textwidth}
+      \begin{block}{TRL Goal}
+
+      \textbf{Current:} TRL 2-3\\
+      \textbf{Target:} TRL 5
+
+      \end{block}
+
+      \vspace{0.5cm}
+
+    \end{column}
+
+    \begin{column}{0.7\textwidth}
+      \begin{columns}
+        \begin{column}{0.33\textwidth}
+          \centering
+          \only<1->{\only<1>{\alert{\textbf{TRL 3}}}%
+          \only<2->{\textbf{TRL 3}}\\
+          \small Components\\
+          \vspace{0.2cm}
+          \includegraphics[width=0.8\textwidth]{images/5_metrics_of_success/puzzle.png}}
+        \end{column}
+
+        \begin{column}{0.33\textwidth}
+          \centering
+          \only<2->{\only<2>{\alert{\textbf{TRL 4}}}%
+          \only<3->{\textbf{TRL 4}}\\
+          \small Integration\\
+          \vspace{0.2cm}
+          \includegraphics[width=0.8\textwidth]{images/5_metrics_of_success/puzzle_complete.png}}
+        \end{column}
+
+        \begin{column}{0.33\textwidth}
+          \centering
+          \only<3->{\alert<3>{\textbf{TRL 5}}\\
+          \small Hardware\\
+          \vspace{0.2cm}
+          \begin{tikzpicture}
+            \node[anchor=south west,inner sep=0] (controller) at (0,0) {\includegraphics[width=0.8\columnwidth]{images/5_metrics_of_success/controller.png}};
+            \node[anchor=center,inner sep=2pt] at (2.48,1.88) {\includegraphics[width=0.3\columnwidth]{images/5_metrics_of_success/emerson_logo_only.png}};
+          \end{tikzpicture}}
+        \end{column}
+      \end{columns}
+    \end{column}
+  \end{columns}
+
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/6_Risks_and_Contingencies.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/6_Risks_and_Contingencies.tex
@ -0,0 +1,13 @@
+\begin{frame}{Four primary risks are identified with clear mitigation and contingency plans}
+
+  \begin{enumerate}
+    \item \alert{Computational Tractability of Synthesis}
+
+    \item \alert{Discrete-Continuous Interface Complexity}
+
+    \item \alert{Procedure Formalization Completeness}
+
+    \item \alert{Hardware-in-the-Loop Integration}
+  \end{enumerate}
+
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/6_Risks_and_Contingencies_v2.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/6_Risks_and_Contingencies_v2.tex
@ -0,0 +1,13 @@
+\begin{frame}{Four primary risks are identified with clear mitigation and contingency plans}
+
+  \begin{enumerate}
+    \item<1-> \alert<1>{Computational Tractability of Synthesis}
+
+    \item<2-> \alert<2>{Discrete-Continuous Interface Complexity}
+
+    \item<3-> \alert<3>{Procedure Formalization Completeness}
+
+    \item<4-> \alert<4>{Hardware-in-the-Loop Integration}
+  \end{enumerate}
+
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/7_Broader_Impacts.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/7_Broader_Impacts.tex
@ -0,0 +1,75 @@
+\begin{frame}{Broader Impact: Multi-billion dollar O\&M cost reduction}
+
+  \begin{block}{The Economic Opportunity}
+    \small
+    Datacenter electricity demand projected to reach \textbf{1,050 TWh/year by 2030}
+  \end{block}
+
+  \vspace{0.5cm}
+
+  \textbf{If supplied by nuclear power:}
+
+  \begin{align*}
+    \text{Total annual cost} &= 1,050 \text{ TWh/yr} \times \$88.24/\text{MWh} \\
+    &= \textbf{\$92.7 billion/year}
+  \end{align*}
+
+  \pause
+
+  \vspace{0.3cm}
+
+  \textbf{O\&M represents 23-30\% of LCOE:}
+
+  \begin{align*}
+    \text{O\&M costs} &= \$92.7\text{B} \times 0.23\text{-}0.30 \\
+    &= \textbf{\$21-28 billion/year}
+  \end{align*}
+
+  \pause
+
+  \vspace{0.5cm}
+
+  \begin{center}
+    \large
+    \textbf{Autonomous control directly addresses\\
+    this multi-billion dollar challenge}
+  \end{center}
+
+\end{frame}
+
+\begin{frame}{Beyond nuclear: A generalizable framework for safety-critical autonomy}
+
+  \begin{columns}
+    \begin{column}{0.5\textwidth}
+      \begin{block}{Why Nuclear First?}
+        \small
+        \begin{itemize}
+          \item Highest regulatory requirements
+          \item Most safety-critical domain
+          \item Procedures already documented
+          \item Establishes regulatory pathway
+        \end{itemize}
+      \end{block}
+    \end{column}
+
+    \begin{column}{0.5\textwidth}
+      \begin{block}{Future Applications}
+        \small
+        \begin{itemize}
+          \item Chemical process control
+          \item Aerospace systems
+          \item Autonomous transportation
+          \item Critical infrastructure
+        \end{itemize}
+      \end{block}
+    \end{column}
+  \end{columns}
+
+  \vspace{1cm}
+
+  \begin{center}
+    \textbf{Translate procedures $\rightarrow$ Synthesize logic $\rightarrow$ Verify behavior}\\
+    \small Applicable to any hybrid system with documented operational requirements
+  \end{center}
+
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/7_Broader_Impacts_v2.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/7_Broader_Impacts_v2.tex
@ -0,0 +1,64 @@
+\begin{frame}{Reducing operations costs for new nuclear power is a billion
+  dollar problem}
+  \centering
+
+  \only<1>{
+    \includegraphics[width=0.8\textwidth]{images/7_broader_impacts/billion.jpg}
+  }
+  
+  \only<2>{
+    \begin{tikzpicture}
+      % Adjustable parameters
+      \def\iconsize{1.6cm}
+      \def\xspacing{1.7cm}
+      \def\yspacing{1.0cm}
+
+      % 12 Senior Operators (2 per shift <20> 6 shifts)
+      \foreach \row in {0,...,5} {
+        \foreach \col in {0,...,9} {
+          \node at (\col*\xspacing, -\row*\yspacing)
+            {\includegraphics[width=\iconsize]{images/7_broader_impacts/billion.jpg}
+            };
+        }
+      }
+
+    \end{tikzpicture}
+  }
+\end{frame}
+
+% \begin{frame}{Beyond nuclear: A generalizable framework for safety-critical autonomy}
+%
+%   \begin{columns}
+%     \begin{column}{0.5\textwidth}
+%       \begin{block}{Why Nuclear First?}
+%         \small
+%         \begin{itemize}
+%           \item Highest regulatory requirements
+%           \item Most safety-critical domain
+%           \item Procedures already documented
+%           \item Establishes regulatory pathway
+%         \end{itemize}
+%       \end{block}
+%     \end{column}
+%
+%     \begin{column}{0.5\textwidth}
+%       \begin{block}{Future Applications}
+%         \small
+%         \begin{itemize}
+%           \item Chemical process control
+%           \item Aerospace systems
+%           \item Autonomous transportation
+%           \item Critical infrastructure
+%         \end{itemize}
+%       \end{block}
+%     \end{column}
+%   \end{columns}
+%
+%   \vspace{1cm}
+%
+%   \begin{center}
+%     \textbf{Translate procedures $\rightarrow$ Synthesize logic $\rightarrow$ Verify behavior}\\
+%     \small Applicable to any hybrid system with documented operational requirements
+%   \end{center}
+%
+% \end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/7_Broader_Impacts_v3.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/7_Broader_Impacts_v3.tex
@ -0,0 +1,62 @@
+\begin{frame}{Reducing operations costs for new nuclear power is a billion
+  dollar problem}
+  \centering
+
+    \includegraphics[width=0.8\textwidth]{images/7_broader_impacts/billion.jpg}
+  % 
+  % \only<2>{
+  %   \begin{tikzpicture}
+  %     % Adjustable parameters
+  %     \def\iconsize{1.6cm}
+  %     \def\xspacing{1.7cm}
+  %     \def\yspacing{1.0cm}
+  %
+  %     % 12 Senior Operators (2 per shift <20> 6 shifts)
+  %     \foreach \row in {0,...,5} {
+  %       \foreach \col in {0,...,9} {
+  %         \node at (\col*\xspacing, -\row*\yspacing)
+  %           {\includegraphics[width=\iconsize]{images/7_broader_impacts/billion.jpg}
+  %           };
+  %       }
+  %     }
+  %
+  %   \end{tikzpicture}
+  % }
+\end{frame}
+
+% \begin{frame}{Beyond nuclear: A generalizable framework for safety-critical autonomy}
+%
+%   \begin{columns}
+%     \begin{column}{0.5\textwidth}
+%       \begin{block}{Why Nuclear First?}
+%         \small
+%         \begin{itemize}
+%           \item Highest regulatory requirements
+%           \item Most safety-critical domain
+%           \item Procedures already documented
+%           \item Establishes regulatory pathway
+%         \end{itemize}
+%       \end{block}
+%     \end{column}
+%
+%     \begin{column}{0.5\textwidth}
+%       \begin{block}{Future Applications}
+%         \small
+%         \begin{itemize}
+%           \item Chemical process control
+%           \item Aerospace systems
+%           \item Autonomous transportation
+%           \item Critical infrastructure
+%         \end{itemize}
+%       \end{block}
+%     \end{column}
+%   \end{columns}
+%
+%   \vspace{1cm}
+%
+%   \begin{center}
+%     \textbf{Translate procedures $\rightarrow$ Synthesize logic $\rightarrow$ Verify behavior}\\
+%     \small Applicable to any hybrid system with documented operational requirements
+%   \end{center}
+%
+% \end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/8_Money_Slide.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/8_Money_Slide.tex
@ -0,0 +1,35 @@
+\begin{frame}[plain]
+    \LARGE\textbf{Formally Verified Autonomous Hybrid Control}
+
+    \vspace{0.2cm}
+
+  \begin{columns}[T]
+    % Left column: Contact info
+    \begin{column}{0.35\textwidth}
+      \normalsize Enabling Economic Viability of Next-Generation Nuclear Power
+
+      \vspace{0.5cm}
+
+      \large\textbf{Dane A. Sabo}\\
+      \small dane.sabo@pitt.edu
+
+      \vspace{0.5cm}
+
+      \textbf{Advisor:}\\
+      Dr. Daniel G. Cole\\
+      \small dgcole@pitt.edu
+
+      \vspace{0.5cm}
+
+      University of Pittsburgh\\
+      Department of Mechanical Engineering and Materials Science
+    \end{column}
+
+    % Right column: Money image
+    \begin{column}{0.65\textwidth}
+      \centering
+      \includegraphics[height=0.7\textheight]{images/money.png}
+    \end{column}
+  \end{columns}
+
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/slides/8_Money_Slide_v2.tex
+++ b/Presentations/20251215-Emerson-Pres/slides/8_Money_Slide_v2.tex
@ -0,0 +1,66 @@
+\begin{frame}[plain]
+    \LARGE\textbf{Formally Verified Autonomous Hybrid Control}
+
+    \vspace{0.2cm}
+
+  \begin{columns}[T]
+    % Left column: Contact info
+    \begin{column}{0.35\textwidth}
+      \normalsize Enabling Economic Viability of Next-Generation Nuclear Power
+
+      \vspace{0.5cm}
+
+      \large\textbf{Dane A. Sabo}\\
+      \small dane.sabo@pitt.edu
+
+      \vspace{0.5cm}
+
+      \textbf{Advisor:}\\
+      Dr. Daniel G. Cole\\
+      \small dgcole@pitt.edu
+
+      \vspace{0.5cm}
+
+      University of Pittsburgh\\
+      Department of Mechanical Engineering and Materials Science
+    \end{column}
+
+    % Right column: Mode graph
+    \begin{column}{0.65\textwidth}
+      \centering
+      \begin{tikzpicture}[
+        state/.style={circle, draw=textcolor, fill=secondary, minimum size=1.2cm},
+        transition/.style={->, >=stealth, thick}
+      ]
+
+        % States arranged vertically
+        \coordinate (start) at (0,1.5);
+        \node[state] (s0) at (0,0) {\scriptsize MODE 5};
+        \node[state] (s1) at (0,-2) {\scriptsize MODE 4};
+        \node[state] (s2) at (1,-4) {\scriptsize MODE 3};
+        \node[state] (s3) at (3,-5.) {\scriptsize MODE 2};
+        \node[state] (s4) at (5,-6) {\scriptsize MODE 1};
+        \node[state] (s5) at (3,-1.5) {\scriptsize SCRAM};
+
+        % Transitions
+      \draw[transition] (start) -- node[midway, right] {\scriptsize Start} (s0);
+        \draw[transition] (s0) -- (s1);
+        \draw[transition] (s1) -- (s2);
+        \draw[transition] (s2) -- (s3);
+        \draw[transition] (s3) -- (s4);
+        \draw[transition] (s2) to[bend right] (s5);
+        \draw[transition] (s1) to[bend right] (s5);
+        \draw[transition] (s3) to[bend right] (s5);
+        \draw[transition] (s4) to[bend right] (s5);
+
+        \draw[transition] (s0) to[loop left] (s0);
+        \draw[transition] (s1) to[loop left] (s1);
+        \draw[transition] (s2) to[loop left] (s2);
+        \draw[transition] (s3) to[loop below] (s3);
+        \draw[transition] (s4) to[loop below] (s4);
+
+      \end{tikzpicture}
+    \end{column}
+  \end{columns}
+
+\end{frame}
--- a/Presentations/20251215-Emerson-Pres/speaker-notes.md
+++ b/Presentations/20251215-Emerson-Pres/speaker-notes.md
@ -0,0 +1,440 @@
+# Speaker Notes: Formally Verified Autonomous Hybrid Control
+
+**Presentation for Engineering PhDs**
+**Audience:** General engineering background, not necessarily control/nuclear/formal methods experts
+
+---
+
+## Slide 1: Title & Roadmap
+
+**Central Thesis:** Formally verified autonomous hybrid control is both *necessary* and *achievable* for next-generation nuclear power.
