Multi-level editorial pass: Gopen's Sense of Structure + Heilmeier alignment

TACTICAL (sentence-level):
- Improved topic-stress positioning for better flow
- Tightened verb choices (active vs passive)
- Condensed choppy sequences into stronger compound sentences
- Enhanced topic strings between sentences

OPERATIONAL (paragraph/section):
- Strengthened transitions between paragraphs and sections
- Improved logical flow within sections
- Enhanced coherence of argument progression

STRATEGIC (document-level):
- Sharpened Heilmeier question answers at section endings
- Improved document-level coherence and linking
- Strengthened connections between sections

Focus: genuine clarity improvements without nitpicking

1-goals-and-outcomes/research_statement_v1.tex

@@ -2,14 +2,14 @@
 This research develops autonomous control systems that provide mathematical guarantees of safe and correct behavior.
 
 % INTRODUCTORY PARAGRAPH Hook
-Human operators control nuclear reactors today. They follow detailed written procedures and switch between control objectives as plant conditions change.
+Nuclear reactors today require human operators who follow detailed written procedures and switch between control objectives as plant conditions change.
 % Gap
-Small modular reactors face a fundamental economic challenge. Their per-megawatt staffing costs far exceed those of conventional plants, threatening economic viability. Autonomous control could manage complex operational sequences without constant supervision—but only if it provides safety assurance equal to or exceeding that of human operators.
+Small modular reactors face a fundamental economic challenge: per-megawatt staffing costs far exceed those of conventional plants, threatening economic viability. Autonomous control could manage complex operational sequences without constant supervision—but only if it provides safety assurance equal to or exceeding that of human operators.
 
 % APPROACH PARAGRAPH Solution
-This research unifies formal methods with control theory. The result: hybrid control systems correct by construction.
+This research unifies formal methods with control theory to produce hybrid control systems correct by construction.
 % Rationale
-Human operators already work this way—they use discrete logic to switch between continuous control modes. Formal methods generate provably correct switching logic but cannot verify continuous dynamics. Control theory verifies continuous behavior but cannot prove discrete logic correctness. End-to-end correctness requires both.
+Human operators already work this way—using discrete logic to switch between continuous control modes. Formal methods generate provably correct switching logic but cannot verify continuous dynamics. Control theory verifies continuous behavior but cannot prove discrete logic correctness. End-to-end correctness requires both.
 % Hypothesis and Technical Approach
 Three stages bridge this gap. First, NASA's Formal Requirements Elicitation Tool (FRET) translates written operating procedures into temporal logic specifications. FRET structures requirements by scope, condition, component, timing, and response. Realizability checking exposes conflicts and ambiguities before implementation begins. Second, reactive synthesis generates deterministic automata provably correct by construction. Third, reachability analysis verifies that continuous controllers satisfy each discrete mode's requirements. Engineers design these controllers using standard control theory.
 

1-goals-and-outcomes/v1.tex

@@ -6,16 +6,16 @@ This research develops autonomous hybrid control systems that provide mathematic
 % INTRODUCTORY PARAGRAPH Hook
 Nuclear power plants demand the highest levels of control system reliability. Control system failures risk economic losses, service interruptions, or radiological release.
 % Known information
-Extensively trained human operators control nuclear plants today. They follow detailed written procedures and strict regulatory requirements. They switch between control modes based on plant conditions and procedural guidance.
+Extensively trained human operators control nuclear plants today, following detailed written procedures and strict regulatory requirements. They switch between control modes based on plant conditions and procedural guidance.
 % Gap
-This reliance on human operators prevents autonomous control. It creates a fundamental economic challenge for next-generation reactor designs. Small modular reactors face per-megawatt staffing costs far exceeding those of conventional plants. This threatens economic viability. Autonomous control could manage complex operational sequences without constant supervision—but only if it provides safety 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, threatening economic viability. Autonomous control could manage complex operational sequences without constant supervision—but only if it provides safety assurance equal to or exceeding that of human operators.
 
 % APPROACH PARAGRAPH Solution
-This research unifies formal methods with control theory. The result: hybrid control systems correct by construction.
+This research unifies formal methods with control theory to produce hybrid control systems correct by construction.
 % Rationale
-Human operators already work this way—they use discrete logic to switch between continuous control modes. Formal methods generate provably correct switching logic from written requirements but cannot verify continuous dynamics. Control theory verifies continuous behavior but cannot prove discrete switching correctness. End-to-end correctness requires both.
+Human operators already work this way—using discrete logic to switch between continuous control modes. Formal methods generate provably correct switching logic from written requirements but cannot verify continuous dynamics. Control theory verifies continuous behavior but cannot prove discrete switching correctness. End-to-end correctness requires both.
 % Hypothesis
-Two steps close this gap. First, reactive synthesis generates discrete mode transitions directly from written operating procedures. Second, reachability analysis verifies continuous behavior against discrete requirements. These steps transform operating procedures into logical specifications constraining continuous dynamics. The result: autonomous controllers provably free from design defects. 
+Two steps close this gap. First, reactive synthesis generates discrete mode transitions directly from written operating procedures. Second, reachability analysis verifies continuous behavior against discrete requirements. These steps transform operating procedures into logical specifications that constrain continuous dynamics, producing autonomous controllers provably free from design defects. 
 
