Editorial pass: Gopen structure + flow + Heilmeier alignment

Three-level editorial improvements:

TACTICAL (sentence-level):
- Applied Gopen's issue-point and topic-stress positioning throughout
- Improved verb choice and sentence clarity
- Tightened passive constructions to active voice
- Enhanced topic strings for better paragraph coherence

OPERATIONAL (paragraph-level):
- Strengthened transitions between subsections
- Improved flow within complex technical sections
- Made mode classification rationale more explicit
- Enhanced coherence in verification methodology

STRATEGIC (document-level):
- Made Heilmeier Catechism alignment explicit in section transitions
- Added structured mapping of sections to Heilmeier questions in Sec 1
- Strengthened summary sections to reinforce question-answer structure
- Improved subsection headings to signal content and purpose

Changes preserve all technical content while significantly improving
clarity, flow, and argument structure.

1-goals-and-outcomes/research_statement_v1.tex

@@ -2,9 +2,9 @@
 This research develops autonomous control systems with mathematical guarantees of safe and correct behavior.
 
 % INTRODUCTORY PARAGRAPH Hook
-Extensively trained operators manage nuclear reactors by following detailed written procedures. Plant conditions guide their decisions when they switch between control objectives.
+Extensively trained operators manage nuclear reactors by following detailed written procedures. When operators switch between control objectives, plant conditions guide their decisions.
 % Gap
-Small modular reactors face a fundamental economic challenge: their per-megawatt staffing costs significantly exceed those of conventional plants, threatening their viability. Autonomous control systems must manage complex operational sequences safely—without constant supervision—while providing assurance equal to or exceeding that of human-operated systems.
+Small modular reactors face a fundamental economic challenge: their per-megawatt staffing costs significantly exceed those of conventional plants, threatening their viability. To address this challenge, autonomous control systems must manage complex operational sequences safely—without constant supervision—while providing assurance equal to or exceeding that of human-operated systems.
 
 % APPROACH PARAGRAPH Solution
 We combine formal methods from computer science with control theory to
@@ -13,10 +13,10 @@ build hybrid control systems that are correct by construction.
 Hybrid systems mirror how operators work: discrete
 logic switches between continuous control modes. Existing formal methods
 generate provably correct switching logic but cannot handle continuous dynamics
-during transitions. Control theory verifies continuous behavior but
+during transitions. Control theory, conversely, verifies continuous behavior but
 cannot prove the correctness of discrete switching decisions. 
 % Hypothesis and Technical Approach
-Our methodology bridges this gap in three stages. First, we translate written
+Our methodology bridges this gap through three stages. First, we translate written
 operating procedures into temporal logic specifications using NASA's Formal
 Requirements Elicitation Tool (FRET). FRET structures requirements into scope,
 condition, component, timing, and response elements. Realizability

1-goals-and-outcomes/v1.tex

@@ -11,7 +11,7 @@ or radiological release.
 % Known information
 Nuclear plant operations rely on extensively trained human operators
 who follow detailed written procedures and strict regulatory requirements to
-manage reactor control. Plant conditions and procedural guidance inform their decisions when they switch between different control modes.
+manage reactor control. When operators switch between different control modes, plant conditions and procedural guidance inform their decisions.
 % Gap
 This reliance on human operators prevents autonomous control and
 creates a fundamental economic challenge for next-generation reactor designs.
@@ -33,9 +33,8 @@ Control theory verifies continuous behavior but cannot prove the correctness of
 Our approach closes this gap by synthesizing discrete mode transitions directly
 from written operating procedures and verifying continuous behavior between
 transitions. We formalize existing procedures into logical
-specifications and verify continuous dynamics against transition requirements. This approach produces autonomous controllers that are provably free from design
-defects. We conduct this work within the University of Pittsburgh Cyber Energy Center,
-which provides access to industry collaboration and Emerson control hardware. Solutions developed here align with practical implementation
+specifications and verify continuous dynamics against transition requirements. This approach produces autonomous controllers provably free from design
+defects. The University of Pittsburgh Cyber Energy Center provides access to industry collaboration and Emerson control hardware, ensuring that solutions developed here align with practical implementation
 requirements.
 
 % OUTCOMES PARAGRAPHS
@@ -87,10 +86,10 @@ If this research is successful, we will be able to do the following:
 These three outcomes—procedure translation, continuous verification, and hardware demonstration—establish a complete methodology from regulatory documents to deployed systems.
 