+
+**Roadmap Overview:**
+1. **The Problem:** Economic challenge + fundamental human reliability limits
+2. **The Technical Challenge:** Hybrid systems and why current methods fall short
+3. **The Solution:** Three-thrust approach with formal guarantees + hardware-in-the-loop
+4. **The Impact:** Beyond nuclear applications
+
+---
+
+## Slide 2: Economic Challenge
+
+### Small modular reactors face an unsustainable staffing cost problem
+
+**The Economic Reality:**
+- Current requirement: 2+ Reactor Operators + 1+ Senior Reactor Operator per unit
+- Training timeline: up to 6 years to become licensed reactor operator
+- Small modular reactors have same staffing overhead but lower power output
+- Result: Higher per-megawatt O&M costs threaten economic viability
+
+**The Market Opportunity:**
+- Datacenter demand projected: 1,050 TWh annually by 2030
+- Nuclear O&M costs: 23-30% of levelized cost ($88.24/MWh)
+- Annual O&M for datacenter demand alone: **$21-28 billion**
+
+**Key message:** Automation is not optional---it's economically essential
+
+---
+
+## Slide 3: Safety Imperative
+
+### Human operators are the root cause of 70-80% of nuclear incidents
+
+**The Human Error Problem:**
+- 70-80% of events attributed to human error (multiple independent analyses)
+- IAEA categorical statement: "Human error was the root cause of ALL severe accidents"
+  - Three Mile Island, Chernobyl, Fukushima
+
+**Three Mile Island (1979):**
+- 100+ simultaneous alarms overwhelmed operators
+- Operators shut down emergency cooling based on incorrect assessment
+- Result: 44% of fuel melted
+- Risk assessment was off by **500-fold** (5% actual vs 0.01% predicted)
+
+**Fundamental Cognitive Limitations:**
+- Working memory: 7±2 items (Miller, 1956)
+- Human Error Probability degrades under stress:
+  - Optimal conditions: 0.001-0.01 (0.1-1%)
+  - Accident conditions: **0.1-1.0 (10-100%)** = essentially guaranteed failure
+- **Four decades of training improvements haven't changed the 70-80% ratio**
+
+---
+
+## Slide 4: The Paradox
+
+### Nuclear control faces a fundamental tension
+
+**The Paradox:** Human operators are both essential for flexibility and the primary source of failure
+
+**Why We Need Humans:**
+- Strategic decision-making
+- Procedure interpretation
+- Handling novel situations
+- Adaptive judgment
+- Legal authority (10 CFR 55)
+
+**Why Humans Fail:**
+- Working memory: 7±2 items
+- Response time: seconds vs milliseconds
+- Cognitive biases (confirmation, anchoring)
+- Stress degrades performance 10-50x
+- Error rates: 0.001 → 1.0 under accident conditions
+
+**Current Division of Labor:**
+- **Automated:** Emergency protection (trip systems, ECCS) = terminal operations
+- **Manual:** Strategic operations (startup, mode transitions, power changes) = routine operations
+- **Problem:** This is backwards! We automate terminal ops but manually handle routine ops.
+
+**Goal:** Combine the reliability of automation with the sophistication of human decision-making
+
+---
+
+## Slide 5: Hybrid Systems
+
+### Hybrid systems combine continuous dynamics with discrete mode switching
+
+**Nuclear plants are inherently hybrid systems**
+
+**Continuous Dynamics:**
+- Reactor temperature, neutron flux, pressure, flow rates, heat transfer
+- Governed by differential equations: ẋ(t) = f(x(t), q(t), u(t))
+
+**Discrete Decisions:**
+- Mode transitions, control strategy changes, safety system actuation, procedure steps
+- Governed by logic: q(k+1) = ν(x(k), q(k), u(k))
+
+**Example: Reactor Startup**
+- Cold Shutdown → Heatup → Approach Criticality → Low Power
+- Each mode has continuous dynamics; transitions are discrete strategic decisions
+- **This is exactly what human operators do today**
+
+---
+
+## Slide 6: Current Gaps
+
+### Existing methods can handle either continuous or discrete, but not both
+
+**Formal Methods (HARDENS):**
+- Can verify discrete logic (requirements → verified binaries)
+- Achieved in 9 months, low cost
+- **BUT:** Cannot handle continuous dynamics
+
+**Control Theory:**
+- Can verify continuous stability (Lyapunov, LQR, robust control)
+- **BUT:** Cannot verify discrete transitions or mode switching
+
+**THE GAP:** Hybrid system verification with formal guarantees spanning both continuous and discrete
+
+**HARDENS Achievement:**
+- Complete RTS verification (discrete only)
+- TRL 3-4, no experimental validation
+- Requirements → formal specs → verified implementation
+- But: No continuous dynamics, no closed-loop verification
+
+**We need to bridge this gap.**
+
+---
+
+## Slide 7: Approach Overview
+
+### Unifying discrete synthesis and continuous verification enables end-to-end guarantees
+
+**Three-Thrust Integrated Approach:**
+
+**Thrust 1 (Procedures → Temporal Logic):**
+- Use NASA FRET to translate written procedures to formal specifications
+- Example: "If high temp, insert rods until reset" becomes G(T_high → X(rods ∧ ...))
+- Realizability checking catches errors in procedures *before* implementation
+
+**Thrust 2 (Temporal Logic → Discrete Automaton):**
+- Reactive synthesis generates correct-by-construction state machine
+- Discrete controller is mathematically guaranteed to follow specifications
+
+**Thrust 3 (Continuous Controllers):**
+- Use reachability analysis and barrier certificates
+- Compositional verification: local proofs, global guarantees
+
+**Innovation:** Each piece uses state-of-the-art tools; innovation is in the integration
+
+---
+
+## Slide 8: Thrust 1 - Procedures to Logic
+
+### NASA's FRET tool translates procedures into unambiguous logic
+
+**The Challenge:** Natural language is ambiguous; machines need precise specifications
+
+**Example Translation:**
+- **Natural:** "If a high temperature alarm triggers, control rods must immediately insert and remain inserted until operator reset."
+- **Logic:** G(HighTemp → X(RodsInserted ∧ (¬RodsWithdrawn U OpReset)))
+
+**FRETish Structure:** 6 components eliminate ambiguity
+- [Scope] [Condition] [Component] SHALL [Timing] [Response]
+
+**Realizability Checking:** Catches errors *before* implementation
+- Detects conflicting requirements
+- Identifies undefined behaviors (gaps left to human judgment)
+- These are "bugs in the procedures"---better to find them early!
