Developers increasingly provide AI coding assistants with persistent context through configuration files such as CLAUDE.md, AGENTS.md, and .cursorrules. These files describe code elements, architecture, and development conventions, forming the context that guides AI tool behavior across sessions. As software evolves, this context can become stale, a phenomenon we call context rot. While AI configuration artifacts are new, the underlying consistency problem connects to decades of software documentation research. Researchers have built tools to check consistency between documentation and code, spanning README files, code comments, API documentation, architecture descriptions, and installation instructions. We argue that this existing toolbox is an immediate starting point for detecting context rot, and we present a research roadmap mapping documentation consistency approaches to corresponding problems in this new setting. As preliminary evidence, applying an existing README/wiki consistency checker to a statistically representative sample of 356 repositories identifies stale code element references in 23.0% of repositories, showing that traditional documentation consistency tools can already surface context rot.