 \textbf{What is new:} We unify discrete synthesis with continuous verification to enable end-to-end correctness guarantees for hybrid systems.
-Formal methods verify discrete logic. Control theory verifies
+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
+as contracts that continuous controllers must satisfy. This treatment enables independent
 verification of each layer while guaranteeing correct composition.
 
 % Outcome Impact
@@ -105,4 +104,13 @@ costs through increased autonomy. This research provides the tools to
 achieve that autonomy while maintaining the exceptional safety record the
 nuclear industry requires.
 
-The following sections systematically answer the Heilmeier Catechism questions that define this research: Section 2 examines the state of the art, establishing what has been done and what remains impossible with current approaches. Section 3 presents our hybrid control synthesis methodology, demonstrating what is new and why it will succeed where prior work has not. Section 4 defines how we measure success through Technology Readiness Level advancement from analytical concepts to hardware demonstration. Section 5 identifies risks that could prevent success and establishes contingencies. Section 6 addresses who cares and why now, examining the economic imperative driving autonomous nuclear control and the broader impact on safety-critical systems. Section 8 provides the research schedule and deliverables, answering how long this work will take.
+The following sections systematically answer the Heilmeier Catechism questions that define this research: 
+\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 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.

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

@@ -5,7 +5,7 @@
 \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, and Extensive Damage Mitigation Guidelines (EDMGs) cover catastrophic damage scenarios. These procedures must comply with 10 CFR 50.34(b)(6)(ii); NUREG-0899
-provides development guidance~\cite{NUREG-0899, 10CFR50.34}. Their 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. However, 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.
+provides development guidance~\cite{NUREG-0899, 10CFR50.34}. However, their 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, but 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.
 
 \textbf{LIMITATION:} \textit{Procedures lack formal verification of correctness
 and completeness.} Current procedure development relies on expert judgment and
@@ -37,7 +37,7 @@ startup/shutdown sequences, mode transitions, and procedure implementation.
 
 \subsection{Human Factors in Nuclear Accidents}
 
-Procedures lack formal verification despite rigorous development. This subsection examines the second pillar of current practice: the human operators who execute these procedures. Procedures define what to do; human operators determine when and how to apply them. This approach introduces fundamental reliability limitations.
+Despite rigorous development, procedures lack formal verification. This subsection examines the second pillar of current practice: the human operators who execute these procedures. Procedures define what to do; human operators determine when and how to apply them. This approach introduces fundamental reliability limitations.
 
 Current-generation nuclear power plants employ over 3,600 active NRC-licensed
 reactor operators in the United States~\cite{operator_statistics}. These
@@ -47,12 +47,12 @@ 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, motivating formal automated control with mathematical safety guarantees.
+Despite decades
+of improvements in training and procedures, human error persistently contributes to nuclear safety incidents. This persistence motivates formal automated control with mathematical safety guarantees.
 Under 10 CFR Part 55, operators hold legal authority to make critical decisions,
 including departing from normal regulations during emergencies. The Three Mile
 Island (TMI) accident demonstrated how personnel error, design
-deficiencies, and component failures combined to cause partial meltdown. Operators
+deficiencies, and component failures 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
@@ -80,18 +80,17 @@ limitations are fundamental to human-driven control, not remediable defects.
 
 \subsection{Formal Methods}
 
-Procedures lack formal verification, and human operators introduce persistent reliability issues. Formal methods offer an alternative: mathematical guarantees of correctness that eliminate both human error and procedural ambiguity. This subsection examines recent formal methods applications in nuclear control and identifies the verification gap that remains for autonomous hybrid systems.
+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. This subsection examines recent formal methods applications in nuclear control and identifies the verification gap that remains for autonomous hybrid systems.
 
-\subsubsection{HARDENS}
+\subsubsection{HARDENS: The State of Formal Methods in Nuclear Control}
 
 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 aimed to address a fundamental dilemma: existing U.S. nuclear control
-rooms rely on analog technologies from the 1950s--60s. This technology is
-obsolete compared to modern control systems and incurs significant risk and
-cost. The NRC contracted Galois, a formal methods firm, to demonstrate that
+HARDENS addressed a fundamental dilemma: existing U.S. nuclear control
+rooms rely on analog technologies from the 1950s--60s. This technology incurs 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)
@@ -151,7 +150,7 @@ under harsh environments, human-system interaction in realistic
 operational contexts, and regulatory acceptance of formal methods as
 primary assurance evidence.
 