+
+**Output:** Unambiguous temporal logic ready for synthesis
+
+---
+
+## Slide 9: Thrust 2 - Reactive Synthesis
+
+### Reactive synthesis generates provably correct discrete controllers
+
+**What is Reactive Synthesis?**
+- **Input:** Temporal logic formula (what *should* happen)
+- **Output:** Finite state machine (how to *make it* happen)
+- **Guarantee:** If a solution exists, it is correct by construction
+
+**Example: Simplified Reactor Automaton**
+- **Nodes** = discrete modes (what control strategy to use)
+- **Edges** = transition conditions (when to switch)
+- No switching errors possible---the automaton is mathematically guaranteed to satisfy specifications
+
+**This is the "Operator's Decision-Making" Automated**
+
+**Tool:** Strix (SYNTCOMP competition winner)
+
+**Output:** Discrete controller with formal correctness guarantee
+
+---
+
+## Slide 10: Thrust 3 - Continuous Verification
+
+### Continuous controllers verified using three complementary techniques
+
+**Three Types of Continuous Modes:**
+1. **Stabilizing:** Stay in current mode (e.g., full-power operation)
+2. **Transitory:** Drive toward next mode (e.g., startup heatup)
+3. **Expulsory:** Force to safe mode (e.g., SCRAM)
+
+**Three Verification Techniques:**
+
+1. **Reachability Analysis:**
+   - Compute reachable state sets
+   - Verify boundary conditions met
+   - Recent advances: Neural Hamilton-Jacobi for high dimensions
+
+2. **Assume-Guarantee:**
+   - Local verification, global guarantees
+   - Each mode verified independently
+
+3. **Barrier Certificates:**
+   - Prove safe set forward invariance
+   - Guarantee transitions occur correctly
+
+**Key Innovation:** Design continuous controllers *after* synthesizing automaton
+- Automaton defines transition boundaries
+- Design each mode to satisfy its local transitions
+- Compositional verification avoids intractable global analysis
+
+**Output:** Verified continuous modes + discrete automaton = Complete hybrid controller
+
+---
+
+## Slide 11: Key Insight
+
+### Automaton-first design makes verification tractable
+
+**Traditional Approach (Intractable):**
+- Design everything at once
+- Verify entire trajectory through all modes
+- Computationally intractable for complex systems
+
+**Our Approach (Tractable):**
+1. **Synthesize Discrete Automaton** (tells us what boundaries to verify)
+2. **Define Transition Boundaries** (from automaton structure)
+3. **Design Continuous Modes Locally** (each controller designed for its specific job)
+4. **Verify Each Mode Independently** (local verification is tractable)
+5. **Compose via Assume-Guarantee** (interface contracts guarantee composition)
+
+**Key Message:** Decomposition is the key to tractable verification
+
+---
+
+## Slide 12: Demonstration
+
+### SmAHTR autonomous startup provides a rigorous test case
+
+**Small Modular Advanced High Temperature Reactor (SmAHTR):**
+- Liquid-salt cooled reactor design
+- Well-documented startup procedures
+- Representative of next-generation SMR designs
+
+**Startup Sequence:**
+Cold → Controlled Heating → Approach Criticality → Low-Power Physics → Full Power
+
+Each mode has different control objective:
+- Temp control → Ramp rate → Reactivity → Neutron flux → Load following
+
+**Implementation Platform:**
+- **Simulation:** High-fidelity Simulink model (thermal-hydraulics + neutron kinetics)
+- **Hardware:** Emerson Ovation control system (industry standard)
+- **Integration:** ARCADE platform (hardware-in-the-loop)
+- **Validation:** Real-time performance on actual control equipment
+
+**Why This Matters:**
+- Multiple coordinated subsystems
+- Strict timing/temperature constraints
+- Complex nonlinear dynamics
+- **This is not a toy problem**---it's representative of deployment challenges
+
+---
+
+## Slide 13: Expected Outcomes
+
+### Success measured by progression to TRL 5
+
+**Technology Readiness Level Progression:**
+- **Current:** TRL 2-3 (basic concepts, HARDENS precedent)
+- **Target:** TRL 5 (validated prototype in relevant environment)
+- **Gap:** Experimental validation with continuous dynamics
+
+**Three Concrete Deliverables:**
+
+**1. Procedure Translation Methodology**
+- Engineers generate verified controllers from regulatory procedures
+- No formal methods expertise required
+
+**2. Continuous Verification Framework**
+- Standard control design + iterative verification
+- Mathematical proof of safe mode transitions
+
+**3. SmAHTR Hardware-in-the-Loop Demonstration**
+- Autonomous startup on industrial control hardware
+- Real-time performance validation
+- Clear path to deployment
+
+**Key Message:** TRL 5 proves both theoretical validity and practical implementability
+
+---
+
+## Slide 14: Broader Impact
+
+### This methodology generalizes to any safety-critical hybrid system
+
+**Common Pattern Across Domains:**
+- Written procedures exist
+- Continuous dynamics + discrete decisions
+- Safety is paramount
+- Autonomy has economic benefits
+
+**Application Domains:**
+- **Chemical Process:** Batch processes, safety interlocks
+- **Aerospace:** Flight phases, emergency procedures
+- **Autonomous Transport:** Driving modes, emergency maneuvers
+- **Medical Devices:** Therapy modes, patient monitoring
+- **Power Grid:** Generation modes, fault response
+
+**Economic Multiplier:**
+- Nuclear O&M (datacenter demand): $21-28B annually
+- Broader safety-critical infrastructure: **Much larger**
+
+**Regulatory Pathway:**
+- Proving concept in nuclear (highest safety bar)
+- Establishes precedent: mathematical proof as regulatory evidence
+- Easier adoption in other industries
+
+**Key Message:** Nuclear is the proving ground; impact extends far beyond
+
+---
+
+## Slide 15: Innovation Summary
+
+### The innovation is systematic integration to bridge a fundamental gap
+
+**What's NOT New (but state-of-the-art):**
+- Temporal logic
+- Reactive synthesis
+- Reachability analysis
+- Barrier certificates
+- Hardware-in-the-loop
+
+These are mature techniques from computer science and control theory.
+
+**What IS New:**
+- **Integration:** Unifying discrete and continuous verification
+- **Methodology:** Systematic tool-supported workflow
+- **Decomposition:** Automaton-first design enables tractable verification
+- **Practical:** Targets existing industrial hardware
+
+**Comparison to HARDENS:**
+| Feature | HARDENS (2022) | This Work |
+|---------|----------------|-----------|
+| Discrete verification | ✓ | ✓ |
+| Continuous verification | ✗ | ✓ |
+| Hybrid system verification | ✗ | ✓ |
+| Experimental validation | TRL 3-4 | TRL 5 |
+| Hardware-in-the-loop | ✗ | ✓ |
+
+**Key Enabling Insight:**
+Automaton-first design makes continuous verification tractable by decomposing the problem into local verifications with compositional guarantees
+
+---
+
+## Slide 16: Conclusion
+
+### Formally verified autonomous hybrid control: necessary, achievable, timely
+
+**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**
+
+**This Research Closes the Gap:**
+HARDENS (Discrete) + Continuous Verification = Complete Hybrid System
+
+**Vision:** Control engineers generate high-assurance autonomous controllers from procedures.
+- No formal methods PhD required
+- Mathematical proof included
+- Deployable on existing industrial hardware
+
+---
+
+## Slide 17: Questions
+
+**Contact Information:**
+- Dane A. Sabo: dane.sabo@pitt.edu
+- Dr. Dan G. Cole: dgcole@pitt.edu
+- University of Pittsburgh, Cyber Energy Center
+
+---
+
+## Key Talking Points to Remember
+
+### Opening (Slides 1-4)
+- Hook with economics: $21-28B annual market
+- Pivot to safety: 70-80% human error is a fundamental problem
+- The paradox: We need human sophistication but can't tolerate human unreliability
+
+### Technical Middle (Slides 5-11)
+- Hybrid systems are how nuclear plants actually operate
+- Current tools only handle half the problem
+- Our innovation: integration of existing tools with automaton-first decomposition
+- Emphasize "correct by construction" throughout
+
+### Demonstration & Impact (Slides 12-16)
+- SmAHTR is real, not toy problem
+- TRL 5 means practical feasibility, not just theory
+- Nuclear is proving ground, but impact is much broader
+- Now is the right time: economics + safety + technical maturity converge
+
+### Anticipate Questions
+- **"Why not just train operators better?"** → 40 years of improvements haven't changed 70-80% ratio; cognitive limits are fundamental
+- **"How does this compare to ML/AI approaches?"** → We provide mathematical proofs, not statistical confidence
+- **"What about edge cases?"** → That's the point! Realizability checking finds specification gaps; formal verification proves all cases
+- **"Timeline?"** → HARDENS did discrete in 9 months; we're building on that foundation
+- **"Why nuclear first?"** → Highest safety bar + best documented procedures + huge economic driver
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+                    \node[anchor=center] at ([yshift=0.3cm, xshift=-0.3cm]computer.center) {
+                        \includegraphics[width=1.0cm]{images/5_metrics_of_success/nuclear-plant.png}
+                    };
+
+                    \node[below=0.1cm of computer, text width=3cm, align=center] {\small Digital Twin};
+
+                    % Bidirectional arrows
+                    \draw[->, >=stealth, very thick, draw=textcolor]
+                        ([yshift=0.3cm]engineer.east) -- ([yshift=0.3cm]computer.west)
+                        node[midway, above, text width=2cm, align=center] {\scriptsize Design};
+                    \draw[->, >=stealth, very thick, draw=textcolor]
+                        ([yshift=-0.3cm]computer.west) -- ([yshift=-0.3cm]engineer.east)
+                        node[midway, below, text width=2cm, align=center] {\scriptsize Validate};
+                \end{tikzpicture}
+            };
+
+            %Author Block
+            \node(author)[anchor = west] at (0,6) {\parbox[c]{5cm}{\raggedright\insertauthor}};
+
+            \node(institute)[anchor = north, below = 0.1cm of author] {\parbox[c]{5cm}{\raggedright\small\insertinstitute}};
+
+            \node(date)[anchor = north, below = 0.25cm of institute] {\parbox[c]{5cm}{\raggedright\small\insertdate}};
+
+            %logo
+            \node(logo)[anchor = south west] at (0,.75) {\includegraphics[width = 3cm]{images/logo.png}};
+
+            %Surrounding Structure
+            \fill[secondary] (0,0) rectangle(\paperwidth, 0.5);
+        \end{tikzpicture}
+    \end{beamercolorbox}
+}
+
+\mode<all>
--- a/Presentations/20251215-Emerson-Pres/theme/beamerouterthemedane_native.sty
+++ b/Presentations/20251215-Emerson-Pres/theme/beamerouterthemedane_native.sty
@ -0,0 +1,86 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% OUTER THEME - The bones. Heading, footer, and navigation.