 The University of Pittsburgh Cyber Energy Center provides access to industry collaboration and Emerson control hardware. This ensures solutions align with practical implementation requirements.
 

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

@@ -4,17 +4,17 @@
 
 No current approach provides end-to-end correctness guarantees for autonomous control. Human-centered operation cannot eliminate reliability limits. Formal methods verify either discrete or continuous behavior—never both simultaneously. 
 
-Three subsections structure this analysis. The first examines reactor operators and their operating procedures. The second addresses fundamental limitations of human-based operation. The third analyzes formal methods approaches that verify discrete logic or continuous dynamics—but not both together.
+This analysis proceeds through three subsections. The first examines reactor operators and their operating procedures. The second addresses fundamental limitations of human-based operation. The third analyzes formal methods approaches that verify discrete logic or continuous dynamics—but not both together.
 
 Section 3 addresses the verification gap these limits create.
 
 \subsection{Current Reactor Procedures and Operation}
 
-Current practice rests on two critical components: procedures and operators. Procedures define what must be done. Operators execute those procedures. This subsection examines procedures—their hierarchy, development process, and role in defining operational modes. The next subsection examines operators—their reliability limits and contribution to accidents.
+Current practice rests on two critical components: procedures and operators. Procedures define what must be done; operators execute those procedures. This subsection examines procedures—their hierarchy, development process, and role in defining operational modes. The next subsection examines operators—their reliability limits and contribution to accidents.
 
 Nuclear plant procedures form a strict 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, while Extensive Damage Mitigation Guidelines (EDMGs) cover catastrophic damage. All procedures must comply with 10 CFR 50.34(b)(6)(ii); NUREG-0899 provides development guidance~\cite{NUREG-0899, 10CFR50.34}. 
 
-Procedure development rests on expert judgment and simulator validation—not formal verification. Regulations mandate rigorous assessment. 10 CFR 55.59~\cite{10CFR55.59} requires technical evaluation, simulator validation testing, and biennial review. Yet key safety properties escape formal verification. No mathematical proof confirms that procedures cover all possible plant states. No proof confirms that required actions complete within available time. No proof guarantees that transitions between procedure sets maintain safety invariants.
+Procedure development rests on expert judgment and simulator validation—not formal verification. Regulations mandate rigorous assessment; 10 CFR 55.59~\cite{10CFR55.59} requires technical evaluation, simulator validation testing, and biennial review. Yet key safety properties escape formal verification: no mathematical proof confirms that procedures cover all possible plant states, that required actions complete within available time, or that transitions between procedure sets maintain safety invariants.
 
 \textbf{LIMITATION:} \textit{Procedures lack formal verification of correctness
 and completeness.} No proof exists that procedures cover all
@@ -31,9 +31,9 @@ Highly automated systems already handle reactor protection: automatic trips on s
 
 \subsection{Human Factors in Nuclear Accidents}
 
-The previous subsection established that procedures lack formal verification despite rigorous development. This represents only half the reliability challenge. Even perfect procedures cannot guarantee safe operation when executed imperfectly.
+The previous subsection established that procedures lack formal verification despite rigorous development, representing only half the reliability challenge. Even perfect procedures cannot guarantee safe operation when executed imperfectly.
 
-Human operators—the second pillar of current practice—introduce reliability limitations independent of procedure quality. Procedures define what to do. Operators determine when and how to act. This discretion introduces persistent failure modes that training cannot eliminate.
+Human operators—the second pillar of current practice—introduce reliability limitations independent of procedure quality. While procedures define what to do, operators determine when and how to act. This discretion introduces persistent failure modes that training cannot eliminate.
 
 Current-generation nuclear power plants employ over 3,600 active NRC-licensed
 reactor operators in the United States~\cite{operator_statistics}. These
@@ -63,11 +63,11 @@ limitations are fundamental to human-driven control, not remediable defects.
 
