Same idea, three names
GEMINI.md is to Gemini what CLAUDE.md is to Claude Code and AGENTS.md is to Codex: a markdown file the agent reads before doing anything. Hierarchy: ~/.gemini/GEMINI.md (user global) → repo-root GEMINI.md (project) → nested GEMINI.md (subdirectory rules). Files merge top-down; closer-to-CWD wins.
Gemini also reads AGENTS.md as a fallback (Codex compat). If both exist, GEMINI.md wins. Configure other fallback names in ~/.gemini/settings.json via contextFileName.