+% Defines: background, frame title, footline, page geometry
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\mode<presentation>
+
+%%%%% SET PAGE SIZE
+\geometry{papersize={19cm,12cm}}
+
+% Customize navigation symbols
+\setbeamertemplate{navigation symbols}{}
+
+%%%%%% BACKGROUND
+\setbeamertemplate{background}{
+    %CREATE TIKZ PICTURE OF BOXES LAYOUT
+    \begin{tikzpicture}
+        \useasboundingbox (0,0) rectangle(\paperwidth,\paperheight);
+
+        \ifnum\thepage>0\relax%
+        %LOAD BACKGROUND IMAGE
+            \node at (current page.center){\includegraphics[height=\paperheight]{images/back.jpg}};
+            \fill[primary,opacity=0.925] (0,0) rectangle(\paperwidth,\paperheight);
+        \fi
+
+        \if\gridmode1
+            \draw[opacity=.3,secondary](0,0) grid (\pagewidth,\pageheight);
+            \draw[step=4cm, opacity=.3, red](0,0) grid (\pagewidth,\pageheight);
+        \fi
+
+    \end{tikzpicture}
+}
+
+%%%%%% HEADER
+\defbeamertemplate*{frametitle}{dane}[1][]{
+  \begin{beamercolorbox}[wd=\paperwidth,ht=2cm]{frametitle}
+      \begin{tikzpicture}
+          \useasboundingbox[fill=primary](0,0) rectangle(\the\paperwidth,2);
+
+          \fill[tertiary] (0,0) rectangle(1,2);
+          \fill[secondary] (1.05,0) rectangle(\paperwidth,2);
+
+           \ifx\insertframesubtitle\@empty%
+                %NO SUBTITLE
+              {\node[anchor=west, headingcolor,font=\large] at
+              (1.05,1.0){\parbox[l]{17cm}{\raggedright \insertframetitle}};}
+            \else% INCLUDE SUBTITLE
+              {\node[anchor= west, headingcolor,font=\normalsize] at
+                (1.05,1.31){\parbox[l]{17cm}{\raggedright \insertframetitle}};%
+               \node[anchor= west, headingcolor,font=\footnotesize] at
+               (1.05,0.31){\textit{\insertframesubtitle}};
+               }%
+            \fi
+      \end{tikzpicture}
+  \end{beamercolorbox}
+}
+
+%%%%% FOOTER
+\defbeamertemplate*{footline}{dane}[1][]{
+    \begin{beamercolorbox}[wd=\paperwidth,ht=0.05cm]{footline}
+
+         \begin{tikzpicture}
+             \includegraphics[width = 2cm]{images/logo.png}
+         \end{tikzpicture}
+
+         \begin{tikzpicture}
+             %CREATE BOUNDING BOX
+             \useasboundingbox[fill=secondary](0,\paperheight-0.5cm) rectangle(\paperwidth,\paperheight);
+
+             %INSERT SECTION NAME
+             \node[anchor=west, tertiary] at (0.1,\paperheight-0.25cm){\insertshorttitle};
+             %INSERT FRAME NUMBER
+              \node[anchor=east, tertiary] at (\paperwidth-0.1cm,\paperheight-0.25cm) {\insertframenumber/\inserttotalframenumber};
+         \end{tikzpicture}
+    \end{beamercolorbox}
+}
+
+%%%%%% NOTES
+\if\notemode1
+    \setbeameroption{show notes on second screen = right}
+\fi
+\if\notemode2
+    \setbeameroption{show only notes}
+\fi
+
+\mode<all>
--- a/Presentations/20251215-Emerson-Pres/theme/beamerthemedane_native.sty
+++ b/Presentations/20251215-Emerson-Pres/theme/beamerthemedane_native.sty
@ -0,0 +1,39 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% DANE NATIVE BEAMER THEME
+% A clean, modular beamer theme
+%
+% Author: Dane A. Sabo
+% License: MIT
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\mode<presentation>
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% REQUIREMENTS
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\RequirePackage{tikz}
+\RequirePackage{xcolor}
+\RequirePackage{graphicx}
+\RequirePackage{pgfplots}
+\RequirePackage{geometry}
+
+% Configure pgfplots
+\pgfplotsset{compat=1.18}
+
+% Load TikZ libraries
+\usetikzlibrary{positioning}
+\usetikzlibrary{calc}
+\usetikzlibrary{arrows,chains,decorations.markings,shadows,shapes.arrows,arrows.meta}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% LOAD THEME COMPONENTS
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Load in order: color, font, inner, outer
+% This ensures proper dependency resolution
+
+\usecolortheme{dane_native}
+\usefonttheme{dane_native}
+\useinnertheme{dane_native}
+\useoutertheme{dane_native}
+
+\mode<all>
--- a/Presentations/20251215-Emerson-Pres/two_loop_fine_sweep.jl
+++ b/Presentations/20251215-Emerson-Pres/two_loop_fine_sweep.jl
@ -0,0 +1,177 @@
+using DifferentialEquations
+using Plots
+
+"""
+Two-Loop Reactor System - FINE Parameter Sweep over μ
+Using ONLY constants from Python script
+"""
+
+println("=== Two-Loop Reactor: Fine μ Sweep ===\n")
+
+# Constants from Python script
+const C_0 = 33.33       # Base Heat Capacity [%-sec/°F]
+const τ_0 = 0.75 * C_0  # Base Time Constant [sec]
+
+# Initial conditions from Python script
+const T_initial = 450.0  # All temperatures start at 450°F
+
+# Power levels from Python script
+const P_r = 100.0   # Reactor power
+const Q_sg = 50.0   # Heat removal per steam generator (equal loading)
+
+println("=== Parameters (from Python script) ===")
+println("C_0 = $C_0 %-sec/°F")
+println("τ_0 = $τ_0 sec")
+println("P_r = $P_r")
+println("Q_sg = $Q_sg per SG")
+
+# Two-loop system ODEs
+function two_loop!(du, u, p, t)
+    T_hot, T_cold1, T_cold2 = u
+    μ = p[1]
+
+    # System parameters (from Python script)
+    C_r = μ * C_0
+    C_sg = (1 - μ) * C_0 / 2
+    W = C_0 / (2 * τ_0)
+
+    # Energy balances (exactly from Python script)
+    # C_r * dT_hot/dt = P_r - W*(T_hot - T_cold1) - W*(T_hot - T_cold2)
+    du[1] = (P_r - W * (T_hot - T_cold1) - W * (T_hot - T_cold2)) / C_r
+
+    # C_sg * dT_cold1/dt = W*(T_hot - T_cold1) - Q1
+    du[2] = (W * (T_hot - T_cold1) - Q_sg) / C_sg
+
+    # C_sg * dT_cold2/dt = W*(T_hot - T_cold2) - Q2
+    du[3] = (W * (T_hot - T_cold2) - Q_sg) / C_sg
+
+    return du
+end
+
+# Initial conditions (exact, from Python script)
+u0 = [T_initial, T_initial, T_initial]
+
+println("\n=== Initial Conditions ===")
+println("T_hot_0 = $T_initial °F")
+println("T_cold1_0 = $T_initial °F")
+println("T_cold2_0 = $T_initial °F")
+
+# Fine μ sweep
+μ_values = range(0.5, 0.75, length=50)  # VERY FINE sweep
+println("\n=== μ Sweep ===")
+println("μ range: [0.5, 0.75]")
+println("Number of cases: $(length(μ_values))")
+
+# Time span
+tspan = (0.0, 30.0)
+t_save = range(0, 30, length=300)
+
+# Solve for all μ values
+println("\nSolving $(length(μ_values)) cases...")
+all_sols = []
+for (i, μ) in enumerate(μ_values)
+    if i % 10 == 0
+        print(".")
+    end
+    p = [μ]
+    prob = ODEProblem(two_loop!, u0, tspan, p)
+    sol = solve(prob, Tsit5(), saveat=t_save)
+    push!(all_sols, sol)
+end
+println(" Done!")
+
+# Extract data
+times = all_sols[1].t
+all_T_hot = [[sol.u[i][1] for i in 1:length(sol)] for sol in all_sols]
+all_T_cold1 = [[sol.u[i][2] for i in 1:length(sol)] for sol in all_sols]
+all_T_cold2 = [[sol.u[i][3] for i in 1:length(sol)] for sol in all_sols]
+
+# Compute T_ave for each μ
+all_T_ave = []
+for (i, μ) in enumerate(μ_values)
+    T_ave = μ * all_T_hot[i] .+ (1 - μ) * (all_T_cold1[i] .+ all_T_cold2[i]) ./ 2
+    push!(all_T_ave, T_ave)
+end
+
+# Compute envelopes
+T_hot_min = [minimum([all_T_hot[i][j] for i in 1:length(μ_values)]) for j in 1:length(times)]
+T_hot_max = [maximum([all_T_hot[i][j] for i in 1:length(μ_values)]) for j in 1:length(times)]
+T_ave_min = [minimum([all_T_ave[i][j] for i in 1:length(μ_values)]) for j in 1:length(times)]
+T_ave_max = [maximum([all_T_ave[i][j] for i in 1:length(μ_values)]) for j in 1:length(times)]
+
+println("\n=== Creating Plots ===")
+
+# Plot 1: T_hot reach tube
+p1 = plot(times, T_hot_min, fillrange=T_hot_max,
+         xlabel="Time (s)", ylabel="T_hot (°F)",
+         title="Hot Leg Temperature Reach Tube",
+         fillalpha=0.4, color=:red, lw=2,
+         label="Reach tube", legend=:bottomright)
+
+# Plot 2: T_ave reach tube
+p2 = plot(times, T_ave_min, fillrange=T_ave_max,
+         xlabel="Time (s)", ylabel="T_avg (°F)",
+         title="Average Temperature Reach Tube",
+         fillalpha=0.4, color=:orange, lw=2,
+         label="Reach tube", legend=:bottomright)
+
+# Plot 3: Phase portrait - just the reach tube boundary
+p3 = plot(xlabel="T_avg (°F)", ylabel="T_hot (°F)",
+         title="Phase Portrait: T_hot vs T_avg",
+         legend=:bottomright, size=(700, 700))
+
+# Plot the envelope
+plot!(p3, [T_ave_min; reverse(T_ave_max)], [T_hot_min; reverse(T_hot_max)],
+      seriestype=:shape, fillalpha=0.3, color=:purple,
+      label="Reachable region", lw=2)
+
+# Add boundary traces
+plot!(p3, T_ave_min, T_hot_min, color=:blue, lw=2, label="μ = 0.5")
+plot!(p3, T_ave_max, T_hot_max, color=:red, lw=2, label="μ = 0.75")
+
+# Plot 4: ΔT reach tube
+ΔT_min = [minimum([all_T_hot[i][j] - all_T_cold1[i][j] for i in 1:length(μ_values)]) for j in 1:length(times)]
+ΔT_max = [maximum([all_T_hot[i][j] - all_T_cold1[i][j] for i in 1:length(μ_values)]) for j in 1:length(times)]
+
+p4 = plot(times, ΔT_min, fillrange=ΔT_max,
+         xlabel="Time (s)", ylabel="ΔT = T_hot - T_cold (°F)",
+         title="Loop Temperature Difference",
+         fillalpha=0.4, color=:green, lw=2,
+         label="Reach tube", legend=:bottomright)
+
+plot_combined = plot(p1, p2, p3, p4, layout=(2, 2), size=(1400, 1000),
+                    plot_title="Two-Loop Reactor: μ Uncertainty [0.5, 0.75]")
+savefig(plot_combined, "two_loop_fine_sweep.png")
+println("Saved: two_loop_fine_sweep.png")
+
+# Detailed phase portrait
+p_phase = plot(xlabel="T_avg (°F)", ylabel="T_hot (°F)",
+              title="Phase Portrait: T_hot vs T_avg\n(μ uncertainty: [0.5, 0.75])",
+              size=(1000, 900), legend=:bottomright)
+
+# Plot all trajectories (lightly)
+for (i, μ) in enumerate(μ_values)
+    color_val = (μ - minimum(μ_values)) / (maximum(μ_values) - minimum(μ_values))
+    plot!(p_phase, all_T_ave[i], all_T_hot[i],
+          color=cgrad(:viridis)[color_val], lw=1, alpha=0.2, label="")
+end
+
+# Add thick envelope
+plot!(p_phase, [T_ave_min; reverse(T_ave_max)], [T_hot_min; reverse(T_hot_max)],
+      seriestype=:shape, fillalpha=0.2, color=:purple,
+      label="Reachable region", lw=3)
+
+# Mark extremes
+plot!(p_phase, all_T_ave[1], all_T_hot[1],
+      color=:blue, lw=3, label="μ = 0.5", linestyle=:dash)
+plot!(p_phase, all_T_ave[end], all_T_hot[end],
+      color=:red, lw=3, label="μ = 0.75", linestyle=:dash)
+
+savefig(p_phase, "phase_portrait_fine.png")
+println("Saved: phase_portrait_fine.png")
+
+println("\n✓ Complete!")
+println("\nResults:")
+println("  T_hot range: [$(round(minimum(T_hot_min), digits=1)), $(round(maximum(T_hot_max), digits=1))] °F")
+println("  T_avg range: [$(round(minimum(T_ave_min), digits=1)), $(round(maximum(T_ave_max), digits=1))] °F")
+println("  ΔT range: [$(round(minimum(ΔT_min), digits=1)), $(round(maximum(ΔT_max), digits=1))] °F")
--- a/Presentations/20251215-Emerson-Pres/two_loop_linearized_reachability.jl
+++ b/Presentations/20251215-Emerson-Pres/two_loop_linearized_reachability.jl
@ -0,0 +1,215 @@
+using ReachabilityAnalysis
+using LinearAlgebra
+using Plots
+
+"""
+Two-Loop Reactor: Linearized Reachability Analysis
+
+Since the nonlinear system is causing issues with all algorithms,
+let's linearize around an equilibrium point and use LGG09.
+
+This is actual formal reachability analysis - the linearization is
+a standard approximation technique used in control theory.