 \subsection{Formal Methods}
 
-The previous subsections established two fundamental limitations. First, procedures lack formal verification. Second, human operators introduce persistent reliability issues that training cannot eliminate. Both represent fundamental constraints—not remediable defects.
+The previous subsections established two fundamental limitations: procedures lack formal verification, and human operators introduce persistent reliability issues that training cannot eliminate. Both represent fundamental constraints—not remediable defects.
 
-Formal methods could eliminate these limitations by providing mathematical guarantees of correctness. Yet even the most advanced formal methods applications in nuclear control leave a critical verification gap.
+Formal methods could eliminate these limitations by providing mathematical guarantees of correctness, yet even the most advanced formal methods applications in nuclear control leave a critical verification gap.
 
-This subsection examines two approaches illustrating this gap. HARDENS verified discrete logic without continuous dynamics. Differential dynamic logic handles hybrid verification only post-hoc. Each demonstrates the current state of formal methods. Each reveals the verification gap this research addresses.
+This subsection examines two approaches illustrating this gap. HARDENS verified discrete logic without continuous dynamics, while differential dynamic logic handles hybrid verification only post-hoc. Each demonstrates the current state of formal methods and reveals the verification gap this research addresses.
 
 \subsubsection{HARDENS: Formal Methods in Nuclear Control}
 
@@ -160,10 +160,10 @@ design loop for complex systems like nuclear reactor startup procedures.
 
 This section addressed two Heilmeier questions: What has been done? What are the limits of current practice?
 
-\textbf{What has been done?} Three approaches currently exist. Each has fundamental limitations. First, human operators provide operational flexibility but introduce persistent reliability constraints that training cannot eliminate. Second, HARDENS verified discrete logic but omitted continuous dynamics. Third, differential dynamic logic expresses hybrid properties but requires post-design expert analysis. None addresses both discrete and continuous verification compositionally.
+\textbf{What has been done?} Three approaches currently exist, each with fundamental limitations. First, human operators provide operational flexibility but introduce persistent reliability constraints that training cannot eliminate. Second, HARDENS verified discrete logic but omitted continuous dynamics. Third, differential dynamic logic expresses hybrid properties but requires post-design expert analysis. None addresses both discrete and continuous verification compositionally.
 
-\textbf{What are the limits of current practice?} A clear verification gap emerges. No existing methodology synthesizes provably correct hybrid controllers from operational procedures with verification integrated into design. Current approaches verify discrete logic or continuous dynamics—never both compositionally. Training improvements cannot overcome human reliability limits. Post-hoc verification cannot scale to system design.
+\textbf{What are the limits of current practice?} A clear verification gap emerges: no existing methodology synthesizes provably correct hybrid controllers from operational procedures with verification integrated into design. Current approaches verify discrete logic or continuous dynamics—never both compositionally. Training improvements cannot overcome human reliability limits, and post-hoc verification cannot scale to system design.
 
-The verification gap is clear. No existing methodology synthesizes provably correct hybrid controllers from operational procedures. Economic pressures demand autonomous control. Technical maturity now enables it. 
+This verification gap is clear and consequential. Economic pressures demand autonomous control; technical maturity now enables it. 
 
-Section 3 addresses the next two Heilmeier questions. What is new? Why will it succeed? It presents the technical approach that closes this gap.
+Section 3 addresses the next two Heilmeier questions—What is new? Why will it succeed?—presenting the technical approach that closes this gap.

3-research-approach/v3.tex

@@ -23,13 +23,13 @@ This section presents the complete technical approach for synthesizing provably
 % ----------------------------------------------------------------------------
 % 1. INTRODUCTION AND HYBRID SYSTEMS DEFINITION
 % ----------------------------------------------------------------------------
-Previous approaches verified either discrete switching logic or continuous control behavior—never both simultaneously. Engineers validate continuous controllers through extensive simulation trials. They test discrete switching logic through simulated control room testing and human factors research. Neither method provides rigorous guarantees. Both consume enormous resources.
+Previous approaches verified either discrete switching logic or continuous control behavior—never both simultaneously. Engineers validate continuous controllers through extensive simulation trials and test discrete switching logic through simulated control room testing and human factors research. Neither method provides rigorous guarantees; both consume enormous resources.
 
-This approach bridges that gap. It composes formal methods with control-theoretic verification. It formalizes reactor operations as hybrid automata.
+This approach bridges that gap by composing formal methods with control-theoretic verification and formalizing reactor operations as hybrid automata.
 
 Hybrid system verification faces a fundamental challenge: discrete transitions change the governing vector field, creating discontinuities that traditional verification techniques cannot handle directly.
 
-This methodology decomposes the problem. It verifies discrete switching logic and continuous mode behavior separately, then composes them to guarantee correctness 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 methodology decomposes the problem by verifying discrete switching logic and continuous mode behavior separately, then composing them to guarantee correctness for 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 systems require mathematical formalization. This work draws on automata theory, temporal logic, and control theory to provide that description.
 