-\subsubsection{Sequent Calculus and Differential Dynamic Logic}
+\subsubsection{Differential Dynamic Logic: Post-Hoc Hybrid Verification}
 
 HARDENS verified discrete control logic but omitted continuous dynamics—a fundamental limitation for hybrid systems. Other researchers pursued a complementary approach: extending temporal logics to handle hybrid systems directly. This work produced differential dynamic logic (dL). dL introduces two additional operators
 into temporal logic: the box operator and the diamond operator. The box operator
@@ -186,8 +185,10 @@ design loop for complex systems like nuclear reactor startup procedures.
 
 \subsection{Summary: The Verification Gap}
 
+This section answered two Heilmeier questions:
+
 \textbf{What has been done?} Human operators provide operational flexibility but introduce persistent reliability limitations—four decades of training improvements have failed to eliminate them. 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 does not 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. Closing this gap enables autonomous control that addresses the economic constraints threatening small modular reactor viability while maintaining the safety assurance the nuclear industry requires.
+\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.
 
-Section 3 presents our methodology for bridging this gap through compositional hybrid verification, establishing what is new and why it will succeed.
+The economic imperative is clear: small modular reactors cannot compete with per-megawatt staffing costs matching large conventional plants. The technical capability gap is equally clear: current approaches verify either discrete logic or continuous dynamics, never both compositionally. Section 3 presents our methodology for bridging this gap, establishing what is new and why it will succeed where prior work has not.

3-research-approach/v3.tex

@@ -15,9 +15,9 @@
 % ----------------------------------------------------------------------------
 % 1. INTRODUCTION AND HYBRID SYSTEMS DEFINITION
 % ----------------------------------------------------------------------------
-Previous approaches to autonomous control 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 of control system behavior despite consuming enormous resources. HAHACS bridges this gap by composing formal methods from computer science with control-theoretic verification, formalizing reactor operations using hybrid automata.
+Previous approaches to autonomous control 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. Despite consuming enormous resources, neither method provides rigorous guarantees of control system behavior. HAHACS bridges this gap by composing formal methods from computer science with control-theoretic verification, formalizing reactor operations using hybrid automata.
 
-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—designed for purely discrete or purely continuous systems—cannot handle this interaction directly. Our methodology decomposes the problem: we verify discrete switching logic and continuous mode behavior separately, then compose them to reason about the complete hybrid system. This two-layer approach mirrors reactor operations, where discrete supervisory logic determines which control mode is active, and continuous controllers govern plant behavior within each mode.
+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—designed for purely discrete or purely continuous systems—cannot handle this interaction directly. Our methodology decomposes the problem by verifying discrete switching logic and continuous mode behavior separately, then composing them to reason about the complete hybrid system. This two-layer approach mirrors reactor operations: discrete supervisory logic determines which control mode is active, while continuous controllers govern plant behavior within each mode.
 
 Building a high-assurance hybrid autonomous control system (HAHACS) requires
 a mathematical description of the system. This work draws on
@@ -52,7 +52,7 @@ where:
 
 Creating a HAHACS requires constructing such a tuple together with proof artifacts that demonstrate the control system's actual implementation satisfies its intended behavior.
 
-\textbf{What is new?} Reactive synthesis, reachability analysis, and barrier certificates each exist independently. Our contribution is the architecture that composes them into a complete methodology for hybrid control synthesis. The novelty lies in three innovations. First, we use discrete synthesis to define entry/exit/safety contracts that bound continuous verification, inverting the traditional approach of verifying a complete hybrid system globally. Second, we classify continuous modes by objective (transitory, stabilizing, expulsory) to select appropriate verification tools, enabling mode-local analysis with provable composition. Third, we leverage existing procedural structure to avoid global hybrid system analysis, making the approach tractable for complex systems like nuclear reactor startup. No prior work integrates these techniques into a systematic design methodology from procedures to verified implementation.
+\textbf{What is new?} Reactive synthesis, reachability analysis, and barrier certificates each exist independently. Our contribution is the architecture that composes them into a complete methodology for hybrid control synthesis. Three innovations provide the novelty. First, we use discrete synthesis to define entry/exit/safety contracts that bound continuous verification, inverting the traditional approach of verifying a complete hybrid system globally. Second, we classify continuous modes by objective (transitory, stabilizing, expulsory) to select appropriate verification tools, enabling mode-local analysis with provable composition. Third, we leverage existing procedural structure to avoid global hybrid system analysis, making the approach tractable for complex systems like nuclear reactor startup. No prior work integrates these techniques into a systematic design methodology from procedures to verified implementation.
 
