Editorial pass: tactical, operational, and strategic improvements

Pass 1 (Tactical/Sentence-level):
- Improved topic-stress positioning for clearer emphasis
- Shortened complex sentences for better readability
- Strengthened verb choices and reduced passive voice
- Eliminated unnecessary repetition
- Enhanced topic strings (subject consistency)

Pass 2 (Operational/Paragraph-Section):
- Smoothed transitions between paragraphs
- Removed redundant text in subsection openings
- Improved flow within sections

Pass 3 (Strategic/Document-level):
- Strengthened Heilmeier question linkages between sections
- Clarified section-to-section transitions
- Maintained overall argument coherence

Focus: clarity and impact over nitpicking. All edits preserve technical accuracy while improving readability.

1-goals-and-outcomes/research_statement_v1.tex

@@ -2,18 +2,18 @@
 This research develops autonomous control systems with mathematical guarantees of safe and correct behavior.
 
 % INTRODUCTORY PARAGRAPH Hook
-Nuclear reactors require extensively trained operators who follow detailed written procedures, switching between control objectives based on plant conditions.
+Nuclear reactors require extensively trained operators who follow detailed written procedures and switch between control objectives based on plant conditions.
 % Gap
-Small modular reactors face a fundamental economic challenge: per-megawatt staffing costs significantly exceed those of conventional plants, threatening economic viability. These reactors need autonomous control systems that manage complex operational sequences safely without constant supervision—systems providing assurance equal to or exceeding that of human-operated systems.
+Small modular reactors face a fundamental economic challenge: per-megawatt staffing costs significantly exceed those of conventional plants, threatening their economic viability. Autonomous control systems can manage complex operational sequences without constant supervision—if they provide assurance equal to or exceeding human-operated systems.
 
 % APPROACH PARAGRAPH Solution
-Formal methods from computer science combine with control theory to build hybrid control systems correct by construction. 
+This research combines formal methods from computer science with control theory to build hybrid control systems correct by construction. 
 % Rationale
-Hybrid systems mirror operator decision-making: discrete logic switches between continuous control modes. Existing formal methods generate provably correct switching logic but fail during transitions with continuous dynamics. Control theory verifies continuous behavior but fails to prove discrete switching correctness. 
+Hybrid systems mirror how operators work: discrete logic switches between continuous control modes. Existing formal methods generate provably correct switching logic but fail when continuous dynamics govern transitions. Control theory verifies continuous behavior but cannot prove discrete switching correctness. Neither approach alone provides end-to-end correctness guarantees.
 % Hypothesis and Technical Approach
-Three stages bridge this gap. First, written operating procedures translate into temporal logic specifications using NASA's Formal Requirements Elicitation Tool (FRET), which structures requirements into scope, condition, component, timing, and response elements. Realizability checking identifies conflicts and ambiguities before implementation. Second, reactive synthesis generates deterministic automata—provably correct by construction. Third, standard control theory designs continuous controllers for each discrete mode while reachability analysis verifies them. Continuous modes classify by transition objectives. Assume-guarantee contracts and barrier certificates prove safe mode transitions. This enables local verification of continuous modes without global trajectory analysis across the entire hybrid system. An Emerson Ovation control system demonstrates the methodology. 
+Three stages bridge this gap. First, written operating procedures translate into temporal logic specifications using NASA's Formal Requirements Elicitation Tool (FRET), which structures requirements into scope, condition, component, timing, and response. Realizability checking identifies conflicts and ambiguities before implementation. Second, reactive synthesis generates deterministic automata—provably correct by construction. Third, standard control theory designs continuous controllers for each discrete mode, which reachability analysis then verifies. Continuous modes classify by transition objectives: transitory modes drive the plant between conditions, stabilizing modes maintain operation within regions, and expulsory modes ensure safety under failures. Assume-guarantee contracts and barrier certificates prove safe mode transitions, enabling local verification without global trajectory analysis. An Emerson Ovation control system demonstrates the methodology. 
 % Pay-off
-This autonomous control approach manages complex nuclear power operations while maintaining safety guarantees, directly addressing the economic constraints threatening small modular reactor viability.
+This autonomous control approach manages complex nuclear power operations while maintaining safety guarantees, directly addressing the economic constraints that threaten small modular reactor viability.
 
 % OUTCOMES PARAGRAPHS
 If this research is successful, we will be able to do the following:

1-goals-and-outcomes/v1.tex

@@ -6,16 +6,16 @@ This research develops autonomous hybrid control systems with mathematical guara
 % INTRODUCTORY PARAGRAPH Hook
 Nuclear power plants require the highest levels of control system reliability. Control system failures risk economic losses, service interruptions, or radiological release.
 % Known information
-Nuclear plant operations rely on extensively trained human operators who follow detailed written procedures and strict regulatory requirements, switching between control modes based on plant conditions and procedural guidance.
+Nuclear plant operations rely on extensively trained human operators. These operators follow detailed written procedures and strict regulatory requirements, switching between control modes based on plant conditions and procedural guidance.
 % Gap
-Human operator reliance prevents autonomous control and creates a fundamental economic challenge for next-generation reactor designs. Small modular reactors face per-megawatt staffing costs far exceeding those of conventional plants, threatening economic viability. The nuclear industry needs autonomous control systems that safely manage complex operational sequences without constant human supervision—systems providing assurance equal to or exceeding that of human operators.
+This reliance on human operators prevents autonomous control and creates a fundamental economic challenge for next-generation reactor designs. Small modular reactors face per-megawatt staffing costs far exceeding those of conventional plants—a gap that threatens their economic viability. Autonomous control systems could manage complex operational sequences without constant human supervision, but only if they provide assurance equal to or exceeding that of human operators.
 
 % APPROACH PARAGRAPH Solution
-Formal methods combine with control theory to build hybrid control systems correct by construction.
+This research combines formal methods with control theory to build hybrid control systems correct by construction.
 % Rationale
-Hybrid systems mirror how operators work: discrete logic switches between continuous control modes. Existing formal methods generate provably correct switching logic from written requirements but fail with continuous dynamics during transitions. Control theory verifies continuous behavior but fails to prove discrete switching correctness. No existing approach provides end-to-end correctness guarantees.
+Hybrid systems mirror how operators work: discrete logic switches between continuous control modes. Existing formal methods generate provably correct switching logic from written requirements but fail when continuous dynamics govern transitions. Control theory verifies continuous behavior but cannot prove discrete switching correctness. Neither approach alone guarantees end-to-end correctness.
 % Hypothesis
-This approach closes the gap by synthesizing discrete mode transitions directly from written operating procedures and verifying continuous behavior between transitions. Existing procedures formalize into logical specifications while continuous dynamics verify against transition requirements, producing autonomous controllers provably free from design defects. 
+This approach closes the gap by synthesizing discrete mode transitions directly from written operating procedures and verifying continuous behavior between transitions. Operating procedures formalize into logical specifications. Continuous dynamics verify against transition requirements. The result: autonomous controllers provably free from design defects. 
 
 The University of Pittsburgh Cyber Energy Center provides access to industry collaboration and Emerson control hardware, ensuring solutions align with practical implementation
 requirements.
@@ -29,10 +29,10 @@ This approach produces three concrete outcomes:
   \item \textbf{Translate written procedures into verified control logic.}
     % Strategy
     We develop a methodology for converting existing written operating
-    procedures into formal specifications that can be automatically synthesized
+    procedures into formal specifications. Reactive synthesis tools then
-    into discrete control logic. This process uses structured intermediate
+    automatically generate discrete control logic from these specifications.
-    representations to bridge natural language procedures and mathematical
+    Structured intermediate representations bridge natural language procedures
-    logic.
+    and mathematical logic.
     % Outcome
     Control system engineers generate verified mode-switching controllers
     directly from regulatory procedures without formal methods expertise,
@@ -68,7 +68,7 @@ This approach produces three concrete outcomes:
 % IMPACT PARAGRAPH Innovation
 These three outcomes—procedure translation, continuous verification, and hardware demonstration—establish a complete methodology from regulatory documents to deployed systems.
 