+"""
+
+println("=== Two-Loop Reactor: Linearized Reachability ===\n")
+
+# Constants
+const C_0 = 33.33
+const τ_0 = 0.75 * C_0
+const μ = 0.6
+const P_r = 100.0
+const Q2 = 50.0
+
+C_r = μ * C_0
+C_sg = (1 - μ) * C_0 / 2
+W = C_0 / (2 * τ_0)
+
+println("=== System Parameters ===")
+println("C_r = $C_r, C_sg = $C_sg, W = $W")
+
+# Find equilibrium with Q1 = 50
+# At equilibrium: dT/dt = 0
+# From equations:
+# P_r - W*(T_hot - T_cold1) - W*(T_hot - T_cold2) = 0
+# W*(T_hot - T_cold1) - Q1 = 0  =>  T_hot - T_cold1 = Q1/W
+# W*(T_hot - T_cold2) - Q2 = 0  =>  T_hot - T_cold2 = Q2/W
+
+Q1_nominal = 50.0
+T_hot_eq = 453.0  # Approximate equilibrium
+T_cold1_eq = T_hot_eq - Q1_nominal/W
+T_cold2_eq = T_hot_eq - Q2/W
+
+println("\n=== Equilibrium Point (Q1 = $Q1_nominal) ===")
+println("T_hot_eq = $T_hot_eq °F")
+println("T_cold1_eq = $T_cold1_eq °F")
+println("T_cold2_eq = $T_cold2_eq °F")
+
+# Linearize around equilibrium
+# State: x = [T_hot - T_hot_eq, T_cold1 - T_cold1_eq, T_cold2 - T_cold2_eq, Q1 - Q1_nominal]
+#
+# Original equations:
+# dT_hot/dt = (P_r - W*(T_hot - T_cold1) - W*(T_hot - T_cold2)) / C_r
+# dT_cold1/dt = (W*(T_hot - T_cold1) - Q1) / C_sg
+# dT_cold2/dt = (W*(T_hot - T_cold2) - Q2) / C_sg
+# dQ1/dt = 0
+#
+# Linearized (using deviations from equilibrium):
+# dx1/dt = (-W*x1 + W*x2 + W*x3) / C_r
+# dx2/dt = (W*x1 - W*x2 - x4) / C_sg
+# dx3/dt = (W*x1 - W*x3) / C_sg
+# dx4/dt = 0
+
+A = [
+    -W/C_r      W/C_r       W/C_r       0.0;
+    W/C_sg     -W/C_sg      0.0        -1.0/C_sg;
+    W/C_sg      0.0        -W/C_sg      0.0;
+    0.0         0.0         0.0         0.0
+]
+
+println("\n=== Linearized System Matrix A ===")
+display(A)
+println()
+
+# Initial set: Small deviations from equilibrium
+# Starting close to equilibrium but with full Q1 uncertainty
+δT_init = 2.0  # ±2°F initial temperature deviation
+Q1_min = 45.0
+Q1_max = 55.0
+
+X0 = Hyperrectangle(
+    low=[-δT_init, -δT_init, -δT_init, Q1_min - Q1_nominal],
+    high=[δT_init, δT_init, δT_init, Q1_max - Q1_nominal]
+)
+
+println("\n=== Initial Set (deviations from equilibrium) ===")
+println("δT_hot ∈ [-$δT_init, $δT_init]")
+println("δT_cold1 ∈ [-$δT_init, $δT_init]")
+println("δT_cold2 ∈ [-$δT_init, $δT_init]")
+println("δQ1 ∈ [$(Q1_min - Q1_nominal), $(Q1_max - Q1_nominal)]")
+
+# Create linear system
+sys = @system(x' = A*x, x ∈ Universe(4))
+
+# Create IVP
+prob = InitialValueProblem(sys, X0)
+
+println("\n=== Solving with LGG09 (Exact for Linear Systems!) ===")
+
+# Solve - LGG09 is EXACT for linear systems!
+# Must specify vars and dimension
+sol = solve(prob, T=30.0, alg=LGG09(δ=0.5, vars=[1, 2, 3, 4], dim=4))
+
+println("✓ Success! Computed $(length(sol)) reach sets")
+println("\nNote: LGG09 provides EXACT reachability for linear systems!")
+
+# Convert back to absolute temperatures for plotting
+println("\n=== Creating Plots ===")
+
+# Extract and shift back to absolute coordinates
+function plot_absolute(sol, var_idx, eq_val, ylabel_text, title_text, color_choice)
+    # Get the reach sets
+    times = Float64[]
+    lower = Float64[]
+    upper = Float64[]
+
+    for reach_set in sol
+        t = inf(reach_set.t_start)
+        set = reach_set.X
+
+        # Project to variable
+        proj = project(set, var_idx)
+
+        # Get bounds
+        low_val = low(proj)[1] + eq_val
+        high_val = high(proj)[1] + eq_val
+
+        push!(times, t)
+        push!(lower, low_val)
+        push!(upper, high_val)
+    end
+
+    p = plot(times, lower, fillrange=upper,
+             xlabel="Time (s)", ylabel=ylabel_text,
+             title=title_text,
+             fillalpha=0.5, color=color_choice, lw=2,
+             label="Reach tube", legend=:topright)
+    return p
+end
+
+p1 = plot_absolute(sol, 1, T_hot_eq, "T_hot (°F)", "Hot Leg Temperature", :red)
+p2 = plot_absolute(sol, 2, T_cold1_eq, "T_cold1 (°F)", "Cold Leg 1 (SG1 - Uncertain)", :blue)
+p3 = plot_absolute(sol, 3, T_cold2_eq, "T_cold2 (°F)", "Cold Leg 2 (SG2 - Known)", :green)
+
+# Phase portrait: T_hot vs T_cold1
+p4 = plot(xlabel="T_cold1 (°F)", ylabel="T_hot (°F)",
+         title="Phase Portrait: T_hot vs T_cold1",
+         legend=:topright)
+
+for reach_set in sol
+    set = reach_set.X
+
+    # Project to (x2, x1)
+    proj = project(set, [2, 1])
+
+    # Get vertices and shift
+    verts = vertices_list(proj)
+    verts_abs = [[v[1] + T_cold1_eq, v[2] + T_hot_eq] for v in verts]
+
+    # Plot polygon
+    xs = [v[1] for v in verts_abs]
+    ys = [v[2] for v in verts_abs]
+    push!(xs, xs[1])  # Close the polygon
+    push!(ys, ys[1])
+
+    plot!(p4, xs, ys, fillalpha=0.3, color=:purple, lw=0, label="")
+end
+plot!(p4, [], [], fillalpha=0.3, color=:purple, label="Reachable sets")
+
+plot_combined = plot(p1, p2, p3, p4, layout=(2, 2), size=(1400, 1000),
+                    plot_title="Linearized Reachability Analysis: Q1 ∈ [$Q1_min, $Q1_max]")
+savefig(plot_combined, "two_loop_linearized_reachability.png")
+println("Saved: two_loop_linearized_reachability.png")
+
+# Detailed phase portrait
+p_phase = plot(xlabel="T_cold1 (°F)", ylabel="T_hot (°F)",
+              title="Phase Portrait: T_hot vs T_cold1\n(Linearized Reachability: Q1 ∈ [$Q1_min, $Q1_max])",
+              size=(1000, 900), legend=:topright)
+
+for (i, reach_set) in enumerate(sol)
+    set = reach_set.X
+    proj = project(set, [2, 1])
+    verts = vertices_list(proj)
+    verts_abs = [[v[1] + T_cold1_eq, v[2] + T_hot_eq] for v in verts]
+
+    xs = [v[1] for v in verts_abs]
+    ys = [v[2] for v in verts_abs]
+    push!(xs, xs[1])
+    push!(ys, ys[1])
+
+    alpha_val = 0.2 + 0.3 * (i / length(sol))  # Fade over time
+    plot!(p_phase, xs, ys, fillalpha=alpha_val, color=:purple, lw=0.5, label="")
+end
+
+plot!(p_phase, [], [], fillalpha=0.5, color=:purple, label="Reachable region")
+
+savefig(p_phase, "phase_portrait_linearized.png")
+println("Saved: phase_portrait_linearized.png")
+
+println("\n✓ Complete!")
+println("\n=== Results ===")
+println("This is FORMAL reachability analysis using linear approximation.")
+println("LGG09 provides EXACT reachable sets for linear systems.")
+println("\nThe linearization is valid near the equilibrium point.")
+println("For large deviations, use parameter sweeps (our previous approach).")
+
+# Print final bounds
+final_set = sol[end].X
+println("\n=== Final Reachable Set (t=30s) ===")
+proj1 = project(final_set, 1)
+proj2 = project(final_set, 2)
+proj3 = project(final_set, 3)
+
+println("T_hot ∈ [$(round(low(proj1)[1] + T_hot_eq, digits=1)), $(round(high(proj1)[1] + T_hot_eq, digits=1))] °F")
+println("T_cold1 ∈ [$(round(low(proj2)[1] + T_cold1_eq, digits=1)), $(round(high(proj2)[1] + T_cold1_eq, digits=1))] °F")
+println("T_cold2 ∈ [$(round(low(proj3)[1] + T_cold2_eq, digits=1)), $(round(high(proj3)[1] + T_cold2_eq, digits=1))] °F")
--- a/Presentations/20251215-Emerson-Pres/two_loop_reachability.jl
+++ b/Presentations/20251215-Emerson-Pres/two_loop_reachability.jl
@ -0,0 +1,185 @@
+using ReachabilityAnalysis
+using Plots
+
+"""
+Two-Loop Reactor: Formal Reachability Analysis with SG1 Efficiency Uncertainty
+
+Using ReachabilityAnalysis.jl with set-based methods (not parameter sweeps!)
+
+Key insight: We'll treat Q1 as an uncertain INPUT, not a state variable.
+This avoids the @taylorize issues we had before.
+"""
+
+println("=== Two-Loop Reactor: Formal Reachability Analysis ===\n")
+
+# Constants from Python script
+const C_0 = 33.33       # Base Heat Capacity [%-sec/°F]
+const τ_0 = 0.75 * C_0  # Base Time Constant [sec]
+const μ = 0.6           # Fixed reactor water mass fraction
+const P_r = 100.0       # Reactor power
+const Q2 = 50.0         # SG2 heat removal (KNOWN)
+
+println("=== Parameters ===")
+println("C_0 = $C_0 %-sec/°F")
+println("τ_0 = $τ_0 sec")
+println("μ = $μ (fixed)")
+println("P_r = $P_r")
+println("Q2 = $Q2 (SG2 - KNOWN)")
+
+# System parameters
+C_r = μ * C_0
+C_sg = (1 - μ) * C_0 / 2
+W = C_0 / (2 * τ_0)
+
+println("\nComputed parameters:")
+println("C_r = $C_r")
+println("C_sg = $C_sg")
+println("W = $W")
+
+# Initial conditions (non-equilibrium)
+const T_hot_0 = 455.0
+const T_cold1_0 = 450.0
+const T_cold2_0 = 450.0
+
+println("\n=== Initial Conditions ===")
+println("T_hot_0 = $T_hot_0 °F")
+println("T_cold1_0 = $T_cold1_0 °F")
+println("T_cold2_0 = $T_cold2_0 °F")
+
+# Q1 uncertainty range
+const Q1_min = 45.0
+const Q1_max = 55.0
+const Q1_center = (Q1_min + Q1_max) / 2
+
+println("\n=== Q1 Uncertainty (SG1 Heat Removal) ===")
+println("Q1 ∈ [$Q1_min, $Q1_max]")
+println("Q1_center = $Q1_center")
+
+# Define the system using @taylorize
+# We'll approximate Q1 uncertainty by adding it as a 4th state with Q̇1 = 0
+@taylorize function two_loop_with_Q1!(du, u, p, t)
+    T_hot, T_cold1, T_cold2, Q1 = u
+
+    # Energy balances
+    du[1] = (P_r - W * (T_hot - T_cold1) - W * (T_hot - T_cold2)) / C_r
+    du[2] = (W * (T_hot - T_cold1) - Q1) / C_sg
+    du[3] = (W * (T_hot - T_cold2) - Q2) / C_sg
+    du[4] = 0.0  # Q1 is constant uncertain parameter
+
+    return du
+end
+
+# Initial set: Small box around initial point for temps, larger for Q1
+# Using Hyperrectangle for initial set
+X0_low = [T_hot_0 - 0.1, T_cold1_0 - 0.1, T_cold2_0 - 0.1, Q1_min]
+X0_high = [T_hot_0 + 0.1, T_cold1_0 + 0.1, T_cold2_0 + 0.1, Q1_max]
+X0 = Hyperrectangle(low=X0_low, high=X0_high)
+
+println("\n=== Initial Set ===")
+println("X0 = Hyperrectangle")
+println("  T_hot ∈ [$(T_hot_0 - 0.1), $(T_hot_0 + 0.1)]")
+println("  T_cold1 ∈ [$(T_cold1_0 - 0.1), $(T_cold1_0 + 0.1)]")
+println("  T_cold2 ∈ [$(T_cold2_0 - 0.1), $(T_cold2_0 + 0.1)]")
+println("  Q1 ∈ [$Q1_min, $Q1_max]")
+
+# Create the initial value problem
+prob = @ivp(x' = two_loop_with_Q1!(x), dim: 4, x(0) ∈ X0)
+
+println("\n=== Solving Reachability Problem ===")
+println("Using TMJets algorithm (Taylor models)...")
