\section*{Declarations}

\noindent\textbf{Funding.} None.

\noindent\textbf{Competing interests.} None.

\noindent\textbf{Ethics.} Not applicable; the article contains no research involving human participants or animals.

\noindent\textbf{Data availability.} The \LaTeX{} source and the finite checks of the worked examples are archived in the repository \url{https://github.com/creelie/sensor-resilience-certificates}, release \releaseTag, on Zenodo at \href{https://doi.org/\zenodoCodeID}{doi:\zenodoCodeID}. No statement of the paper depends on them. OpenAI Codex and Anthropic Claude assisted with exposition, figures and the finite checks; the authors checked every proof and are responsible for the text.