-\textbf{What makes this research new?} This work unifies discrete synthesis with continuous verification to enable end-to-end correctness guarantees for hybrid systems. Formal methods verify discrete logic; control theory verifies continuous dynamics. No existing methodology bridges both with compositional guarantees. This work establishes that bridge by treating discrete specifications as contracts that continuous controllers must satisfy, enabling independent verification of each layer while guaranteeing correct composition.
+\textbf{What makes this research new?} This work unifies discrete synthesis with continuous verification to enable end-to-end correctness guarantees for hybrid systems. Formal methods verify discrete logic. Control theory verifies continuous dynamics. No existing methodology bridges both with compositional guarantees. This work establishes that bridge by treating discrete specifications as contracts that continuous controllers must satisfy. Independent verification of each layer becomes possible while guaranteeing correct composition. Section 2 (State of the Art) examines why prior work has not achieved this integration. Section 3 (Research Approach) details how this integration will be accomplished.
 
 % Outcome Impact
 If successful, control engineers create autonomous controllers from
@@ -82,13 +82,13 @@ costs through increased autonomy. This research provides the tools to
 achieve that autonomy while maintaining the exceptional safety record the
 nuclear industry requires.
 
-These three outcomes establish a complete methodology from regulatory documents to deployed systems. The following sections systematically answer the Heilmeier Catechism questions that define this research: 
+These three outcomes establish a complete methodology from regulatory documents to deployed systems. This proposal follows the Heilmeier Catechism, with each section explicitly answering its assigned questions:
 \begin{itemize}
   \item \textbf{Section 2 (State of the Art):} What has been done? What are the limits of current practice?
-  \item \textbf{Section 3 (Research Approach):} What is new? Why will it succeed where prior work has not?
+  \item \textbf{Section 3 (Research Approach):} What is new? Why will it succeed where prior work has failed?
   \item \textbf{Section 4 (Metrics for Success):} How do we measure success?
   \item \textbf{Section 5 (Risks and Contingencies):} What could prevent success?
   \item \textbf{Section 6 (Broader Impacts):} Who cares? Why now? What difference will it make?
   \item \textbf{Section 8 (Schedule):} How long will it take?
 \end{itemize}
-This structure ensures each section explicitly addresses its assigned questions while building toward a complete research plan.
+Each section begins by stating its Heilmeier questions and ends by summarizing its answers, ensuring both local clarity and global coherence.

2-state-of-the-art/v2.tex

@@ -1,10 +1,14 @@
 \section{State of the Art and Limits of Current Practice}
 
-\textbf{What has been done? What are the limits of current practice?} This section answers these Heilmeier questions by examining how nuclear reactors operate today and why current approaches—both human-centered and formal methods—cannot provide autonomous control with end-to-end correctness guarantees. We examine reactor operators and their operating procedures, investigate the fundamental limitations of human-based operation, and review formal methods approaches that verify discrete logic or continuous dynamics but not both together. Understanding these limits establishes the verification gap our work addresses.
+\textbf{What has been done? What are the limits of current practice?} This section answers these Heilmeier questions by examining how nuclear reactors operate today and why current approaches—both human-centered and formal methods—cannot provide autonomous control with end-to-end correctness guarantees. Three subsections structure this analysis. First, we examine reactor operators and their operating procedures. Second, we investigate the fundamental limitations of human-based operation. Third, we review formal methods approaches that verify discrete logic or continuous dynamics but not both together. Understanding these limits establishes the verification gap that Section 3 addresses through compositional hybrid synthesis.
 
 \subsection{Current Reactor Procedures and Operation}
 
-Nuclear plant procedures form a hierarchy. Normal operating procedures govern routine operations; abnormal operating procedures handle off-normal conditions. Emergency Operating Procedures (EOPs) manage design-basis accidents. Severe Accident Management Guidelines (SAMGs) address beyond-design-basis events; Extensive Damage Mitigation Guidelines (EDMGs) cover catastrophic damage. These procedures must comply with 10 CFR 50.34(b)(6)(ii); NUREG-0899 provides development guidance~\cite{NUREG-0899, 10CFR50.34}. Expert judgment and simulator validation drive development, not formal verification. Technical evaluation, simulator validation testing, and biennial review under 10 CFR 55.59~\cite{10CFR55.59} assess procedures rigorously, yet this rigor cannot provide formal verification of key safety properties. No mathematical proof exists that procedures cover all possible plant states, that required actions complete within available timeframes, or that transitions between procedure sets maintain safety invariants.
+Current practice must be understood before its limits can be identified. This subsection examines the hierarchy of nuclear plant procedures, the role of operators in executing them, and the operational modes that govern reactor control.
+
+Nuclear plant procedures form a hierarchy. Normal operating procedures govern routine operations. Abnormal operating procedures handle off-normal conditions. Emergency Operating Procedures (EOPs) manage design-basis accidents. Severe Accident Management Guidelines (SAMGs) address beyond-design-basis events. Extensive Damage Mitigation Guidelines (EDMGs) cover catastrophic damage. These procedures must comply with 10 CFR 50.34(b)(6)(ii); NUREG-0899 provides development guidance~\cite{NUREG-0899, 10CFR50.34}. 
+
+Procedure development relies on expert judgment and simulator validation—not formal verification. Technical evaluation, simulator validation testing, and biennial review under 10 CFR 55.59~\cite{10CFR55.59} assess procedures rigorously. Yet this rigor cannot provide formal verification of key safety properties. No mathematical proof confirms that procedures cover all possible plant states. No proof verifies that required actions complete within available timeframes. No proof establishes that procedure-set transitions maintain safety invariants.
 
 \textbf{LIMITATION:} \textit{Procedures lack formal verification of correctness
 and completeness.} Current procedure development relies on expert judgment and
@@ -21,7 +25,7 @@ The division between automated and human-controlled functions reveals the fundam
 
 \subsection{Human Factors in Nuclear Accidents}
 
-Procedures lack formal verification despite rigorous development—this represents only half the reliability challenge. The second pillar of current practice—human operators executing these procedures—introduces additional reliability limitations independent of procedure quality. Procedures define what to do; human operators determine when and how. Even perfect procedures cannot eliminate human error.
+Procedures lack formal verification despite rigorous development. This represents only half the reliability challenge. The other half emerges from procedure execution: even perfect procedures cannot guarantee safe operation when humans execute them imperfectly. Human operators—the second pillar of current practice—introduce reliability limitations independent of procedure quality. Procedures define what to do. Human operators determine when and how. Perfect procedures cannot eliminate human error.
 
 Current-generation nuclear power plants employ over 3,600 active NRC-licensed
 reactor operators in the United States~\cite{operator_statistics}. These
@@ -31,16 +35,12 @@ shift supervisors~\cite{10CFR55}. Staffing typically requires at least two ROs
 and one SRO for current-generation units~\cite{10CFR50.54}. Becoming a reactor
 operator requires several years of training.
 