@@ -58,23 +58,23 @@ where:
 
 A HAHACS requires this tuple together with proof artifacts demonstrating that the control system's actual implementation satisfies its intended behavior.
 
-\textbf{What is new in this research?} Existing approaches verify either discrete logic or continuous dynamics—never both compositionally. Section 2 established this limitation: reactive synthesis, reachability analysis, and barrier certificates exist independently but have never been integrated into a systematic design methodology. Prior work cannot span from procedures to verified implementation.
+\textbf{What is new in this research?} Existing approaches verify either discrete logic or continuous dynamics—never both compositionally. Section 2 established this limitation: reactive synthesis, reachability analysis, and barrier certificates exist independently but have never been integrated into a systematic design methodology that spans from procedures to verified implementation.
 
 Three innovations enable compositional verification:
 
 \begin{enumerate}
-\item \textbf{Contract-based decomposition:} Discrete synthesis defines entry/exit/safety contracts that bound continuous verification. This transforms an intractable global problem into tractable local problems. It replaces traditional global hybrid system verification.
+\item \textbf{Contract-based decomposition:} Discrete synthesis defines entry/exit/safety contracts that bound continuous verification, transforming an intractable global problem into tractable local problems and replacing traditional global hybrid system verification.
-\item \textbf{Mode classification:} Continuous modes classify by control objective—transitory, stabilizing, or expulsory. This classification matches appropriate verification tools to each mode type. It enables mode-local analysis with provable composition guarantees.
+\item \textbf{Mode classification:} Continuous modes classify by control objective—transitory, stabilizing, or expulsory. This classification matches appropriate verification tools to each mode type and enables mode-local analysis with provable composition guarantees.
-\item \textbf{Procedure-driven structure:} Nuclear procedures already decompose operations into discrete phases with explicit transition criteria. This existing structure avoids artificial abstractions. It makes the approach tractable for complex systems like nuclear reactor startup.
+\item \textbf{Procedure-driven structure:} Nuclear procedures already decompose operations into discrete phases with explicit transition criteria. This existing structure avoids artificial abstractions and makes the approach tractable for complex systems like nuclear reactor startup.
 \end{enumerate}
 
 \textbf{Why will it succeed?} Three factors ensure practical feasibility.
 
-First, \textit{existing structure}: Nuclear procedures already decompose operations into discrete phases with explicit transition criteria. The approach formalizes this existing structure. It avoids imposing artificial abstractions. Domain experts can adopt the methodology without formal methods training.
+First, \textit{existing structure}: Nuclear procedures already decompose operations into discrete phases with explicit transition criteria. The approach formalizes this existing structure without imposing artificial abstractions, enabling domain experts to adopt the methodology without formal methods training.
 
-Second, \textit{bounded complexity}: Mode-level verification checks each mode against local contracts. This avoids global hybrid system analysis. The decomposition bounds computational complexity. It transforms an intractable global problem into tractable local verifications.
+Second, \textit{bounded complexity}: Mode-level verification checks each mode against local contracts, avoiding global hybrid system analysis. This decomposition bounds computational complexity by transforming an intractable global problem into tractable local verifications.
 
-Third, \textit{industrial validation}: The Emerson collaboration provides domain expertise to validate procedure formalization. It provides industrial hardware to demonstrate implementation feasibility. This ensures solutions address real deployment constraints—not just theoretical correctness.
+Third, \textit{industrial validation}: The Emerson collaboration provides domain expertise to validate procedure formalization and industrial hardware to demonstrate implementation feasibility, ensuring solutions address real deployment constraints—not just theoretical correctness.
 
 These factors combine to demonstrate 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.
 
@@ -142,9 +142,9 @@ These factors combine to demonstrate feasibility on production control systems w
 
 \subsection{System Requirements, Specifications, and Discrete Controllers}
 
-The previous subsection established the hybrid automaton formalism. This mathematical framework describes discrete modes, continuous dynamics, guards, and invariants. It provides the mathematical structure for hybrid control. But a critical question remains: where do these formal descriptions originate?
+The previous subsection established the hybrid automaton formalism—a mathematical framework describing discrete modes, continuous dynamics, guards, and invariants. This provides the mathematical structure for hybrid control, but a critical question remains: where do these formal descriptions originate?
 
