\section{Broader Impacts} \textbf{Who cares? Why now? What difference will it make?} The nuclear industry, datacenter operators, and clean energy advocates all face the same economic constraint: high operating costs driven by staffing requirements. AI infrastructure demands, growing exponentially, have made this constraint urgent. Nuclear power presents both a compelling application domain and an urgent economic challenge. Recent interest in powering artificial intelligence infrastructure has renewed focus on small modular reactors (SMRs), particularly for hyperscale datacenters requiring hundreds of megawatts of continuous power. Deploying SMRs at datacenter sites minimizes transmission losses and eliminates emissions. However, nuclear power economics at this scale demand careful attention to operating costs. The U.S. Energy Information Administration's Annual Energy Outlook 2022 projects advanced nuclear power entering service in 2027 will cost \$88.24 per megawatt-hour~\cite{eia_lcoe_2022}. Datacenter electricity demand is projected to reach 1,050 terawatt-hours annually by 2030~\cite{eesi_datacenter_2024}. Nuclear power supplying this demand would generate total annual costs exceeding \$92 billion. Operations and maintenance represents a substantial component of this figure. The EIA estimates that fixed O\&M costs alone account for \$16.15 per megawatt-hour, with additional variable O\&M costs embedded in fuel and operating expenses~\cite{eia_lcoe_2022}. Combined, O\&M-related costs represent approximately 23--30\% of the total levelized cost of electricity, translating to \$21--28 billion annually for projected datacenter demand. \textbf{What difference will it make?} This research directly addresses the \$21--28 billion annual O\&M cost challenge through high-assurance autonomous control, making small modular reactors economically viable for datacenter power. Current nuclear operations require full control room staffing for each reactor—whether large conventional units or small modular designs. For large reactors producing 1,000+ MW, staffing costs spread across substantial output. Small modular reactors producing 50-300 MW face the same staffing requirements with far lower output, making per-megawatt costs prohibitive. These staffing requirements drive the economic challenge that threatens SMR deployment for datacenter applications. Synthesizing provably correct hybrid controllers from formal specifications automates routine operational sequences that currently require constant human oversight. This enables a fundamental shift from direct operator control to supervisory monitoring, where operators oversee multiple autonomous reactors rather than manually controlling individual units. The correct-by-construction methodology is critical for this transition. Traditional automation approaches cannot provide sufficient safety guarantees for nuclear applications, where regulatory requirements and public safety concerns demand the highest levels of assurance. By formally verifying both the discrete mode-switching logic and the continuous control behavior, this research will produce controllers with mathematical proofs of correctness. These guarantees enable automation to safely handle routine operations---startup sequences, power level changes, and normal operational transitions---that currently require human operators to follow written procedures. Operators will remain in supervisory roles to handle off-normal conditions and provide authorization for major operational changes, but the routine cognitive burden of procedure execution shifts to provably correct automated systems that are much cheaper to operate. SMRs represent an ideal deployment target for this technology. Nuclear Regulatory Commission certification requires extensive documentation of control procedures, operational requirements, and safety analyses written in structured natural language. As described in our approach, these regulatory documents can be translated into temporal logic specifications using tools like FRET, then synthesized into discrete switching logic using reactive synthesis tools, and finally verified using reachability analysis and barrier certificates for the continuous control modes. The infrastructure of requirements and specifications already exists as part of the licensing process, creating a direct pathway from existing regulatory documentation to formally verified autonomous controllers. Beyond reducing operating costs for new reactors, this research will establish a generalizable framework for autonomous control of safety-critical systems. The methodology of translating operational procedures into formal specifications, synthesizing discrete switching logic, and verifying continuous mode behavior applies to any hybrid system with documented operational requirements. Potential applications include chemical process control, aerospace systems, and autonomous transportation, where similar economic and safety considerations favor increased autonomy with provable correctness guarantees. Demonstrating this approach in nuclear power---one of the most regulated and safety-critical domains---will establish both the technical feasibility and regulatory pathway for broader adoption across critical infrastructure. This section establishes impact by answering three Heilmeier questions: \textbf{Who cares?} The nuclear industry, datacenter operators, and any organization facing high operating costs from staffing-intensive safety-critical control. \textbf{Why now?} AI infrastructure demands have made nuclear economics urgent. Formal methods tools have matured to where compositional hybrid verification has become achievable. \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. One question remains: \textbf{How long will it take?} Section 8 provides a structured 24-month research plan progressing through milestones tied to Technology Readiness Level advancement.