-Human error persistently contributes to nuclear safety incidents despite decades of improvements in training and procedures. This persistence motivates formal automated control with mathematical safety guarantees. Under 10 CFR Part 55, operators hold legal authority to make critical decisions, including authority to depart from normal regulations during emergencies. The Three Mile
+Human error persistently contributes to nuclear safety incidents despite decades of improvements in training and procedures. This persistence motivates formal automated control with mathematical safety guarantees. Under 10 CFR Part 55, operators hold legal authority to make critical decisions, including authority to depart from normal regulations during emergencies. The Three Mile Island (TMI) accident demonstrated how personnel error, design deficiencies, and component failures combine to cause disaster. Operators misread confusing and contradictory indications. They then shut off the emergency water system~\cite{Kemeny1979}. The President's Commission on TMI identified a
-Island (TMI) accident demonstrated how personnel error, design
-deficiencies, and component failures can combine to cause disaster. Operators
-misread confusing and contradictory indications, then shut off the emergency water
-system~\cite{Kemeny1979}. The President's Commission on TMI identified a
 fundamental ambiguity: placing responsibility for safe power plant operations on
 the licensee without formally verifying that operators can fulfill this
 responsibility does not guarantee safety. This tension between operational
 flexibility and safety assurance remains unresolved. The person responsible for
-reactor safety often becomes the root cause of failures.
+reactor safety often becomes the root cause of failure.
 
 Multiple independent analyses converge on a striking statistic: human error accounts for 70--80\% of nuclear power plant events, compared to approximately 20\% for equipment failures~\cite{WNA2020}. More significantly, human factors—poor safety management and safety culture—caused all severe accidents at nuclear power plants: Three Mile Island, Chernobyl, and Fukushima Daiichi~\cite{hogberg_root_2013}. A detailed analysis
 of 190 events at Chinese nuclear power plants from
@@ -56,9 +56,9 @@ limitations are fundamental to human-driven control, not remediable defects.
 
 \subsection{Formal Methods}
 
-Current practice reveals two critical limitations: procedures lack formal verification, and human operators introduce persistent reliability issues despite four decades of training improvements. Formal methods offer an alternative—mathematical guarantees of correctness that eliminate both human error and procedural ambiguity. 
+Current practice reveals two critical limitations: procedures lack formal verification, and human operators introduce persistent reliability issues that four decades of training improvements have failed to eliminate. Training and procedural improvements cannot solve these problems. What can? Formal methods offer an alternative—mathematical guarantees of correctness that eliminate both human error and procedural ambiguity. 
 
-Yet even the most advanced formal methods applications in nuclear control leave a critical verification gap for autonomous hybrid systems. The following subsections examine why.
+Yet even the most advanced formal methods applications in nuclear control leave a critical verification gap for autonomous hybrid systems. This subsection examines two approaches that illustrate this gap: HARDENS, which verified discrete logic without continuous dynamics, and differential dynamic logic, which handles hybrid verification only post-hoc. Each demonstrates the current state of formal methods while revealing the verification gap this research addresses.
 
 \subsubsection{HARDENS: The State of Formal Methods in Nuclear Control}
 
@@ -66,7 +66,7 @@ The High Assurance Rigorous Digital Engineering for Nuclear Safety (HARDENS)
 project represents the most advanced application of formal methods to nuclear
 reactor control systems to date~\cite{Kiniry2024}.
 
-HARDENS addressed a fundamental dilemma: existing U.S. nuclear control rooms rely on analog technologies from the 1950s--60s, which incur significant risk and cost compared to modern control systems. The NRC contracted Galois, a formal methods firm, to demonstrate that Model-Based Systems Engineering and formal methods could design, verify, and implement a complex protection system meeting regulatory criteria at a fraction of typical cost. The project delivered a Reactor Trip System (RTS) implementation with full traceability from NRC Request for Proposals and IEEE standards through formal architecture specifications to verified software.
+HARDENS addressed a fundamental dilemma: existing U.S. nuclear control rooms rely on analog technologies from the 1950s--60s. These technologies incur significant risk and cost compared to modern control systems. The NRC contracted Galois, a formal methods firm, to demonstrate that Model-Based Systems Engineering and formal methods could design, verify, and implement a complex protection system meeting regulatory criteria at a fraction of typical cost. The project delivered a Reactor Trip System (RTS) implementation with full traceability from NRC Request for Proposals and IEEE standards through formal architecture specifications to verified software.
 
 HARDENS employed formal methods tools and techniques across the verification
 hierarchy. High-level specifications used Lando, SysMLv2, and FRET (NASA Formal
@@ -121,7 +121,7 @@ primary assurance evidence.
 
 \subsubsection{Differential Dynamic Logic: Post-Hoc Hybrid Verification}
 
-HARDENS verified discrete control logic without continuous dynamics. Other researchers attacked the problem from the opposite direction: extending temporal logics to handle hybrid systems directly. This work produced differential dynamic logic (dL). dL introduces two additional operators
+HARDENS verified discrete control logic without continuous dynamics. Other researchers attacked the problem from the opposite direction: extending temporal logics to handle hybrid systems directly. This complementary approach produced differential dynamic logic (dL). dL introduces two additional operators
 into temporal logic: the box operator and the diamond operator. The box operator
 \([\alpha]\phi\) states that for some region \(\phi\), the hybrid system
 \(\alpha\) always remains within that region. In this way, it is a safety
@@ -158,6 +158,6 @@ This section establishes the current state of practice by answering two Heilmeie
 
 \textbf{What has been done?} Human operators provide operational flexibility but introduce persistent reliability limitations that four decades of training improvements have failed to eliminate. Formal methods provide correctness guarantees but have not scaled to complete hybrid control design. HARDENS verified discrete logic without continuous dynamics. Differential dynamic logic expresses hybrid properties but requires post-design expert analysis and fails to scale to system synthesis.
 
-\textbf{What are the limits of current practice?} No existing methodology synthesizes provably correct hybrid controllers from operational procedures with verification integrated into the design process. This gap between discrete-only formal methods and post-hoc hybrid verification prevents autonomous nuclear control with end-to-end correctness guarantees.
+\textbf{What are the limits of current practice?} No existing methodology synthesizes provably correct hybrid controllers from operational procedures with verification integrated into the design process. Current approaches verify either discrete logic or continuous dynamics—never both compositionally. This gap between discrete-only formal methods and post-hoc hybrid verification prevents autonomous nuclear control with end-to-end correctness guarantees.
 
-Two imperatives emerge. The economic imperative: small modular reactors cannot compete with per-megawatt staffing costs matching large conventional plants. The technical imperative: current approaches verify either discrete logic or continuous dynamics, never both compositionally. These limitations define the research opportunity. Section 3 bridges this gap by establishing what makes this approach new and why it will succeed where prior work has failed.
+Two imperatives emerge. Economic imperative: small modular reactors cannot compete with per-megawatt staffing costs matching large conventional plants. Technical imperative: current approaches lack compositional verification for hybrid systems. These limitations define the research opportunity. Section 3 addresses this gap by establishing what makes this approach new and why it will succeed where prior work has failed.

3-research-approach/v3.tex

@@ -15,17 +15,21 @@
 % ----------------------------------------------------------------------------
 % 1. INTRODUCTION AND HYBRID SYSTEMS DEFINITION
 % ----------------------------------------------------------------------------
-Previous approaches verified either discrete switching logic or continuous control behavior, never both simultaneously. Continuous controllers rely on extensive simulation trials for validation; discrete switching logic undergoes simulated control room testing and human factors research. Neither method provides rigorous guarantees despite consuming enormous resources. HAHACS bridges this gap by composing formal methods from computer science with control-theoretic verification, formalizing reactor operations as hybrid automata.
+Previous approaches verified either discrete switching logic or continuous control behavior—never both simultaneously. Continuous controllers rely on extensive simulation trials for validation. Discrete switching logic undergoes simulated control room testing and human factors research. Neither method provides rigorous guarantees despite consuming enormous resources. 
 
-Hybrid system verification faces a fundamental challenge: the interaction between discrete and continuous dynamics. Discrete transitions change the governing vector field, creating discontinuities in system behavior. Traditional verification techniques fail to handle this interaction directly. Our methodology decomposes the problem by verifying discrete switching logic and continuous mode behavior separately, then composes them to establish guarantees for the complete hybrid system. This two-layer approach mirrors reactor operations: discrete supervisory logic determines which control mode is active; continuous controllers govern plant behavior within each mode.
+This work bridges the gap. It composes formal methods from computer science with control-theoretic verification. Reactor operations formalize as hybrid automata.
 