-The answer lies in existing practice. Nuclear operations already possess a natural hybrid structure. This structure maps directly to the formalism through three control scopes: strategic, operational, and tactical. The approach constructs formal hybrid systems from existing operational knowledge. It leverages decades of domain expertise already encoded in operating procedures. It avoids imposing artificial abstractions.
+The answer lies in existing practice: nuclear operations already possess a natural hybrid structure that maps directly to the formalism through three control scopes: strategic, operational, and tactical. The approach constructs formal hybrid systems from existing operational knowledge, leveraging decades of domain expertise already encoded in operating procedures without imposing artificial abstractions.
 
 Human control of nuclear power divides into three scopes: strategic, operational, and tactical. Strategic control represents high-level, long-term decision making spanning months or years: managing labor needs and supply chains to optimize scheduled maintenance and downtime.
 
@@ -260,9 +260,9 @@ FRET has been successfully applied to spacecraft control systems, autonomous veh
 
 \subsection{Discrete Controller Synthesis}
 
-The previous subsection demonstrated how operating procedures translate into temporal logic specifications using FRET. These specifications define what the system must do. But a critical gap remains: how do we implement those requirements?
+The previous subsection demonstrated how operating procedures translate into temporal logic specifications using FRET, defining what the system must do. A critical gap remains: how do we implement those requirements?
 
-Reactive synthesis bridges this gap. It automatically constructs controllers guaranteed to satisfy temporal logic specifications. It automates the creation of reactive programs from temporal logic—programs that take input for a given state and produce output. The current discrete state and guard condition status form the input. The next discrete state forms the output.
+Reactive synthesis bridges this gap by automatically constructing controllers guaranteed to satisfy temporal logic specifications. It automates the creation of reactive programs from temporal logic—programs that take input for a given state and produce output, where the current discrete state and guard condition status form the input and 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. Unrealizable specifications indicate conflicting or impossible requirements in
 the original procedures—this realizability check catches errors before implementation. 
@@ -289,9 +289,9 @@ Reactive synthesis produces discrete mode-switching logic from procedures. This
 
 \subsection{Continuous Control Modes}
 
-Reactive synthesis produces a provably correct discrete controller. This controller determines when to switch between modes. However, hybrid control requires more than correct mode switching. The continuous dynamics executing within each discrete mode must also verify against requirements.
+Reactive synthesis produces a provably correct discrete controller that determines when to switch between modes. However, hybrid control requires more than correct mode switching: the continuous dynamics executing within each discrete mode must also verify against requirements.
 
-Control objectives determine the verification approach. Modes classify into three types—transitory, stabilizing, and expulsory. Each requires different verification tools matched to its distinct purpose. This subsection describes each type and its verification method. 
+Control objectives determine the verification approach. Modes classify into three types—transitory, stabilizing, and expulsory—each requiring different verification tools matched to its distinct purpose. This subsection describes each type and its verification method. 
 
 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 confirms whether an implementation satisfies its specification without prescribing how to write the software. Engineers design continuous controllers using standard control theory techniques. This work assumes that capability exists. The contribution lies in the verification framework. It confirms that candidate controllers compose correctly with the discrete layer to produce a safe hybrid system.
 
@@ -344,7 +344,7 @@ The following subsections detail each mode type and its verification approach. W
 
 \subsubsection{Transitory Modes}
 
-Transitory modes—the first of three continuous controller types—execute transitions between operating conditions. Their purpose is to move the plant from one discrete operating condition to another. They start from entry conditions, reach exit conditions, and maintain safety invariants throughout. Examples include power ramp-up sequences, cooldown procedures, and load-following maneuvers.
+Transitory modes—the first of three continuous controller types—execute transitions between operating conditions, moving the plant from one discrete operating condition to another. They 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 has a formal statement. 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:
 \[
@@ -392,11 +392,9 @@ appropriate to the fidelity of the reactor models available.
 
 \subsubsection{Stabilizing Modes}
 
-Transitory modes drive the system toward exit conditions. Reachability analysis verifies whether the target can be reached. Stabilizing modes address a different question.
+While transitory modes drive the system toward exit conditions using reachability analysis to verify whether the target can be reached, stabilizing modes address a different question: rather than "can the system reach a target?" they ask "will the system stay within bounds?" 
 
-Rather than asking "can the system reach a target?" stabilizing modes ask "will the system stay within bounds?" Transitory modes aim to reach a target; stabilizing modes 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.
+Transitory modes aim to reach a target; stabilizing modes 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: barrier certificates.
-
-Reachability analysis answers "can the system reach a target?" Stabilizing modes instead ask "does the system stay within bounds?" Barrier certificates provide the appropriate verification tool for this question.
 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
@@ -443,11 +441,9 @@ controller.
 