 \textbf{Why will it succeed?} Three factors ensure practical feasibility. First, nuclear procedures already decompose operations into discrete phases with explicit transition criteria—we formalize existing structure rather than impose artificial abstractions. Second, mode-level verification avoids the state explosion that makes global hybrid system analysis intractable, keeping computational complexity bounded by verifying each mode against local contracts. Third, the Emerson collaboration provides both domain expertise to validate procedure formalization and industrial hardware to demonstrate implementation feasibility. We demonstrate feasibility on production control systems with realistic reactor models, not merely prove it in principle.
 
@@ -120,7 +120,7 @@ Creating a HAHACS requires constructing such a tuple together with proof artifac
 
 \subsection{System Requirements, Specifications, and Discrete Controllers}
 
-The eight-tuple definition formalizes discrete modes, continuous dynamics, guards, and invariants. This subsection shows how to construct such systems from existing operational knowledge. Nuclear operations already possess a natural hybrid structure that maps directly to this automaton formalism.
+The eight-tuple hybrid automaton formalism 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.
 
 Human control of nuclear power divides into three scopes: strategic,
 operational, and tactical. Strategic control represents high-level,
@@ -272,6 +272,8 @@ room for interpretation is a weakness that must be addressed.
 % 3. DISCRETE CONTROLLER SYNTHESIS
 % ----------------------------------------------------------------------------
 
+\subsection{Discrete Controller Synthesis}
+
 With system requirements defined as temporal logic specifications, we now build
 the discrete control system through reactive synthesis.
 Reactive synthesis automates the creation of reactive programs from temporal logic specifications.
@@ -280,25 +282,20 @@ an output. Our systems fit this model: the current discrete state and
 status of guard conditions form the input; the next discrete
 state forms the output. 
 
-Reactive synthesis solves the following problem: given an LTL formula $\varphi$
+Reactive synthesis solves a fundamental problem: given an LTL formula $\varphi$
 that specifies 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 called \emph{realizable}. The synthesis algorithm
 either produces a correct-by-construction controller or reports that no such
-controller can exist. This realizability check is itself valuable: an
+controller can exist. This realizability check provides immediate value: an
 unrealizable specification indicates conflicting or impossible requirements in
-the original procedures. 
+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 focus their effort where it belongs: on specifying system behavior. This has two critical implications. First, it makes discrete controller creation tractable. The reasons the controller
-changes between modes can be traced back to the specification and thus to any
-requirements, providing a trace for liability and justification of system
-behavior. Second, discrete control decisions made by humans depend on the
-human operator operating correctly. Humans are intrinsically probabilistic
-and cannot eliminate human error. By defining the behavior of this
-system using temporal logics and synthesizing the controller using deterministic
-algorithms, we are assured that strategic decisions will always be made
-according to operating procedures.
+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 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
+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.
 
 (Talk about how one would go from a discrete automaton to actual code)
 
@@ -318,9 +315,9 @@ according to operating procedures.
 
 Reactive synthesis produces a provably correct discrete controller from operating procedures. This discrete controller determines when to switch between modes—but hybrid control requires more. The continuous dynamics executing within each discrete mode must also be verified to ensure the complete system behaves correctly.
 
-This subsection describes the continuous control modes that execute within each discrete state and explains how we verify they satisfy the requirements imposed by the discrete layer. Three mode types—transitory, stabilizing, and expulsory—require different verification approaches. 
+This subsection describes the continuous control modes that execute within each discrete state and explains how we verify they satisfy the requirements imposed by the discrete layer. We classify modes into three types—transitory, stabilizing, and expulsory—each requiring different verification approaches matched to their control objectives. 
 