-Building a high-assurance hybrid autonomous control system (HAHACS) requires
+Hybrid system verification faces a fundamental challenge: the interaction between discrete and continuous dynamics creates discontinuities in system behavior when discrete transitions change the governing vector field. Traditional verification techniques fail to handle this interaction directly. 
+
+Our methodology decomposes the problem. It verifies discrete switching logic and continuous mode behavior separately, then composes them to establish guarantees for the complete hybrid system. This two-layer approach mirrors reactor operations. Discrete supervisory logic determines which control mode is active. Continuous controllers govern plant behavior within each mode.
+
+Building a high-assurance hybrid autonomous control system requires
 a mathematical description of the system. This work draws on
 automata theory, temporal logic, and control theory to provide that description. A hybrid system is a
 dynamical system with both continuous and discrete states. This proposal
 addresses continuous autonomous hybrid systems specifically: systems with no external input where continuous
 states remain continuous when discrete states change. These continuous states represent physical quantities that remain
-Lipschitz continuous. We follow the nomenclature from the Handbook on
+Lipschitz continuous. This work follows the nomenclature from the Handbook on
 Hybrid Systems Control~\cite{HANDBOOK ON HYBRID SYSTEMS}, redefined here
 for convenience:
 
@@ -52,11 +56,11 @@ where:
 
 Creating a HAHACS requires constructing this tuple together with proof artifacts that demonstrate the control system's actual implementation satisfies its intended behavior.
 
-\textbf{What is new in this research?} Reactive synthesis, reachability analysis, and barrier certificates each exist independently. This work composes them into a complete methodology for hybrid control synthesis through three key innovations:
+\textbf{What is new in this research?} Section 2 established that existing approaches verify either discrete logic or continuous dynamics—never both compositionally. Reactive synthesis, reachability analysis, and barrier certificates each exist independently. This work composes them into a complete methodology for hybrid control synthesis through three key innovations:
 
 \begin{enumerate}
 \item \textbf{Contract-based decomposition:} Discrete synthesis defines entry/exit/safety contracts that bound continuous verification, inverting the traditional approach of global hybrid system verification.
-\item \textbf{Mode classification:} Continuous modes classify by objective (transitory, stabilizing, expulsory), selecting appropriate verification tools and enabling mode-local analysis with provable composition.
+\item \textbf{Mode classification:} Continuous modes classify by objective (transitory, stabilizing, expulsory), which selects appropriate verification tools and enables mode-local analysis with provable composition.
 \item \textbf{Procedure-driven structure:} Existing procedural structure avoids global hybrid system analysis, making the approach tractable for complex systems like nuclear reactor startup.
 \end{enumerate}
 
@@ -65,12 +69,12 @@ No prior work integrates these three techniques into a systematic design methodo
 \textbf{Why will it succeed?} Three factors ensure practical feasibility:
 
 \begin{enumerate}
-\item Nuclear procedures already decompose operations into discrete phases with explicit transition criteria—we formalize existing structure rather than impose artificial abstractions.
+\item Nuclear procedures already decompose operations into discrete phases with explicit transition criteria—this work formalizes existing structure rather than imposing artificial abstractions.
 \item Mode-level verification avoids the state explosion that makes global hybrid system analysis intractable, bounding computational complexity by verifying each mode against local contracts.
 \item The Emerson collaboration provides both domain expertise to validate procedure formalization and industrial hardware to demonstrate implementation feasibility.
 \end{enumerate}
 
-We demonstrate feasibility on production control systems with realistic reactor models, not merely in principle. Figure~\ref{fig:hybrid_automaton} illustrates this hybrid structure for a simplified reactor startup sequence.
+This work demonstrates feasibility on production control systems with realistic reactor models, not merely in principle. Figure~\ref{fig:hybrid_automaton} illustrates the hybrid structure for a simplified reactor startup sequence.
 
 \begin{figure} 
   \centering
@@ -136,30 +140,17 @@ We demonstrate feasibility on production control systems with realistic reactor
 
 \subsection{System Requirements, Specifications, and Discrete Controllers}
 
-The hybrid automaton formalism defined above provides a mathematical framework for describing discrete modes, continuous dynamics, guards, and invariants. This subsection shows how to construct such systems from existing operational knowledge rather than imposing artificial abstractions. Nuclear operations already possess a natural hybrid structure that maps directly to this automaton formalism.
+The hybrid automaton formalism provides a mathematical framework for describing discrete modes, continuous dynamics, guards, and invariants. But where do these formal descriptions come from? This subsection shows how to construct such systems from existing operational knowledge rather than imposing artificial abstractions. Nuclear operations already possess a natural hybrid structure. This structure maps directly to the automaton formalism through three control scopes: strategic, operational, and tactical.
 
-Human control of nuclear power divides into three scopes: strategic, operational, and tactical. Strategic control represents high-level, long-term decision making for the plant. Objectives at this level are complex and economic in scale, such as managing labor needs and supply chains to optimize scheduled maintenance and downtime. These decisions span months or years. The lowest level—the
+Human control of nuclear power divides into three scopes: strategic, operational, and tactical. Strategic control represents high-level, long-term decision making for the plant. Objectives at this level are complex and economic in scale, such as managing labor needs and supply chains to optimize scheduled maintenance and downtime. These decisions span months or years. 
-tactical level—controls individual components: pumps, turbines, and
+
-chemistry. Nuclear power
+The lowest level—the tactical level—controls individual components: pumps, turbines, and chemistry. Nuclear power plants have already automated tactical control somewhat through what is generally considered ``automatic control.'' These controls are almost always continuous systems with direct impact on the physical state of the plant. Tactical control objectives include maintaining pressurizer level, maintaining core temperature, and adjusting reactivity with chemical shim.
-plants today have already automated tactical control somewhat; such automation is generally considered ``automatic control.''
-These controls are almost always continuous systems with direct impact on the
-physical state of the plant. Tactical control objectives include maintaining
-pressurizer level, maintaining core temperature, or adjusting reactivity with a
-chemical shim.
 
 The operational control scope links these two extremes, representing the primary responsibility of human operators today. Operational control takes strategic objectives and implements tactical control sequences to achieve them, bridging high-level goals with low-level execution. 
 
-Consider an example: a strategic goal may be to
+An example clarifies this three-level structure. Consider a strategic goal to perform refueling at a certain time. The tactical level currently maintains core temperature. The operational level issues the shutdown procedure, using several smaller tactical goals along the way to achieve this objective. 
-perform refueling at a certain time, while the tactical level of the plant is
-currently focused on maintaining a certain core temperature. The operational
-level issues the shutdown procedure, using several smaller tactical goals along
-the way to achieve this objective. 
 
-This structure reveals why the operational and
+This structure reveals why the operational and tactical levels fundamentally form a hybrid controller. The tactical level represents continuous plant evolution according to control input and control law. The operational level represents discrete state evolution that determines which tactical control law applies. This operational level becomes the target for autonomous control.
-tactical levels fundamentally form a hybrid controller. The tactical level represents
-continuous plant evolution according to the control input and control
-law; the operational level represents discrete state evolution that determines
-which tactical control law applies. This operational level becomes the target for autonomous control.
 
 
 \begin{figure}
@@ -195,12 +186,9 @@ which tactical control law applies. This operational level becomes the target fo
 \end{figure}
 
 
-This operational control level is the main reason nuclear control today requires human operators. The hybrid nature of this control system makes proving controller performance against strategic requirements difficult. Unified infrastructure for building and verifying hybrid systems does not currently exist. Humans fill this layer because their general intelligence provides a safe way to manage the system's hybrid nature. These operators use prescriptive operating
+This operational control level is the main reason nuclear control requires human operators. The hybrid nature of this control system makes proving controller performance against strategic requirements difficult. Unified infrastructure for building and verifying hybrid systems does not currently exist. Humans fill this layer because their general intelligence provides a safe way to manage the system's hybrid nature. These operators follow prescriptive operating manuals. Strict procedures govern what control to implement at any given time. These procedures provide the key to the operational control scope.
-manuals to perform their control with strict procedures on what control to
-implement at a given time. These procedures provide the key to the operational
-control scope.
 