+
+# Solve using TMJets (Taylor model integration)
+# This is ACTUAL reachability analysis, not simulation!
+sol = solve(prob, T=30.0, alg=TMJets(abstol=1e-10, orderT=7, orderQ=1))
+
+println("✓ Reachability computation complete!")
+println("Number of reach sets: $(length(sol))")
+
+# Extract flowpipe projections
+println("\n=== Creating Plots ===")
+
+# Plot 1: T_hot vs time
+p1 = plot(sol, vars=(0, 1),
+         xlabel="Time (s)", ylabel="T_hot (°F)",
+         title="Hot Leg Temperature Reach Tube",
+         lw=0, alpha=0.5, color=:red,
+         lab="Reachable set")
+
+# Plot 2: T_cold1 vs time (affected by Q1 uncertainty)
+p2 = plot(sol, vars=(0, 2),
+         xlabel="Time (s)", ylabel="T_cold1 (°F)",
+         title="Cold Leg 1 (SG1 - Uncertain)",
+         lw=0, alpha=0.5, color=:blue,
+         lab="Reachable set")
+
+# Plot 3: T_cold2 vs time (not affected by Q1)
+p3 = plot(sol, vars=(0, 3),
+         xlabel="Time (s)", ylabel="T_cold2 (°F)",
+         title="Cold Leg 2 (SG2 - Known)",
+         lw=0, alpha=0.5, color=:green,
+         lab="Reachable set")
+
+# Plot 4: Phase portrait T_hot vs T_cold1
+p4 = plot(sol, vars=(2, 1),
+         xlabel="T_cold1 (°F)", ylabel="T_hot (°F)",
+         title="Phase Portrait: T_hot vs T_cold1",
+         lw=0, alpha=0.5, color=:purple,
+         lab="Reachable set")
+
+plot_combined = plot(p1, p2, p3, p4, layout=(2, 2), size=(1400, 1000),
+                    plot_title="Formal Reachability Analysis: SG1 Uncertainty Q1 ∈ [$Q1_min, $Q1_max]")
+savefig(plot_combined, "two_loop_reachability.png")
+println("Saved: two_loop_reachability.png")
+
+# Compute T_avg for each reach set and create phase portrait
+println("\n=== Computing T_avg Reachability ===")
+
+# For T_avg phase portrait, we need to project to (T_avg, T_hot) space
+# T_avg = μ*T_hot + (1-μ)*(T_cold1 + T_cold2)/2
+# This requires linear transformation of the flowpipe
+
+# Let's create a detailed phase portrait plot
+p_phase = plot(xlabel="T_avg (°F)", ylabel="T_hot (°F)",
+              title="Phase Portrait: T_hot vs T_avg\n(Formal Reachability: Q1 ∈ [$Q1_min, $Q1_max])",
+              size=(1000, 900), legend=:topright)
+
+# We'll sample the boundary of each reach set
+println("Extracting reach set boundaries for T_avg computation...")
+for (i, reach_set) in enumerate(sol)
+    if i % 10 == 0
+        # Sample this reach set
+        T_hot_vals = Float64[]
+        T_avg_vals = Float64[]
+
+        # Get the set at this time step
+        set = reach_set.X
+
+        # Sample vertices and some interior points
+        for _ in 1:50
+            # Sample a random point from the set
+            pt = sample(set)
+            T_h = pt[1]
+            T_c1 = pt[2]
+            T_c2 = pt[3]
+
+            T_avg = μ * T_h + (1 - μ) * (T_c1 + T_c2) / 2
+
+            push!(T_hot_vals, T_h)
+            push!(T_avg_vals, T_avg)
+        end
+
+        # Plot the cloud of points
+        scatter!(p_phase, T_avg_vals, T_hot_vals,
+                markersize=2, alpha=0.3, color=:purple, label="")
+    end
+end
+
+savefig(p_phase, "phase_portrait_reachability.png")
+println("Saved: phase_portrait_reachability.png")
+
+println("\n✓ Complete!")
+println("\n=== Reachability Analysis Results ===")
+println("This is FORMAL reachability analysis using Taylor models,")
+println("not simulation-based parameter sweeps!")
+println("\nThe reach tubes show ALL possible trajectories for")
+println("Q1 ∈ [$Q1_min, $Q1_max] with GUARANTEES.")
--- a/Presentations/20251215-Emerson-Pres/two_loop_reachability_v2.jl
+++ b/Presentations/20251215-Emerson-Pres/two_loop_reachability_v2.jl
@ -0,0 +1,150 @@
+using ReachabilityAnalysis
+using Plots
+
+"""
+Two-Loop Reactor: Formal Reachability Analysis with SG1 Efficiency Uncertainty
+
+Attempt #2: Using LGG09 algorithm which doesn't require @taylorize
+This uses zonotope overapproximation instead of Taylor models.
+"""
+
+println("=== Two-Loop Reactor: Formal Reachability (LGG09) ===\n")
+
+# Constants from Python script
+const C_0 = 33.33       # Base Heat Capacity [%-sec/°F]
+const τ_0 = 0.75 * C_0  # Base Time Constant [sec]
+const μ = 0.6           # Fixed reactor water mass fraction
+const P_r = 100.0       # Reactor power
+const Q2 = 50.0         # SG2 heat removal (KNOWN)
+
+# System parameters
+C_r = μ * C_0
+C_sg = (1 - μ) * C_0 / 2
+W = C_0 / (2 * τ_0)
+
+println("=== Parameters ===")
+println("C_0 = $C_0, τ_0 = $τ_0, μ = $μ")
+println("C_r = $C_r, C_sg = $C_sg, W = $W")
+println("P_r = $P_r, Q2 = $Q2")
+
+# Initial conditions (non-equilibrium)
+const T_hot_0 = 455.0
+const T_cold1_0 = 450.0
+const T_cold2_0 = 450.0
+
+# Q1 uncertainty range
+const Q1_min = 45.0
+const Q1_max = 55.0
+
+println("\n=== Q1 Uncertainty ===")
+println("Q1 ∈ [$Q1_min, $Q1_max]")
+
+# Define system WITHOUT @taylorize (for LGG09 algorithm)
+# Treat Q1 as 4th state with Q̇1 = 0
+function two_loop_with_Q1!(dx, x, p, t)
+    T_hot = x[1]
+    T_cold1 = x[2]
+    T_cold2 = x[3]
+    Q1 = x[4]
+
+    # Energy balances
+    dx[1] = (P_r - W * (T_hot - T_cold1) - W * (T_hot - T_cold2)) / C_r
+    dx[2] = (W * (T_hot - T_cold1) - Q1) / C_sg
+    dx[3] = (W * (T_hot - T_cold2) - Q2) / C_sg
+    dx[4] = 0.0  # Q1 is constant uncertain parameter
+
+    return dx
+end
+
+# Initial set
+X0 = Hyperrectangle(
+    low=[T_hot_0 - 0.1, T_cold1_0 - 0.1, T_cold2_0 - 0.1, Q1_min],
+    high=[T_hot_0 + 0.1, T_cold1_0 + 0.1, T_cold2_0 + 0.1, Q1_max]
+)
+
+println("\n=== Initial Set ===")
+println("X0 = Hyperrectangle(4D)")
+
+# Create IVP
+prob = @ivp(x' = two_loop_with_Q1!(x), dim: 4, x(0) ∈ X0)
+
+println("\n=== Solving with LGG09 (Zonotope) ===")
+println("This uses zonotope overapproximation...")
+
+# Try LGG09 algorithm (doesn't require @taylorize)
+try
+    sol = solve(prob, T=30.0, alg=LGG09(δ=0.1))
+
+    println("✓ Success! Computed $(length(sol)) reach sets")
+
+    # Plot results
+    p1 = plot(sol, vars=(0, 1),
+             xlabel="Time (s)", ylabel="T_hot (°F)",
+             title="Hot Leg Temperature",
+             lw=0.5, alpha=0.6, color=:red, lab="Reach sets")
+
+    p2 = plot(sol, vars=(0, 2),
+             xlabel="Time (s)", ylabel="T_cold1 (°F)",
+             title="Cold Leg 1 (SG1 - Uncertain)",
+             lw=0.5, alpha=0.6, color=:blue, lab="Reach sets")
+
+    p3 = plot(sol, vars=(0, 3),
+             xlabel="Time (s)", ylabel="T_cold2 (°F)",
+             title="Cold Leg 2 (SG2 - Known)",
+             lw=0.5, alpha=0.6, color=:green, lab="Reach sets")
+
+    p4 = plot(sol, vars=(2, 1),
+             xlabel="T_cold1 (°F)", ylabel="T_hot (°F)",
+             title="Phase Portrait",
+             lw=0.5, alpha=0.6, color=:purple, lab="Reach sets")
+
+    plot_combined = plot(p1, p2, p3, p4, layout=(2, 2), size=(1400, 1000),
+                        plot_title="Formal Reachability (LGG09): Q1 ∈ [$Q1_min, $Q1_max]")
+    savefig(plot_combined, "two_loop_reachability_lgg09.png")
+    println("\nSaved: two_loop_reachability_lgg09.png")
+
+catch e
+    println("❌ LGG09 failed: $e")
+    println("\nTrying GLGM06 instead...")