-This methodology's scope regarding continuous controller design requires clarification. This work verifies continuous controllers—it 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 can design continuous controllers using standard control theory techniques. Our contribution is the verification framework that confirms candidate controllers compose correctly with the discrete layer to produce a safe hybrid system.
+This methodology's scope regarding continuous controller design 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 can design continuous controllers using standard control theory techniques. Our contribution is the verification framework that confirms 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
@@ -384,7 +381,7 @@ dynamics $\dot{x} = f(x, u(x))$, the controller must satisfy:
 That is, from any valid entry state, the trajectory must eventually reach the
 exit condition without ever leaving the safe region.
 
-Verification of transitory modes uses reachability analysis.
+Reachability analysis provides the natural verification tool for transitory modes.
 Reachability analysis computes the set of all states reachable from a given
 initial set under the system dynamics. For a transitory mode to be valid, the
 reachable set from $\mathcal{X}_{entry}$ must satisfy two conditions:
@@ -402,9 +399,7 @@ reachable within time horizon $T$:
 \]
 
 The discrete controller defines clear boundaries in continuous state
-space, making the verification problem for each transitory mode well-posed. We know
-the possible initial conditions, the target conditions, and the
-safety envelope. The verification task confirms that the candidate
+space, making the verification problem for each transitory mode well-posed. The possible initial conditions, target conditions, and safety envelope are all known. The verification task then confirms that the candidate
 continuous controller achieves the objective from all possible starting points.
 
 Several tools exist for computing reachable sets of hybrid
@@ -427,7 +422,7 @@ appropriate to the fidelity of the reactor models available.
 
 \subsubsection{Stabilizing Modes}
 
-Transitory modes drive the system toward exit conditions. Stabilizing modes, in contrast, maintain the system within a desired operating region indefinitely rather than drive it toward an exit condition. Examples include steady-state power operation, hot standby, and load-following at constant power level. Reachability analysis may not suit validation of stabilizing modes. Instead, we use barrier certificates.
+Transitory modes drive the system toward exit conditions. Stabilizing modes, in contrast, maintain the system within a desired operating region indefinitely. Examples include steady-state power operation, hot standby, and load-following at constant power level. The different control objective requires a different verification approach: reachability analysis answers "can the system reach a target?" while stabilizing modes must prove "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
@@ -479,7 +474,7 @@ controller.
 
 \subsubsection{Expulsory Modes}
 
-Transitory and stabilizing modes handle nominal operations. Expulsory modes handle off-nominal conditions. When the plant deviates from expected behavior, expulsory modes take over to ensure safety. These continuous controllers are designed for robustness rather than optimality. The control objective is to drive 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.
+Transitory and stabilizing modes handle nominal operations; expulsory modes handle off-nominal conditions. When the plant deviates from expected behavior, expulsory modes take over to ensure safety. These continuous controllers prioritize robustness over optimality. The control objective is to drive 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.
 
@@ -556,7 +551,13 @@ 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 methodology—from procedure formalization through discrete synthesis to continuous verification and hardware implementation—establishes the complete research approach. We have shown what is new (compositional hybrid verification integrated into the design process) and why it will succeed (leveraging existing procedural structure, mode-level analysis, and industrial collaboration). Section 4 defines how we measure success: not through theoretical contributions alone, but through Technology Readiness Level advancement that demonstrates both correctness and practical implementability.
+This section answered two Heilmeier questions:
+
+\textbf{What is new?} We integrate reactive synthesis, reachability analysis, and barrier certificates into a compositional architecture for hybrid control synthesis. The methodology inverts traditional approaches by using discrete synthesis to define verification contracts, classifies continuous modes to select appropriate verification tools, and leverages existing procedural structure to avoid intractable global analysis.
+
+\textbf{Why will it succeed?} Nuclear procedures already decompose operations into discrete phases with explicit transition criteria—we formalize existing structure rather than impose artificial abstractions. Mode-level verification avoids state explosion by bounding each verification problem locally. The Emerson collaboration provides domain expertise to validate procedure formalization and industrial hardware to demonstrate practical implementation.
+
+Having established the complete methodology—from procedure formalization through discrete synthesis to continuous verification and hardware implementation—Section 4 addresses the next Heilmeier question: how do we measure success? Not through theoretical contributions alone, but through Technology Readiness Level advancement that demonstrates both correctness and practical implementability.
 
