\documentclass{article}
\title{Certified Correctness Under Distribution Shift}
\author{BlueChips Research}
\date{2026}

\begin{document}
\maketitle

\begin{abstract}
Learning-based systems can appear reliable inside the training distribution while remaining structurally unconstrained outside it. BlueChips research focuses on guarantees that survive perturbation, adversarial input, and scale.
\end{abstract}

\section{Problem}
Critical infrastructure cannot rely on average-case behavior. A power grid cascade, control surface excursion, or network failure is judged by the worst case, not by aggregate performance over familiar data.

\section{Method}
We represent the operating envelope as a bounded structure and certify invariants directly. The objective is not to predict which fault will happen, but to prove which failures cannot propagate beyond a defined boundary.

\[
  \forall x \in \Omega,\quad V(x) \leq \epsilon \Rightarrow C(x) \in \mathcal{B}
\]

\section{Result}
Certified-correctness work produces assumptions, invariants, bounds, and failure conditions that can be inspected directly. The result is evidence a technical reviewer can evaluate instead of a confidence score that must be taken on trust.

\end{document}