-Constructing a HAHACS leverages two key observations about current practice. First, operational scope control is effectively discrete control. Second, operating procedures describe the implementation rules before construction. A HAHACS's intended behavior must be completely described before construction begins. Requirements define the behavior of any control system: statements about what
+Constructing a HAHACS leverages two key observations about current practice. First, operational scope control is effectively discrete control. Second, operating procedures describe implementation rules before construction begins. A HAHACS's intended behavior must be completely described before construction. Requirements define the behavior of any control system: statements about what
 the system must do, must not do, and under what conditions. For nuclear systems,
 these requirements derive from multiple sources including regulatory mandates,
 design basis analyses, and operating procedures. The challenge is formalizing
@@ -247,15 +235,15 @@ eventually reaches operating temperature''), and response properties (``if
 coolant pressure drops, the system initiates shutdown within bounded time'').
 
 
-We use FRET (Formal Requirements Elicitation Tool) to build these temporal logic statements. NASA developed FRET for high-assurance timed systems. FRET provides an intermediate language between temporal logic and natural language, enabling rigid definitions of temporal behavior through syntax accessible to engineers without formal methods expertise. This accessibility proves crucial for industrial feasibility: reducing required expert knowledge makes these tools adoptable by the current workforce.
+This work uses FRET (Formal Requirements Elicitation Tool) to build these temporal logic statements. NASA developed FRET for high-assurance timed systems. FRET provides an intermediate language between temporal logic and natural language, enabling rigid definitions of temporal behavior through syntax accessible to engineers without formal methods expertise. This accessibility proves crucial for industrial feasibility: reducing required expert knowledge makes these tools adoptable by the current nuclear workforce.
 
 FRET's key feature is its ability to start with logically imprecise
-statements and consecutively refine them into well-posed specifications. We can
+statements and refine them consecutively into well-posed specifications. We can
-use this to our advantage by directly importing operating procedures and design
+leverage this by directly importing operating procedures and design
 requirements into FRET in natural language, then iteratively refining them into
 specifications for a HAHACS. This approach provides two distinct benefits. First, it draws a direct link from design documentation to digital system
 implementation. Second, it clearly demonstrates where natural language documents
-are insufficient. Human operators may still use these procedures, making any
+fall short. Human operators may still use these procedures, making any
 room for interpretation a weakness that must be addressed.
 
 FRET has been successfully applied to spacecraft control systems, autonomous vehicle requirements, and medical device specifications. NASA used FRET for the Lunar Gateway project, formalizing flight software requirements that were previously specified only in natural language. The Defense Advanced Research Projects Agency (DARPA) employed FRET in the Assured Autonomy program to verify autonomous systems requirements. These applications demonstrate FRET's maturity for safety-critical domains. Nuclear control procedures present an ideal use case: they are already structured, detailed, and written to minimize ambiguity—precisely the characteristics that enable successful formalization.
@@ -271,21 +259,17 @@ FRET has been successfully applied to spacecraft control systems, autonomous veh
 
 \subsection{Discrete Controller Synthesis}
 
-Temporal logic specifications define what the system must do. Reactive synthesis determines how to implement those requirements, automating the creation of reactive programs from temporal logic—programs that take input for a given state and produce output. 
+Temporal logic specifications define what the system must do. The next question is how to implement those requirements. Reactive synthesis provides the answer.
 
-With system requirements defined as temporal logic specifications, reactive synthesis builds the discrete control system. Reactive synthesis automates the creation of reactive programs from temporal logic specifications—programs that take an input for a given state and produce
+Reactive synthesis automates the creation of reactive programs from temporal logic—programs that take input for a given state and produce output. With system requirements defined as temporal logic specifications, reactive synthesis builds the discrete control system. Our systems fit this model: the current discrete state and status of guard conditions form the input, while the next discrete state forms the output. 
-an output. Our systems fit this model: the current discrete state and
-status of guard conditions form the input, while the next discrete
-state forms the output. 
 
 Reactive synthesis solves a fundamental problem: given an LTL formula $\varphi$ specifying desired system behavior, automatically construct a finite-state machine (strategy) that produces outputs in response to environment inputs such that all resulting execution traces satisfy $\varphi$. If such a strategy exists, the specification is \emph{realizable}. The synthesis algorithm either produces a correct-by-construction controller or reports that no such controller exists. This realizability check provides immediate value: an
 unrealizable specification indicates conflicting or impossible requirements in
 the original procedures, catching errors before implementation. 
 
-Reactive synthesis offers a decisive advantage: the discrete automaton requires no human engineering of its implementation. The resultant automaton is correct by construction, eliminating human error at the implementation stage entirely. Human designers can focus their effort where it belongs: on specifying system behavior rather than implementing switching logic. This shift has two critical implications. First, it provides complete traceability. The reasons the controller
+Reactive synthesis offers a decisive advantage: the discrete automaton requires no human engineering of its implementation. The resultant automaton is correct by construction. This eliminates human error at the implementation stage entirely. Human designers can focus their effort where it belongs: on specifying system behavior rather than implementing switching logic. 
-changes between modes trace back through specifications to requirements, establishing clear liability and justification for system
+
-behavior. Second, it replaces probabilistic human judgment with deterministic guarantees. Human operators cannot eliminate error from discrete control decisions; humans are intrinsically fallible. By defining system behavior using temporal logics and synthesizing the controller using deterministic
+This shift has two critical implications. First, it provides complete traceability. The reasons the controller changes between modes trace back through specifications to requirements, establishing clear liability and justification for system behavior. Second, it replaces probabilistic human judgment with deterministic guarantees. Human operators cannot eliminate error from discrete control decisions. Humans are intrinsically fallible. By defining system behavior using temporal logics and synthesizing the controller using deterministic algorithms, strategic decisions always follow operating procedures exactly—no exceptions, no deviations, no human factors.
-algorithms, strategic decisions always follow operating procedures exactly—no exceptions, no deviations, no human factors.
 
 The synthesized automaton translates directly to executable code through standard compilation techniques. Each discrete state maps to a control mode, guard conditions map to conditional statements, and the transition function defines the control flow. This compilation process preserves the formal guarantees: the implemented code is correct by construction because the automaton it derives from was synthesized to satisfy the temporal logic specifications.
 
@@ -303,11 +287,11 @@ Reactive synthesis has proven successful in robotics, avionics, and industrial c
 
 \subsection{Continuous Control Modes}
 
-Reactive synthesis produces a provably correct discrete controller from operating procedures—an automaton that determines when to switch between modes. But hybrid control requires more than correct mode switching; the continuous dynamics executing within each discrete mode must also be verified to ensure the complete system behaves correctly.
+Reactive synthesis produces a provably correct discrete controller from operating procedures—an automaton that determines when to switch between modes. Hybrid control, however, requires more than correct mode switching. The continuous dynamics executing within each discrete mode must also be verified to ensure correct system behavior.
 
 This subsection describes the continuous control modes executing within each discrete state and explains how they verify against requirements imposed by the discrete layer. The verification approach depends on control objectives. We classify modes into three types—transitory, stabilizing, and expulsory—each requiring different verification tools matched to their distinct purposes. 
 