+
+    try
+        sol = solve(prob, T=30.0, alg=GLGM06(δ=0.1))
+
+        println("✓ Success with GLGM06! Computed $(length(sol)) reach sets")
+
+        # Plot results
+        p1 = plot(sol, vars=(0, 1),
+                 xlabel="Time (s)", ylabel="T_hot (°F)",
+                 title="Hot Leg Temperature",
+                 lw=0.5, alpha=0.6, color=:red, lab="Reach sets")
+
+        p2 = plot(sol, vars=(0, 2),
+                 xlabel="Time (s)", ylabel="T_cold1 (°F)",
+                 title="Cold Leg 1 (SG1 - Uncertain)",
+                 lw=0.5, alpha=0.6, color=:blue, lab="Reach sets")
+
+        p3 = plot(sol, vars=(0, 3),
+                 xlabel="Time (s)", ylabel="T_cold2 (°F)",
+                 title="Cold Leg 2 (SG2 - Known)",
+                 lw=0.5, alpha=0.6, color=:green, lab="Reach sets")
+
+        p4 = plot(sol, vars=(2, 1),
+                 xlabel="T_cold1 (°F)", ylabel="T_hot (°F)",
+                 title="Phase Portrait",
+                 lw=0.5, alpha=0.6, color=:purple, lab="Reach sets")
+
+        plot_combined = plot(p1, p2, p3, p4, layout=(2, 2), size=(1400, 1000),
+                            plot_title="Formal Reachability (GLGM06): Q1 ∈ [$Q1_min, $Q1_max]")
+        savefig(plot_combined, "two_loop_reachability_glgm06.png")
+        println("\nSaved: two_loop_reachability_glgm06.png")
+
+    catch e2
+        println("❌ GLGM06 also failed: $e2")
+        println("\n=== Both algorithms failed ===")
+        println("The system may be too nonlinear for these approximation methods.")
+        println("\nParameter sweep (our previous approach) may be the most practical")
+        println("method for this system, even if it's not formally reachability analysis.")
+    end
+end
+
+println("\n✓ Complete!")
--- a/Presentations/20251215-Emerson-Pres/two_loop_sg_uncertainty.jl
+++ b/Presentations/20251215-Emerson-Pres/two_loop_sg_uncertainty.jl
@ -0,0 +1,179 @@
+using DifferentialEquations
+using Plots
+
+"""
+Two-Loop Reactor: SG1 Heat Removal Uncertainty
+
+Simple, realistic scenario:
+- SG2 efficiency is known: Q2 = 50.0
+- SG1 efficiency is uncertain: Q1 ∈ [45, 55] (±10% due to fouling/conditions)
+- Everything else is exact!
+
+This shows how uncertainty in ONE component propagates through the system.
+"""
+
+println("=== Two-Loop Reactor: SG1 Heat Removal Uncertainty ===\n")
+
+# Constants from Python script
+const C_0 = 33.33       # Base Heat Capacity [%-sec/°F]
+const τ_0 = 0.75 * C_0  # Base Time Constant [sec]
+const μ = 0.6           # Fixed reactor water mass fraction
+const P_r = 100.0       # Reactor power
+const Q2 = 50.0         # SG2 heat removal (KNOWN)
+
+println("=== Parameters ===")
+println("C_0 = $C_0 %-sec/°F")
+println("τ_0 = $τ_0 sec")
+println("μ = $μ (fixed)")
+println("P_r = $P_r")
+println("Q2 = $Q2 (SG2 - KNOWN)")
+
+# Initial conditions (non-equilibrium for interesting dynamics)
+const T_hot_0 = 455.0    # Hot leg slightly elevated
+const T_cold1_0 = 450.0  # Cold legs at reference
+const T_cold2_0 = 450.0
+
+println("\n=== Initial Conditions ===")
+println("T_hot_0 = $T_hot_0 °F")
+println("T_cold1_0 = $T_cold1_0 °F")
+println("T_cold2_0 = $T_cold2_0 °F")
+
+# Two-loop ODEs with Q1 as parameter
+function two_loop!(du, u, p, t)
+    T_hot, T_cold1, T_cold2 = u
+    Q1 = p[1]  # SG1 heat removal (UNCERTAIN)
+
+    # System parameters
+    C_r = μ * C_0
+    C_sg = (1 - μ) * C_0 / 2
+    W = C_0 / (2 * τ_0)
+
+    # Energy balances
+    du[1] = (P_r - W * (T_hot - T_cold1) - W * (T_hot - T_cold2)) / C_r
+    du[2] = (W * (T_hot - T_cold1) - Q1) / C_sg  # Q1 varies!
+    du[3] = (W * (T_hot - T_cold2) - Q2) / C_sg  # Q2 fixed
+
+    return du
+end
+
+# Q1 uncertainty range
+Q1_values = range(45.0, 55.0, length=40)  # Fine sweep over ±10%
+
+println("\n=== Q1 Uncertainty (SG1 Heat Removal) ===")
+println("Q1 range: [45.0, 55.0] (±10% from nominal 50)")
+println("Number of cases: $(length(Q1_values))")
+println("\nPhysical meaning:")
+println("  Q1 = 45: SG1 is 10% less efficient (fouling, poor heat transfer)")
+println("  Q1 = 55: SG1 is 10% more efficient (better conditions)")
+
+# Solve for all Q1 values
+u0 = [T_hot_0, T_cold1_0, T_cold2_0]
+tspan = (0.0, 30.0)
+t_save = range(0, 30, length=300)
+
+println("\nSolving...")
+all_sols = []
+for Q1 in Q1_values
+    p = [Q1]
+    prob = ODEProblem(two_loop!, u0, tspan, p)
+    sol = solve(prob, Tsit5(), saveat=t_save)
+    push!(all_sols, sol)
+end
+println("Done!")
+
+# Extract data
+times = all_sols[1].t
+all_T_hot = [[sol.u[i][1] for i in 1:length(sol)] for sol in all_sols]
+all_T_cold1 = [[sol.u[i][2] for i in 1:length(sol)] for sol in all_sols]
+all_T_cold2 = [[sol.u[i][3] for i in 1:length(sol)] for sol in all_sols]
+
+# Compute T_ave
+all_T_ave = []
+for (i, Q1) in enumerate(Q1_values)
+    T_ave = μ * all_T_hot[i] .+ (1 - μ) * (all_T_cold1[i] .+ all_T_cold2[i]) ./ 2
+    push!(all_T_ave, T_ave)
+end
+
+# Compute reach tube envelopes
+T_hot_min = [minimum([all_T_hot[i][j] for i in 1:length(Q1_values)]) for j in 1:length(times)]
+T_hot_max = [maximum([all_T_hot[i][j] for i in 1:length(Q1_values)]) for j in 1:length(times)]
+T_cold1_min = [minimum([all_T_cold1[i][j] for i in 1:length(Q1_values)]) for j in 1:length(times)]
+T_cold1_max = [maximum([all_T_cold1[i][j] for i in 1:length(Q1_values)]) for j in 1:length(times)]
+T_ave_min = [minimum([all_T_ave[i][j] for i in 1:length(Q1_values)]) for j in 1:length(times)]
+T_ave_max = [maximum([all_T_ave[i][j] for i in 1:length(Q1_values)]) for j in 1:length(times)]
+
+println("\n=== Creating Plots ===")
+
+# Plot 1: T_hot reach tube
+p1 = plot(times, T_hot_min, fillrange=T_hot_max,
+         xlabel="Time (s)", ylabel="T_hot (°F)",
+         title="Hot Leg Temperature",
+         fillalpha=0.4, color=:red, lw=2.5,
+         label="Reach tube", legend=:topright)
+
+# Plot 2: T_cold1 reach tube (affected by Q1 uncertainty)
+p2 = plot(times, T_cold1_min, fillrange=T_cold1_max,
+         xlabel="Time (s)", ylabel="T_cold1 (°F)",
+         title="Cold Leg 1 (SG1 - Uncertain)",
+         fillalpha=0.4, color=:blue, lw=2.5,
+         label="Reach tube", legend=:topright)
+
+# Plot 3: T_ave reach tube
+p3 = plot(times, T_ave_min, fillrange=T_ave_max,
+         xlabel="Time (s)", ylabel="T_avg (°F)",
+         title="Average Primary Temperature",
+         fillalpha=0.4, color=:orange, lw=2.5,
+         label="Reach tube", legend=:topright)
+
+# Plot 4: Phase portrait T_hot vs T_ave
+p4 = plot(xlabel="T_avg (°F)", ylabel="T_hot (°F)",
+         title="Phase Portrait: T_hot vs T_avg",
+         legend=:topright)
+
+# Plot envelope
+plot!(p4, [T_ave_min; reverse(T_ave_max)], [T_hot_min; reverse(T_hot_max)],
+      seriestype=:shape, fillalpha=0.3, color=:purple,
+      label="Reachable region", lw=2.5)
+
+# Mark extremes
+plot!(p4, T_ave_min, T_hot_min, color=:blue, lw=2.5, label="Q1 = 45", linestyle=:dash)
+plot!(p4, T_ave_max, T_hot_max, color=:red, lw=2.5, label="Q1 = 55", linestyle=:dash)
+
+plot_combined = plot(p1, p2, p3, p4, layout=(2, 2), size=(1400, 1000),
+                    plot_title="SG1 Heat Removal Uncertainty: Q1 ∈ [45, 55]")
+savefig(plot_combined, "sg1_uncertainty.png")
+println("Saved: sg1_uncertainty.png")
+
+# Detailed phase portrait
+p_phase = plot(xlabel="T_avg (°F)", ylabel="T_hot (°F)",
+              title="Phase Portrait: T_hot vs T_avg\n(SG1 efficiency uncertainty: Q1 ∈ [45, 55])",
+              size=(1000, 900), legend=:topright)
+
+# Plot all trajectories
+for (i, Q1) in enumerate(Q1_values)
+    color_val = (Q1 - minimum(Q1_values)) / (maximum(Q1_values) - minimum(Q1_values))
+    plot!(p_phase, all_T_ave[i], all_T_hot[i],
+          color=cgrad(:RdBu)[color_val], lw=1.5, alpha=0.3, label="")
+end
+
+# Add envelope
+plot!(p_phase, [T_ave_min; reverse(T_ave_max)], [T_hot_min; reverse(T_hot_max)],
+      seriestype=:shape, fillalpha=0.25, color=:purple,
+      label="Reachable region", lw=3)
+
+# Mark extremes
+plot!(p_phase, all_T_ave[1], all_T_hot[1],
+      color=:blue, lw=3.5, label="Q1 = 45 (low efficiency)", linestyle=:dash)
+plot!(p_phase, all_T_ave[end], all_T_hot[end],
+      color=:red, lw=3.5, label="Q1 = 55 (high efficiency)", linestyle=:dash)
+
+savefig(p_phase, "phase_portrait_sg1.png")
+println("Saved: phase_portrait_sg1.png")
+
+println("\n✓ Complete!")
+println("\n=== Results ===")
+println("T_hot range: [$(round(minimum(T_hot_min), digits=1)), $(round(maximum(T_hot_max), digits=1))] °F")
+println("T_avg range: [$(round(minimum(T_ave_min), digits=1)), $(round(maximum(T_ave_max), digits=1))] °F")
+println("T_cold1 range: [$(round(minimum(T_cold1_min), digits=1)), $(round(maximum(T_cold1_max), digits=1))] °F")
+println("\nΔT_hot = $(round(maximum(T_hot_max) - minimum(T_hot_min), digits=1)) °F")
+println("ΔT_avg = $(round(maximum(T_ave_max) - minimum(T_ave_min), digits=1)) °F")
--- a/Presentations/20251215-Emerson-Pres/two_loop_temp_uncertainty.jl
+++ b/Presentations/20251215-Emerson-Pres/two_loop_temp_uncertainty.jl
@ -0,0 +1,216 @@
+using ReachabilityAnalysis
+using Plots
+
+"""
+Two-Loop Reactor: Temperature Uncertainty Propagation
+
+Simple, clean approach:
+- Uncertainty ONLY in initial temperatures: T_hot, T_cold1, T_cold2
+- Everything else is FIXED: μ = 0.6, Q1 = 50, Q2 = 50, P_r = 100
+- T_avg is derived from the uncertain temperatures
+
+This shows how initial temperature measurement uncertainty propagates.
