# AI provenance — Universal Support Theorems for Resilient Coverage

Version 1.1.1, 28 October 2026. Authors: Deep Bhattacharjee (corresponding), Ushashi Bhattacharya, Sanjeevan Singha Roy. Text classification: a mix of human-written and AI-generated. The authors declare that all parts have been checked and understood by a human.

OpenAI Codex assisted with:
- developing and writing the mathematical arguments of version 1.0.0;
- the exact-arithmetic check programs in the repository (Python, `code/`);
- the figures and the first typesetting.

Anthropic Claude / Claude Code assisted with versions 1.1.0 and 1.1.1:
- a line-by-line check of every proof and of the numbers of the worked examples;
- the literature comparison (Toussaint 1983 on largest empty circles with location constraints, Lee 1982 on order-k Voronoi diagrams, So and Ye 2005 on k-coverage), which is now credited in the introduction;
- the corrected support-comparison figure, the REVTeX layout and the removal of software remarks from the text;
- the plain-language abstract of version 1.1.1.

No statement of the paper rests on the programs; every theorem and every number of the worked examples is proved in the text. The authors reviewed the text and take responsibility for it.

AI systems are not authors. The package does not contain prompts or hidden reasoning traces.

Archive: release v1.1.1 of https://github.com/creelie/sensor-resilience-certificates , DOI https://doi.org/10.5281/zenodo.23742526.