 %%% NOTES (Section 5):
 % - Get specific details on ARCADE interface from Emerson collaboration

4-metrics-of-success/v1.tex

@@ -9,8 +9,8 @@ system components operate successfully in a relevant laboratory environment.
 This section explains why TRL advancement provides the most appropriate success
 metric and defines specific criteria for TRL 5.
 
-Technology Readiness Levels provide the ideal success metric: they
-explicitly measure the gap between academic proof-of-concept and practical
+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 aims to bridge. Academic metrics like
 papers published or theorems proved cannot capture practical feasibility.
 Empirical metrics like simulation accuracy or computational speed cannot

5-risks-and-contingencies/v1.tex

@@ -13,10 +13,10 @@ publishable results while clearly identifying remaining barriers to deployment.
 
 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, creating the risk that
+synthesis scales exponentially with specification complexity. This scaling creates the risk that
 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 us from demonstrating the
+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
@@ -37,8 +37,8 @@ minimal viable startup sequence covering only cold shutdown to criticality to lo
 
 \subsection{Discrete-Continuous Interface Formalization}
 
-Computational tractability represents one dimension of risk. A more fundamental challenge represents the second critical assumption: mapping boolean guard
-conditions in temporal logic to continuous state boundaries required for mode
+Computational tractability addresses whether synthesis can complete within practical time bounds. A more fundamental challenge addresses the second critical assumption: whether boolean guard
+conditions in temporal logic can map cleanly to continuous state boundaries required for mode
 transitions. This interface represents the fundamental challenge of hybrid
 systems: relating discrete switching logic to continuous dynamics. Temporal
 logic operates on boolean predicates, while continuous control requires
@@ -149,4 +149,6 @@ extensions, ensuring they address industry-wide practices rather than specific
 quirks.
 
 
-These risks and contingencies demonstrate that while the research faces real challenges, each has identifiable early indicators and viable mitigation strategies. The staged approach ensures valuable contributions even if core assumptions prove invalid: partial success yields publishable results that clearly identify remaining barriers to deployment. With risks addressed and contingencies established, the next section examines broader impacts: who cares about this work and why it matters now.
+This section addressed the Heilmeier question: \textbf{What could prevent success?} Four primary risks—computational tractability, discrete-continuous interface complexity, procedure formalization completeness, and hardware integration—each have identifiable early indicators and viable mitigation strategies. The staged approach ensures valuable contributions even if core assumptions prove invalid: partial success yields publishable results that clearly identify remaining barriers to deployment.
+
+With technical feasibility established and risks addressed, Section 6 examines the final Heilmeier questions: who cares about this work, why does it matter now, and what difference will it make?

6-broader-impacts/v1.tex

@@ -7,8 +7,8 @@ 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 from hydrocarbon-based alternatives. Nuclear power
-economics at this scale, however, demand careful attention to operating costs.
+eliminates emissions from hydrocarbon-based alternatives. 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
@@ -73,7 +73,7 @@ establish both the technical feasibility and regulatory pathway for broader
 adoption across critical infrastructure.
 
 
-These broader impacts answer the final Heilmeier questions: 
+This section answered three Heilmeier questions: 
 
 \textbf{Who cares?} The nuclear industry, datacenter operators, and anyone facing high operating costs from staffing-intensive safety-critical control. 
 
@@ -81,4 +81,4 @@ These broader impacts answer the final Heilmeier questions:
 
 \textbf{What difference will it make?} Enabling autonomous control with mathematical safety guarantees addresses a \$21--28 billion annual cost barrier while establishing a generalizable framework for safety-critical autonomous systems.
 
-The next section presents the timeline for achieving these outcomes through a structured 24-month research plan.
+Section 8 addresses the final Heilmeier question—how long will it take?—presenting a structured 24-month research plan with milestones tied to Technology Readiness Level advancement.

8-schedule/v1.tex

@@ -2,9 +2,8 @@
 
 \textbf{How long will it take?} This research will be conducted over six
 trimesters (24 months) of full-time effort following the proposal defense in
-Spring 2026. All work uses existing computational and experimental resources
-available through the University of Pittsburgh Cyber Energy Center and NRC
-Fellowship funding. The work progresses
+Spring 2026. The University of Pittsburgh Cyber Energy Center and NRC
+Fellowship provide all computational and experimental resources. The work progresses
 sequentially through three main research thrusts before culminating in
 integrated demonstration and validation.