 \subsubsection{Expulsory Modes}
 
-Transitory and stabilizing modes handle nominal operations. Transitory modes move the plant between conditions. Stabilizing modes maintain it within regions. Both assume the plant dynamics match the design model.
+Transitory and stabilizing modes handle nominal operations—transitory modes move the plant between conditions while stabilizing modes maintain it within regions. Both assume the plant dynamics match the design model.
 
-Expulsory modes address a different scenario: situations where the plant deviates from expected behavior. This deviation may result from component failures, sensor degradation, or unanticipated disturbances. For expulsory modes, robustness matters more than optimality.
+Expulsory modes address a different scenario: situations where the plant deviates from expected behavior due to component failures, sensor degradation, or unanticipated disturbances. For expulsory modes, robustness matters more than 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.
-
-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.
 
@@ -525,31 +521,29 @@ outcomes can best align with customer needs.
 
 This section addressed two critical Heilmeier questions: What is new? Why will it succeed?
 
-\textbf{What is new?} Three innovations enable compositional verification. They integrate reactive synthesis, reachability analysis, and barrier certificates. 
+\textbf{What is new?} Three innovations enable compositional verification by integrating reactive synthesis, reachability analysis, and barrier certificates: 
 
-First, \textit{contract-based decomposition} inverts traditional global analysis. Discrete synthesis defines verification contracts that bound continuous verification. 
+First, \textit{contract-based decomposition} inverts traditional global analysis—discrete synthesis defines verification contracts that bound continuous verification. 
 
-Second, \textit{mode classification} matches continuous modes to appropriate verification tools. This enables mode-local analysis with provable composition guarantees. 
+Second, \textit{mode classification} matches continuous modes to appropriate verification tools, enabling mode-local analysis with provable composition guarantees. 
 
-Third, \textit{procedure-driven structure} leverages existing procedural decomposition. This avoids intractable state explosion.
+Third, \textit{procedure-driven structure} leverages existing procedural decomposition to avoid intractable state explosion.
 
 Section 2 established that prior work verified discrete logic or continuous dynamics—never both compositionally. These three innovations enable what global analysis cannot: compositional verification spanning from procedures to verified implementation.
 
-\textbf{Why will it succeed?} Three factors ensure practical feasibility. 
+\textbf{Why will it succeed?} Three factors ensure practical feasibility: 
 
-\textit{Existing structure}: Nuclear procedures already decompose operations into discrete phases with explicit transition criteria. This allows formalization without artificial abstractions. 
+\textit{Existing structure}: Nuclear procedures already decompose operations into discrete phases with explicit transition criteria, allowing formalization without artificial abstractions. 
 
-\textit{Bounded complexity}: Mode-level verification bounds each problem locally. This avoids the state explosion that makes global hybrid system analysis intractable. 
+\textit{Bounded complexity}: Mode-level verification bounds each problem locally, avoiding the state explosion that makes global hybrid system analysis intractable. 
 
-\textit{Industrial validation}: Emerson collaboration provides domain expertise to validate procedure formalization. It provides industrial hardware to demonstrate implementation feasibility. This ensures solutions address real deployment constraints.
+\textit{Industrial validation}: Emerson collaboration provides domain expertise to validate procedure formalization and industrial hardware to demonstrate implementation feasibility, ensuring solutions address real deployment constraints.
 
-The complete technical methodology is now established. 
+With the complete technical methodology established, Sections 2 and 3 have addressed the first four Heilmeier questions—what has been done, what limits current practice, what is new, and why it will succeed. 
 
-Sections 2 and 3 addressed the first four Heilmeier questions. Section 2 established what has been done and what limits current practice. Section 3 explained what is new and why it will succeed. 
+Three questions remain: How will success be measured? What could prevent success? Who cares and what difference will this work make? 
 
-Three questions remain. How will success be measured? What could prevent success? Who cares? What difference will this work make? 
+Section 4 addresses metrics for success, Section 5 identifies what could prevent success, and Section 6 explains who cares and what difference this work will make.
-
-Section 4 addresses metrics for success. Section 5 identifies what could prevent success. Section 6 explains who cares and what difference this work will make.
 
 %%% NOTES (Section 5):
 % - Get specific details on ARCADE interface from Emerson collaboration

4-metrics-of-success/v1.tex

@@ -6,7 +6,7 @@ Section 3 established the technical approach: compositional verification bridges
 
 This section addresses the next Heilmeier question: How will success be measured? 
 
-Success is measured by Technology Readiness Level advancement from fundamental concepts (TRL 2--3) to validated prototype demonstration (TRL 5). At TRL 5, system components operate successfully in a relevant laboratory environment. 
+Success is measured by Technology Readiness Level advancement from fundamental concepts (TRL 2--3) to validated prototype demonstration (TRL 5), where system components operate successfully in a relevant laboratory environment. 
 