+"""
+
+println("=== Two-Loop Reactor: Initial Temperature Uncertainty ===\n")
+
+# ALL parameters are FIXED (no uncertainty)
+const C_0 = 33.33       # Base Heat Capacity [%-sec/°F]
+const τ_0 = 0.75 * C_0  # Base Time Constant [sec]
+const μ = 0.6           # FIXED reactor water mass fraction
+const P_r = 100.0       # FIXED reactor power
+const Q1 = 50.0         # FIXED SG1 heat removal
+const Q2 = 50.0         # FIXED SG2 heat removal
+
+# System parameters (all fixed)
+C_r = μ * C_0
+C_sg = (1 - μ) * C_0 / 2
+W = C_0 / (2 * τ_0)
+
+println("=== Fixed Parameters ===")
+println("C_0 = $C_0 %-sec/°F")
+println("τ_0 = $τ_0 sec")
+println("μ = $μ (FIXED)")
+println("P_r = $P_r (FIXED)")
+println("Q1 = $Q1 (FIXED)")
+println("Q2 = $Q2 (FIXED)")
+println("\nComputed:")
+println("C_r = $C_r")
+println("C_sg = $C_sg")
+println("W = $W")
+
+# Initial temperature uncertainty
+# Realistic: ±2°F measurement uncertainty
+const T_hot_nominal = 455.0
+const T_cold_nominal = 450.0
+const δT = 2.0  # ±2°F uncertainty
+
+println("\n=== Initial Temperature Uncertainty ===")
+println("T_hot ∈ [$(T_hot_nominal - δT), $(T_hot_nominal + δT)] °F")
+println("T_cold1 ∈ [$(T_cold_nominal - δT), $(T_cold_nominal + δT)] °F")
+println("T_cold2 ∈ [$(T_cold_nominal - δT), $(T_cold_nominal + δT)] °F")
+println("\nPhysical meaning: ±$δT°F measurement uncertainty")
+
+# Define system (no @taylorize, just plain function)
+function two_loop!(dx, x, p, t)
+    T_hot = x[1]
+    T_cold1 = x[2]
+    T_cold2 = x[3]
+
+    # Energy balances with FIXED parameters
+    dx[1] = (P_r - W * (T_hot - T_cold1) - W * (T_hot - T_cold2)) / C_r
+    dx[2] = (W * (T_hot - T_cold1) - Q1) / C_sg
+    dx[3] = (W * (T_hot - T_cold2) - Q2) / C_sg
+
+    return dx
+end
+
+# Try using @taylorize for TMJets
+@taylorize function two_loop_taylor!(dx, x, p, t)
+    T_hot = x[1]
+    T_cold1 = x[2]
+    T_cold2 = x[3]
+
+    # Energy balances with FIXED parameters
+    dx[1] = (P_r - W * (T_hot - T_cold1) - W * (T_hot - T_cold2)) / C_r
+    dx[2] = (W * (T_hot - T_cold1) - Q1) / C_sg
+    dx[3] = (W * (T_hot - T_cold2) - Q2) / C_sg
+
+    return dx
+end
+
+# Initial set: Box around nominal temperatures
+X0 = Hyperrectangle(
+    low=[T_hot_nominal - δT, T_cold_nominal - δT, T_cold_nominal - δT],
+    high=[T_hot_nominal + δT, T_cold_nominal + δT, T_cold_nominal + δT]
+)
+
+println("\n=== Attempting TMJets (Taylor Models) ===")
+println("This is FORMAL reachability analysis...")
+
+# Create IVP with @taylorize version
+prob = @ivp(x' = two_loop_taylor!(x), dim: 3, x(0) ∈ X0)
+
+try
+    # Try TMJets - this should work since all parameters are constants!
+    sol = solve(prob, T=30.0, alg=TMJets(abstol=1e-10, orderT=7, orderQ=2))
+
+    println("✓ TMJets SUCCESS! Computed $(length(sol)) reach sets")
+    println("\nThis is FORMAL reachability analysis using Taylor models!")
+
+    # Plot results
+    println("\n=== Creating Plots ===")
+
+    # Plot 1: T_hot reach tube
+    p1 = plot(sol, vars=(0, 1),
+             xlabel="Time (s)", ylabel="T_hot (°F)",
+             title="Hot Leg Temperature",
+             lw=0, alpha=0.5, color=:red,
+             lab="Reach tube")
+
+    # Plot 2: T_cold1 reach tube
+    p2 = plot(sol, vars=(0, 2),
+             xlabel="Time (s)", ylabel="T_cold1 (°F)",
+             title="Cold Leg 1",
+             lw=0, alpha=0.5, color=:blue,
+             lab="Reach tube")
+
+    # Plot 3: T_cold2 reach tube
+    p3 = plot(sol, vars=(0, 3),
+             xlabel="Time (s)", ylabel="T_cold2 (°F)",
+             title="Cold Leg 2",
+             lw=0, alpha=0.5, color=:green,
+             lab="Reach tube")
+
+    # Plot 4: Phase portrait T_hot vs T_cold1
+    p4 = plot(sol, vars=(2, 1),
+             xlabel="T_cold1 (°F)", ylabel="T_hot (°F)",
+             title="Phase Portrait",
+             lw=0, alpha=0.5, color=:purple,
+             lab="Reach tube")
+
+    plot_combined = plot(p1, p2, p3, p4, layout=(2, 2), size=(1400, 1000),
+                        plot_title="Formal Reachability: Initial Temperature Uncertainty ±$(δT)°F")
+    savefig(plot_combined, "temp_uncertainty_reachability.png")
+    println("Saved: temp_uncertainty_reachability.png")
+
+    # Compute T_avg for each reach set
+    println("\n=== Computing T_avg Reach Tube ===")
+
+    times = Float64[]
+    T_avg_min = Float64[]
+    T_avg_max = Float64[]
+    T_hot_vals = Float64[]
+    T_cold1_vals = Float64[]
+    T_cold2_vals = Float64[]
+
+    for (i, reach_set) in enumerate(sol)
+        if i % 5 == 0  # Sample every 5th set
+            t = sup(reach_set.t_start)
+            set = reach_set.X
+
+            # Sample points from the set
+            n_samples = 100
+            T_avg_samples = Float64[]
+
+            for _ in 1:n_samples
+                pt = sample(set)
+                T_h = pt[1]
+                T_c1 = pt[2]
+                T_c2 = pt[3]
+
+                # Compute T_avg = μ*T_hot + (1-μ)*(T_cold1 + T_cold2)/2
+                T_avg = μ * T_h + (1 - μ) * (T_c1 + T_c2) / 2
+
+                push!(T_avg_samples, T_avg)
+
+                if i == length(sol)  # Store final points for phase portrait
+                    push!(T_hot_vals, T_h)
+                    push!(T_cold1_vals, T_c1)
+                    push!(T_cold2_vals, T_c2)
+                end
+            end
+
+            push!(times, t)
+            push!(T_avg_min, minimum(T_avg_samples))
+            push!(T_avg_max, maximum(T_avg_samples))
+        end
+    end
+
+    # Plot T_avg reach tube
+    p_tavg = plot(times, T_avg_min, fillrange=T_avg_max,
+                 xlabel="Time (s)", ylabel="T_avg (°F)",
+                 title="Average Primary Temperature\n(Derived from uncertain T_hot, T_cold1, T_cold2)",
+                 fillalpha=0.5, color=:orange, lw=2,
+                 label="T_avg reach tube", legend=:topright,
+                 size=(1000, 700))
+    savefig(p_tavg, "tavg_reachability.png")
+    println("Saved: tavg_reachability.png")
+
+    # Phase portrait: T_hot vs T_avg
+    if length(T_hot_vals) > 0
+        p_phase = scatter(T_avg_samples, T_hot_vals,
+                         xlabel="T_avg (°F)", ylabel="T_hot (°F)",
+                         title="Phase Portrait: T_hot vs T_avg\n(Final reachable set at t=30s)",
+                         markersize=3, alpha=0.5, color=:purple,
+                         label="Reachable points", legend=:topright,
+                         size=(1000, 900))
+        savefig(p_phase, "phase_portrait_tavg.png")
+        println("Saved: phase_portrait_tavg.png")
+    end
+
+    println("\n✓ Complete!")
+    println("\n=== Results ===")
+    println("This is FORMAL reachability analysis using Taylor models.")
+    println("The reach tubes show ALL possible trajectories starting from")
+    println("initial temperature uncertainty: T ∈ [T_nominal ± $(δT)°F]")
+    println("\nFinal T_avg range: [$(round(minimum(T_avg_min), digits=1)), $(round(maximum(T_avg_max), digits=1))] °F")
+    println("Initial uncertainty ±$(δT)°F → Final spread $(round(maximum(T_avg_max) - minimum(T_avg_min), digits=1))°F")
+
+catch e
+    println("❌ TMJets failed: $e")
+    println("\n=== Falling back to parameter sweep ===")
+
+    # Fine parameter sweep as backup
+    include("two_loop_fine_sweep.jl")
+end
--- a/Presentations/ERLM/main.aux
+++ b/Presentations/ERLM/main.aux
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+INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam5.tfm
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/lm/ec-lmss8.tfm
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/lm/ec-lmsso8.tfm
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/lm/ec-lmsso8.tfm
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/lm/ec-lmsso8.tfm
 INPUT ./images/back.jpg
 INPUT ./images/logo.png
 INPUT ./images/logo.png
@ -729,74 +777,12 @@ INPUT ./images/5_metrics_of_success/emerson_logo_only.png
 INPUT ./images/5_metrics_of_success/emerson_logo_only.png
 INPUT ./images/back.jpg
 INPUT ./images/logo.png
-INPUT ./slides/7_Broader_Impacts_v2.tex
+INPUT ./slides/7_Broader_Impacts_v3.tex
 INPUT ./images/logo.png
 INPUT ./images/7_broader_impacts/billion.jpg
 INPUT ./images/7_broader_impacts/billion.jpg
 INPUT ./images/back.jpg
 INPUT ./images/logo.png
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
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-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
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-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
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-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
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-INPUT ./images/7_broader_impacts/billion.jpg
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-INPUT ./images/7_broader_impacts/billion.jpg
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-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/7_broader_impacts/billion.jpg
-INPUT ./images/back.jpg
-INPUT ./images/logo.png
 INPUT ./slides/8_Money_Slide_v2.tex
 INPUT ./images/logo.png
 INPUT ./images/money.png
@ -807,10 +793,10 @@ OUTPUT main.toc
 OUTPUT main.snm
 INPUT ./main.aux
 INPUT ./main.out
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-INPUT /usr/share/texmf/fonts/type1/public/lm/lmss12.pfb
-INPUT /usr/share/texmf/fonts/type1/public/lm/lmss8.pfb
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-INPUT /usr/share/texmf/fonts/type1/public/lm/lmtt8.pfb
-INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy8.pfb
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/type1/public/lm/lmss12.pfb
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/type1/public/lm/lmss8.pfb
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+INPUT /usr/local/texlive/2025/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb
--- a/Show More
+++ b/Show More