-This methodology's scope requires clarification: this work verifies continuous controllers but does not synthesize them. The distinction parallels model checking in software verification. Model checking verifies whether a given implementation satisfies its specification without prescribing how to write the software. We assume engineers design continuous controllers using standard control theory techniques. Our contribution provides the verification framework confirming that candidate controllers compose correctly with the discrete layer to produce a safe hybrid system.
+This methodology's scope requires clarification: this work verifies continuous controllers but does not synthesize them. The distinction parallels model checking in software verification. Model checking verifies whether a given implementation satisfies its specification without prescribing how to write the software. This work assumes engineers design continuous controllers using standard control theory techniques. The contribution provides the verification framework confirming that candidate controllers compose correctly with the discrete layer to produce a safe hybrid system.
 
 The operational control scope defines go/no-go decisions that determine what
 kind of continuous control to implement. The entry or exit conditions of a
@@ -360,14 +344,16 @@ tools matched to its control objective. Transitory modes drive the plant between
 
 \subsubsection{Transitory Modes}
 
+We now examine each of the three continuous controller types in detail, beginning with transitory modes.
+
 Transitory modes move the plant from one discrete operating condition to another. Their purpose is to execute transitions: start from entry conditions, reach exit conditions, and maintain safety invariants throughout. Examples include power ramp-up sequences, cooldown procedures, and load-following maneuvers.
 
-The control objective for a transitory mode can be stated formally. Given entry conditions $\mathcal{X}_{entry}$, exit conditions $\mathcal{X}_{exit}$, safety invariant $\mathcal{X}_{safe}$, and closed-loop dynamics $\dot{x} = f(x, u(x))$, the controller must satisfy:
+We can state the control objective for a transitory mode formally. Given entry conditions $\mathcal{X}_{entry}$, exit conditions $\mathcal{X}_{exit}$, safety invariant $\mathcal{X}_{safe}$, and closed-loop dynamics $\dot{x} = f(x, u(x))$, the controller must satisfy:
 \[
 \forall x_0 \in \mathcal{X}_{entry}: \exists T > 0: x(T) \in \mathcal{X}_{exit}
 \land \forall t \in [0,T]: x(t) \in \mathcal{X}_{safe}
 \]
-That is, from any valid entry state, the trajectory must eventually reach the
+From any valid entry state, the trajectory must eventually reach the
 exit condition without ever leaving the safe region.
 
 Reachability analysis provides the natural verification tool for transitory modes.
@@ -411,7 +397,9 @@ appropriate to the fidelity of the reactor models available.
 
 \subsubsection{Stabilizing Modes}
 
-Transitory modes drive the system toward exit conditions. Stabilizing modes do the opposite: they maintain the system within a desired operating region indefinitely. Examples include steady-state power operation, hot standby, and load-following at constant power level. This different control objective requires a different verification approach. Reachability analysis answers "can the system reach a target?" Stabilizing modes ask instead "does the system stay within bounds?" Barrier certificates provide the appropriate tool.
+Where transitory modes drive the system toward exit conditions, stabilizing modes do the opposite: they maintain the system within a desired operating region indefinitely. Examples include steady-state power operation, hot standby, and load-following at constant power level. This different control objective requires a different verification approach. 
+
+Reachability analysis answers "can the system reach a target?" Stabilizing modes ask instead "does the system stay within bounds?" Barrier certificates provide the appropriate tool.
 Barrier certificates analyze the dynamics of the system to determine whether
 flux across a given boundary exists. They evaluate whether any trajectory leaves
 a given boundary. This definition exactly matches what defines the validity of a
@@ -463,7 +451,9 @@ controller.
 
 \subsubsection{Expulsory Modes}
 
-Transitory and stabilizing modes handle nominal operations where plant dynamics match the design model. Expulsory modes handle the opposite case: when the plant deviates from expected behavior through component failures, sensor degradation, or unanticipated disturbances. These continuous controllers prioritize robustness over optimality. The control objective shifts from reaching targets or maintaining regions to driving the plant to a safe shutdown state from potentially anywhere in the state space, under degraded or uncertain dynamics. Examples include emergency core cooling, reactor SCRAM sequences, and controlled depressurization procedures.
+The first two mode types—transitory and stabilizing—handle nominal operations where plant dynamics match the design model. Expulsory modes handle the opposite case: when the plant deviates from expected behavior. Component failures, sensor degradation, or unanticipated disturbances cause this deviation.
+
+Expulsory controllers prioritize robustness over optimality. The control objective shifts from reaching targets or maintaining regions to driving the plant to a safe shutdown state from potentially anywhere in the state space, under degraded or uncertain dynamics. Examples include emergency core cooling, reactor SCRAM sequences, and controlled depressurization procedures.
 
 Proving controller correctness through reachability and barrier certificates makes detecting physical failures straightforward. The controller cannot be incorrect for the nominal plant model. When an invariant is violated, the plant dynamics must have changed. The HAHACS identifies faults when continuous controllers violate discrete boundary conditions—a direct consequence of verified nominal control modes. Unexpected behavior implies off-nominal conditions.
 
@@ -510,7 +500,7 @@ safety margins will matter more than performance during emergency shutdown.
 
 \subsection{Industrial Implementation}
 
-The complete methodology—procedure formalization, discrete synthesis, and continuous verification across three mode types—provides a theoretical framework for hybrid control synthesis. Demonstrating practical feasibility requires validation on realistic systems using industrial-grade hardware, advancing from analytical concepts (TRL 2-3) to laboratory demonstration (TRL 5).
+The complete methodology—procedure formalization, discrete synthesis, and continuous verification across three mode types—provides a theoretical framework for hybrid control synthesis. Theory alone, however, does not demonstrate practical feasibility. Validation on realistic systems using industrial-grade hardware is required, advancing from analytical concepts (TRL 2-3) to laboratory demonstration (TRL 5).
 This research will leverage the University of Pittsburgh Cyber Energy Center's
 partnership with Emerson to implement and test the HAHACS methodology on
 production control equipment. Emerson's Ovation distributed control system is widely deployed
@@ -540,13 +530,13 @@ of transferring technology directly to industry with a direct collaboration in
 this research, while getting an excellent perspective of how our research
 outcomes can align best with customer needs.
 
-This section establishes the research methodology by answering two critical Heilmeier questions:
+This section establishes the research approach by answering two critical Heilmeier questions:
 
-\textbf{What is new in this research?} This work integrates reactive synthesis, reachability analysis, and barrier certificates into a compositional architecture for hybrid control synthesis. Three innovations distinguish this approach: using discrete synthesis to define verification contracts (inverting traditional global analysis), classifying continuous modes by objective to select appropriate verification tools, and leveraging existing procedural structure to avoid intractable state explosion.
+\textbf{What is new in this research?} This work integrates reactive synthesis, reachability analysis, and barrier certificates into a compositional methodology for hybrid control synthesis. Three innovations distinguish this approach: using discrete synthesis to define verification contracts (inverting traditional global analysis), classifying continuous modes by objective to select appropriate verification tools, and leveraging existing procedural structure to avoid intractable state explosion. Section 2 established that prior work verified either discrete logic or continuous dynamics—never both compositionally. This section demonstrates how compositional verification enables what global analysis cannot achieve.
 
 \textbf{Why will this approach succeed?} Three factors ensure practical feasibility. First, nuclear procedures already decompose operations into discrete phases with explicit transition criteria—the approach formalizes existing structure rather than imposing artificial abstractions. Second, mode-level verification bounds each verification problem locally, avoiding the state explosion that makes global hybrid system analysis intractable. Third, the Emerson collaboration provides both domain expertise to validate procedure formalization and industrial hardware to demonstrate implementation feasibility.
 