 TRL advancement provides the most appropriate success metric. It explicitly measures the gap between academic proof-of-concept and practical deployment. This section explains why TRLs appropriately measure success. It then defines specific criteria for each level from TRL 3 through TRL 5.
 
@@ -87,16 +87,16 @@ controllers implementable with current technology.
 
 This section answered the Heilmeier question: How will success be measured?
 
-\textbf{Answer:} Technology Readiness Level advancement from 2--3 to 5. Each level demonstrates both theoretical correctness and practical feasibility through progressively integrated validation.
+\textbf{Answer:} Technology Readiness Level advancement from 2--3 to 5, where each level demonstrates both theoretical correctness and practical feasibility through progressively integrated validation:
 
-TRL 3 proves component-level correctness. Each methodology element works independently.
+TRL 3 proves component-level correctness—each methodology element works independently.
 
-TRL 4 demonstrates system-level integration in simulation. Components compose correctly.
+TRL 4 demonstrates system-level integration in simulation—components compose correctly.
 
-TRL 5 validates hardware implementation in a relevant environment. The complete system operates on industrial control hardware.
+TRL 5 validates hardware implementation in a relevant environment—the complete system operates on industrial control hardware.
 
-Achieving TRL 5 proves the methodology produces verified controllers implementable with current technology. The result is not merely theoretically sound—it is practically deployable.
+Achieving TRL 5 proves the methodology produces verified controllers implementable with current technology—not merely theoretically sound but practically deployable.
 
-Sections 2 through 4 addressed five Heilmeier questions. Section 2 established what has been done and what limits current practice. Section 3 explained what is new and why it will succeed. This section defined how to measure success.
+Sections 2 through 4 have addressed five Heilmeier questions: what has been done, what limits current practice, what is new, why it will succeed, and how success will be measured.
 
-But success assumes critical technical challenges can be overcome. Section 5 addresses what could prevent success. It explains how to respond when assumptions fail.
+Success, however, assumes critical technical challenges can be overcome. Section 5 addresses what could prevent success and explains how to respond when assumptions fail.

5-risks-and-contingencies/v1.tex

@@ -2,11 +2,9 @@
 
 \textbf{Heilmeier Question: What could prevent success?}
 
-Section 4 defined success as reaching TRL 5 through component validation, system integration, and hardware demonstration. This assumes critical technical challenges can be overcome.
+Section 4 defined success as reaching TRL 5 through component validation, system integration, and hardware demonstration, assuming critical technical challenges can be overcome.
 
-Every research plan rests on assumptions that might prove false. Three primary risks could prevent reaching TRL 5: computational tractability of synthesis and verification, complexity of the discrete-continuous interface, and completeness of procedure formalization.
+Every research plan rests on assumptions that might prove false. Three primary risks could prevent reaching TRL 5: computational tractability of synthesis and verification, complexity of the discrete-continuous interface, and completeness of procedure formalization. Each risk has identifiable early warning indicators, viable mitigation strategies, and contingency plans that preserve research value even when core assumptions fail. 
-
-Each risk has identifiable early warning indicators. Each has viable mitigation strategies. Each carries contingency plans that preserve research value even when core assumptions fail. 
 
 The staged project structure ensures partial success yields publishable results. It clearly identifies remaining barriers to deployment, even when full success proves elusive.
 
@@ -133,16 +131,12 @@ quirks.
 
 This section answered the Heilmeier question: What could prevent success?
 
-\textbf{Answer:} Three primary risks threaten TRL 5 achievement: computational tractability of synthesis and verification, complexity of the discrete-continuous interface, and completeness of procedure formalization.
+\textbf{Answer:} Three primary risks threaten TRL 5 achievement: computational tractability of synthesis and verification, complexity of the discrete-continuous interface, and completeness of procedure formalization. Each risk has identifiable early warning indicators enabling detection before failure becomes inevitable, viable mitigation strategies preserving research value even when core assumptions fail, and contingency plans that maintain contribution regardless of which technical obstacles prove insurmountable.
 
-Each risk has identifiable early warning indicators. These enable detection before failure becomes inevitable. Each has viable mitigation strategies preserving research value even when core assumptions fail.
+The staged project structure ensures partial success yields publishable results identifying remaining deployment barriers. Even failure advances the field by documenting precisely which barriers remain.
 
