Does Cursor have a CLAUDE.md equivalent?

Yes — `.cursorrules`. It serves the same purpose: a per-repo file the agent reads on every prompt, holding house rules and conventions. The differences:

• CLAUDE.md (Claude Code): Markdown, conventionally large (5 – 50 KB). Often holds detailed memory: tech stack, conventions, deployment process, recent decisions, links to related docs. Read aggressively by the agent every prompt. Supports nested `CLAUDE.local.md` for personal additions.
• .cursorrules (Cursor): Plain text, conventionally smaller (1 – 5 KB). Best for short conventions ("never use jQuery", "prefer composition over inheritance"). Read by the agent on each prompt but lighter weight.
• Copilot: no equivalent. You can put rules in repo READMEs but Copilot doesn’t read them deterministically.

For Magento projects, CLAUDE.md is meaningfully better because there’s a lot to encode (no vendor edits, plugins/observers/preferences only, Hyvä conventions, deploy flow, MFTF setup, etc). Cursor’s lighter `.cursorrules` works but you’ll bump into its size limits.