-The methodology is now complete: procedure formalization, discrete synthesis, continuous verification across three mode types, and hardware implementation. What will be done and why it will work have been established. One critical question remains: \textit{how will success be measured?} Section 4 addresses this through Technology Readiness Level advancement, demonstrating both theoretical correctness and practical implementability as the system progresses from component validation (TRL 3) through integrated simulation (TRL 4) to hardware-in-the-loop testing (TRL 5).
+The methodology is now complete: procedure formalization, discrete synthesis, continuous verification across three mode types, and hardware implementation. Sections 2 and 3 have established what has been done, what is new, and why it will succeed. Three critical questions remain for the complete research plan. Section 4 addresses \textit{How will success be measured?} through Technology Readiness Level advancement. Section 5 addresses \textit{What could prevent success?} through risk analysis and contingency planning. Section 6 addresses \textit{Who cares? Why now? What difference will it make?} through economic and societal impact analysis.
 
 %%% NOTES (Section 5):
 % - Get specific details on ARCADE interface from Emerson collaboration

4-metrics-of-success/v1.tex

@@ -2,13 +2,11 @@
 
 \textbf{How do we measure success?} This research advances through Technology Readiness Levels, progressing from fundamental concepts (TRL 2--3) to validated prototype demonstration (TRL 5).
 
-This work begins at TRL 2--3 and aims to reach TRL 5, where system components operate successfully in a relevant laboratory environment. TRL advancement provides the most appropriate success metric for this work, bridging the gap between academic proof-of-concept and practical deployment. This section explains why, then defines specific criteria for each level from TRL 3 through TRL 5.
+This work begins at TRL 2--3 and aims to reach TRL 5, where system components operate successfully in a relevant laboratory environment. TRL advancement provides the most appropriate success metric for this work by bridging the gap between academic proof-of-concept and practical deployment. This section explains why, then defines specific criteria for each level from TRL 3 through TRL 5.
 
-Technology Readiness Levels provide the ideal success metric by explicitly measuring the gap between academic proof-of-concept and practical deployment—precisely what this work bridges. Academic metrics like papers published or theorems proved fail to capture practical feasibility; empirical metrics like simulation accuracy or computational speed fail to demonstrate theoretical rigor. Only TRLs measure both simultaneously.
+Technology Readiness Levels provide the ideal success metric by explicitly measuring the gap between academic proof-of-concept and practical deployment—precisely what this work bridges. Academic metrics like papers published or theorems proved fail to capture practical feasibility. Empirical metrics like simulation accuracy or computational speed fail to demonstrate theoretical rigor. TRLs measure both simultaneously.
-Advancing from TRL 3 to TRL 5 requires maintaining theoretical rigor while
+
-progressively demonstrating practical feasibility. Formal verification must
+Advancing from TRL 3 to TRL 5 requires maintaining theoretical rigor while progressively demonstrating practical feasibility. Formal verification must remain valid as the system moves from individual components to integrated hardware testing.
-remain valid as the system moves from individual components to integrated
-hardware testing.
 
 The nuclear industry requires extremely high assurance before deploying new
 control technologies. Demonstrating theoretical correctness alone proves
@@ -79,6 +77,6 @@ a relevant laboratory environment. This establishes both theoretical validity
 and practical feasibility, proving the methodology produces verified
 controllers implementable with current technology.
 
-This section establishes success criteria by answering the Heilmeier question \textbf{How do we measure success?} Technology Readiness Level advancement from 2--3 to 5 provides the answer: we measure success by demonstrating both theoretical correctness and practical feasibility through progressively integrated validation. TRL 3 proves component-level correctness, TRL 4 demonstrates system-level integration in simulation, and TRL 5 validates hardware implementation in a relevant environment. Achieving TRL 5 proves the methodology produces verified controllers implementable with current technology.
+This section establishes success criteria by answering the Heilmeier question: \textbf{How do we measure success?} Technology Readiness Level advancement from 2--3 to 5 provides the answer. We measure success by demonstrating both theoretical correctness and practical feasibility through progressively integrated validation. TRL 3 proves component-level correctness. TRL 4 demonstrates system-level integration in simulation. TRL 5 validates hardware implementation in a relevant environment. Achieving TRL 5 proves the methodology produces verified controllers implementable with current technology.
 
-However, reaching TRL 5 depends on several critical assumptions. If these assumptions prove false, the research could stall at lower readiness levels despite sound methodology. Section 5 addresses the complementary Heilmeier question—\textbf{What could prevent success?}—by identifying primary risks, their early warning indicators, and contingency plans that preserve research value even if core assumptions fail.
+Reaching TRL 5 depends on several critical assumptions. If these assumptions prove false, the research could stall at lower readiness levels despite sound methodology. Section 5 addresses the complementary Heilmeier question—\textbf{What could prevent success?}—by identifying primary risks, establishing early warning indicators, and defining contingency plans that preserve research value even when core assumptions fail.

5-risks-and-contingencies/v1.tex

@@ -4,15 +4,7 @@
 
 \subsection{Computational Tractability of Synthesis}
 
-The first major assumption is that formalized startup procedures will yield
+The first major assumption is that formalized startup procedures will yield automata small enough for efficient synthesis and verification. Reactive synthesis scales exponentially with specification complexity. Temporal logic specifications derived from complete startup procedures may produce automata with thousands of states, requiring synthesis times that exceed days or weeks and prevent demonstration of the complete methodology within project timelines. Reachability analysis for continuous modes with high-dimensional state spaces may similarly prove computationally intractable. Either barrier would constitute a fundamental obstacle to achieving research objectives.
-automata small enough for efficient synthesis and verification. Reactive
-synthesis scales exponentially with specification complexity, which means temporal logic specifications derived from complete startup procedures may
-produce automata with thousands of states. Such large automata would require
-synthesis times exceeding days or weeks, preventing demonstration of the
-complete methodology within project timelines. Reachability analysis for
-continuous modes with high-dimensional state spaces may similarly prove
-computationally intractable. Either barrier would constitute a fundamental
-obstacle to achieving research objectives.
 
 Several indicators would provide early warning of computational tractability
 problems. Synthesis times exceeding 24 hours for simplified procedure subsets
@@ -28,19 +20,9 @@ If computational tractability becomes the limiting factor, we reduce scope to a
 
 \subsection{Discrete-Continuous Interface Formalization}
 
-While computational tractability addresses whether synthesis can complete within practical time bounds—a practical constraint—the second risk proves more fundamental: whether boolean guard
+While computational tractability addresses whether synthesis can complete within practical time bounds—a practical constraint—the second risk proves more fundamental: whether boolean guard conditions in temporal logic can map cleanly to continuous state boundaries required for mode transitions. 
-conditions in temporal logic can map cleanly to continuous state boundaries required for mode
+
-transitions. This interface represents the fundamental challenge of hybrid
+This interface represents the fundamental challenge of hybrid systems: relating discrete switching logic to continuous dynamics. Temporal logic operates on boolean predicates. Continuous control requires reasoning about differential equations and reachable sets. Guard conditions requiring complex nonlinear predicates may resist boolean abstraction, making synthesis intractable. Continuous safety regions that cannot be expressed as conjunctions of verifiable constraints would similarly create insurmountable verification challenges. The risk extends beyond static interface definition to dynamic behavior across transitions. Barrier certificates may fail to exist for proposed transitions. Continuous modes may be unable to guarantee convergence to discrete transition boundaries.
-systems: relating discrete switching logic to continuous dynamics. Temporal
-logic operates on boolean predicates, while continuous control requires
-reasoning about differential equations and reachable sets. Guard conditions
-requiring complex nonlinear predicates may resist boolean abstraction, making
-synthesis intractable. Continuous safety regions that cannot be expressed as
-conjunctions of verifiable constraints would similarly create insurmountable
-verification challenges. The risk extends beyond static interface definition to
-dynamic behavior across transitions: barrier certificates may fail to exist for
-proposed transitions, or continuous modes may be unable to guarantee convergence
-to discrete transition boundaries.
 