-The staged project structure ensures partial success yields publishable results. These results identify remaining deployment barriers. This design maintains contribution regardless of which technical obstacles prove insurmountable. Even failure advances the field by documenting precisely which barriers remain.
+Sections 2 through 5 have established the complete technical research plan: Section 2 established what has been done and what limits current practice, identifying the verification gap. Section 3 explained what is new and why it will succeed, presenting three innovations enabling compositional verification. Section 4 defined how to measure success through TRL advancement. This section identified what could prevent success and explained how to respond when assumptions fail.
-
-Sections 2 through 5 established the complete technical research plan. 
-
-Section 2 addressed what has been done and what limits current practice. It established the verification gap. Section 3 explained what is new and why it will succeed. It presented three innovations enabling compositional verification. Section 4 defined how to measure success through TRL advancement. This section identified what could prevent success. It explained how to respond when assumptions fail.
 
 One critical question remains: Who cares? Why now? What difference will it make?
 
-Section 6 connects this technical methodology to urgent economic and societal challenges. It demonstrates why this work matters now.
+Section 6 connects this technical methodology to urgent economic and societal challenges, demonstrating why this work matters now.

6-broader-impacts/v1.tex

@@ -63,16 +63,14 @@ adoption across critical infrastructure.
 
 This section answered three critical Heilmeier questions:
 
-\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 require autonomous control with safety guarantees.
+\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, and clean energy advocates need nuclear power to be economically competitive. All three require autonomous control with safety guarantees.
 
-\textbf{Why now?} Two forces converge to create urgency. \textit{First: exponentially growing demand.} AI infrastructure creates immediate need for economical nuclear power at datacenter scale. Projections show datacenter electricity demand reaching 1,050 terawatt-hours annually by 2030. \textit{Second: technical maturity.} Formal methods tools have matured sufficiently to make compositional hybrid verification computationally achievable. What was theoretically possible but practically intractable a decade ago is now feasible. The problem is urgent. The tools exist.
+\textbf{Why now?} Two forces converge to create urgency. First, \textit{exponentially growing demand}: AI infrastructure creates immediate need for economical nuclear power at datacenter scale, with projections showing datacenter electricity demand reaching 1,050 terawatt-hours annually by 2030. Second, \textit{technical maturity}: formal methods tools have matured sufficiently to make compositional hybrid verification computationally achievable. What was theoretically possible but practically intractable a decade ago is now feasible. The problem is urgent and the tools exist.
 
-\textbf{What difference will it make?} This research addresses a \$21--28 billion annual cost barrier. It enables autonomous control with mathematical safety guarantees. Beyond immediate economic impact, the methodology establishes a generalizable framework for safety-critical autonomous systems across critical infrastructure. It extends beyond nuclear power to any safety-critical system requiring provable correctness.
+\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, extending beyond nuclear power to any safety-critical system requiring provable correctness.
 
-Sections 2 through 6 addressed all but one of the Heilmeier questions. 
+Sections 2 through 6 have addressed all but one Heilmeier question: Section 2 established what has been done and what limits current practice, identifying the verification gap. Section 3 explained what is new and why it will succeed, presenting three innovations enabling compositional verification. Section 4 defined how to measure success through TRL advancement from 3 to 5. Section 5 identified what could prevent success and provided contingencies. This section connected technical methodology to economic and societal impact.
-
-Section 2 established what has been done and what limits current practice. It identified the verification gap. Section 3 explained what is new and why it will succeed. It presented three innovations enabling compositional verification. Section 4 defined how to measure success through TRL advancement from 3 to 5. Section 5 identified what could prevent success and provided contingencies. This section connected technical methodology to economic and societal impact.
 
 One final Heilmeier question remains: How long will it take? 
 
-Section 8 provides the answer. It presents a detailed schedule with milestones and deliverables.
+Section 8 provides the answer with a detailed schedule of milestones and deliverables.

8-schedule/v1.tex

@@ -2,11 +2,11 @@
 
 \textbf{Heilmeier Question: How long will it take?}
 
-Section 6 demonstrated that this work addresses a \$21--28 billion annual cost barrier. It establishes a generalizable framework for safety-critical autonomous systems. 
+Section 6 demonstrated that this work addresses a \$21--28 billion annual cost barrier and establishes a generalizable framework for safety-critical autonomous systems. 
 
 This final section addresses the last Heilmeier question: 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. The University of Pittsburgh Cyber Energy Center and NRC Fellowship provide all computational and experimental resources. Work progresses sequentially through three main research thrusts, culminating in integrated demonstration and validation.
+This research will be conducted over six trimesters (24 months) of full-time effort following the proposal defense in Spring 2026, with all computational and experimental resources provided by the University of Pittsburgh Cyber Energy Center and NRC Fellowship. Work progresses sequentially through three main research thrusts, culminating in integrated demonstration and validation.
 
 The first semester (Spring 2026) focuses on Thrust 1, translating startup
 procedures into formal temporal logic specifications using FRET. This