 Early indicators of interface formalization problems would appear during both
 synthesis and verification phases. Guard conditions requiring complex nonlinear
@@ -140,6 +122,6 @@ extensions, ensuring they address industry-wide practices rather than specific
 quirks.
 
 
-This section identifies barriers to success by answering the Heilmeier question \textbf{What could prevent success?} Four primary risks threaten project completion: computational tractability of synthesis and verification, complexity of the discrete-continuous interface, completeness of procedure formalization, and hardware-in-the-loop integration challenges. Each risk has identifiable early warning indicators and viable mitigation strategies. The staged project structure ensures that partial success yields publishable results while clearly identifying remaining barriers to deployment—even when core assumptions prove invalid, the research produces valuable contributions.
+This section identifies barriers to success by answering the Heilmeier question \textbf{What could prevent success?} Four primary risks threaten project completion: computational tractability of synthesis and verification, complexity of the discrete-continuous interface, completeness of procedure formalization, and hardware-in-the-loop integration challenges. Each risk has identifiable early warning indicators and viable mitigation strategies. The staged project structure ensures that partial success yields publishable results while clearly identifying remaining barriers to deployment—even when core assumptions prove invalid, the research produces valuable contributions that advance the field.
 
-The technical research plan is now complete. What will be done (Section 3), how success will be measured (Section 4), and what might prevent it (this section) have been established. One critical Heilmeier question remains: \textbf{Who cares? Why now? What difference will it make?} Section 6 answers these questions by connecting this technical methodology to urgent economic and infrastructure challenges facing the nuclear industry and broader energy sector.
+The technical research plan is now complete. What will be done (Section 3), how success will be measured (Section 4), and what might prevent it (this section) have been established. One critical Heilmeier question remains: \textbf{Who cares? Why now? What difference will it make?} Section 6 answers by connecting this technical methodology to urgent economic and infrastructure challenges facing the nuclear industry and broader energy sector.

6-broader-impacts/v1.tex

@@ -1,18 +1,14 @@
 \section{Broader Impacts}
 
-\textbf{Who cares? Why now? What difference will it make?} Three stakeholder groups face the same economic constraint: the nuclear industry, datacenter operators, and clean energy advocates. All confront high operating costs driven by staffing requirements. AI infrastructure demands, growing exponentially, have made this constraint urgent.
+\textbf{Who cares? Why now? What difference will it make?} These three Heilmeier questions connect technical methodology to economic and societal impact. Sections 2--5 established the technical research plan: what has been done (Section 2), what is new and why it will succeed (Section 3), how success will be measured (Section 4), and what could prevent success (Section 5). This section addresses the remaining Heilmeier questions by connecting the technical methodology to urgent economic and infrastructure challenges.
 
-Nuclear power presents both a compelling application domain and an urgent
+Three stakeholder groups face the same economic constraint: the nuclear industry, datacenter operators, and clean energy advocates. All confront high operating costs driven by staffing requirements. AI infrastructure demands, growing exponentially, have made this constraint urgent.
-economic challenge. Recent interest in powering artificial intelligence
-infrastructure has renewed focus on small modular reactors (SMRs), particularly
-for hyperscale datacenters requiring hundreds of megawatts of continuous power.
-Deploying SMRs at datacenter sites minimizes transmission losses and
-eliminates emissions. However, nuclear power
-economics at this scale demand careful attention to operating costs.
 
-The U.S. Energy Information Administration's Annual Energy Outlook 2022 projects advanced nuclear power entering service in 2027 will cost \$88.24 per megawatt-hour~\cite{eia_lcoe_2022}. Datacenter electricity demand is projected to reach 1,050 terawatt-hours annually by 2030~\cite{eesi_datacenter_2024}. Nuclear power supplying this demand would generate total annual costs exceeding \$92 billion. Operations and maintenance represents a substantial component. The EIA estimates that fixed O\&M costs alone account for \$16.15 per megawatt-hour, with additional variable O\&M costs embedded in fuel and operating expenses~\cite{eia_lcoe_2022}. Combined, O\&M-related costs represent approximately 23--30\% of the total levelized cost of electricity, translating to \$21--28 billion annually for projected datacenter demand.
+Nuclear power presents both a compelling application domain and an urgent economic challenge. Recent interest in powering artificial intelligence infrastructure has renewed focus on small modular reactors (SMRs), particularly for hyperscale datacenters requiring hundreds of megawatts of continuous power. Deploying SMRs at datacenter sites minimizes transmission losses and eliminates emissions. However, nuclear power economics at this scale demand careful attention to operating costs.
 
-\textbf{What difference will it make?} This research directly addresses the \$21--28 billion annual O\&M cost challenge through high-assurance autonomous control, making small modular reactors economically viable for datacenter power.
+The U.S. Energy Information Administration's Annual Energy Outlook 2022 projects advanced nuclear power entering service in 2027 will cost \$88.24 per megawatt-hour~\cite{eia_lcoe_2022}. Datacenter electricity demand is projected to reach 1,050 terawatt-hours annually by 2030~\cite{eesi_datacenter_2024}. Nuclear power supplying this demand would generate total annual costs exceeding \$92 billion. Operations and maintenance represents a substantial component: the EIA estimates that fixed O\&M costs alone account for \$16.15 per megawatt-hour, with additional variable O\&M costs embedded in fuel and operating expenses~\cite{eia_lcoe_2022}. Combined, O\&M-related costs represent approximately 23--30\% of total levelized cost, translating to \$21--28 billion annually for projected datacenter demand.
+
+\textbf{What difference will it make?} This research directly addresses the \$21--28 billion annual O\&M cost challenge. High-assurance autonomous control makes small modular reactors economically viable for datacenter power while maintaining nuclear safety standards.
 
 Current nuclear operations require full control room staffing for each reactor—whether large conventional units or small modular designs. For large reactors producing 1,000+ MW, staffing costs spread across substantial output. Small modular reactors producing 50-300 MW face the same staffing requirements with far lower output, which makes per-megawatt costs prohibitive. These staffing requirements drive the economic challenge that threatens SMR deployment for datacenter applications. Synthesizing provably correct hybrid controllers from formal
 specifications automates routine operational sequences that currently require
@@ -60,9 +56,9 @@ adoption across critical infrastructure.
 
 This section establishes impact by answering three critical Heilmeier questions:
 
-\textbf{Who cares?} The nuclear industry faces an economic crisis for small modular reactors due to per-megawatt staffing costs. Datacenter operators need hundreds of megawatts of continuous clean power for AI infrastructure. Any organization operating staffing-intensive safety-critical systems faces similar economic pressures.
+\textbf{Who cares?} Three stakeholder groups face the same constraint. The nuclear industry faces an economic crisis for small modular reactors due to per-megawatt staffing costs. Datacenter operators need hundreds of megawatts of continuous clean power for AI infrastructure. Clean energy advocates need nuclear power to be economically competitive. All three groups need autonomous control with safety guarantees.
 
-\textbf{Why now?} Two forces converge to make this research urgent. First, exponentially growing AI infrastructure demands have created immediate need for economical nuclear power at datacenter scale. Second, formal methods tools have matured to where compositional hybrid verification has become computationally achievable—what was theoretically possible but practically intractable a decade ago is now feasible.
+\textbf{Why now?} Two forces converge to make this research urgent. First, exponentially growing AI infrastructure demands have created immediate need for economical nuclear power at datacenter scale. Projections show datacenter electricity demand reaching 1,050 terawatt-hours annually by 2030. Second, formal methods tools have matured to where compositional hybrid verification has become computationally achievable—what was theoretically possible but practically intractable a decade ago is now feasible.
 
 \textbf{What difference will it make?} This research addresses a \$21--28 billion annual cost barrier by enabling autonomous control with mathematical safety guarantees. Beyond immediate economic impact, the methodology establishes a generalizable framework for safety-critical autonomous systems across critical infrastructure.