1. Specifications that live outside the code. We have a lot of code for which "what should this do?" is a subjective answer, because "what was this written to do?" is either oral legend or lost in time. As future Claude sessions add new features, this is how Claude can remember what was intentional in the existing code and what were accidents of implementation. And they're useful for documenters, support, etc.
2. Specifications that stay up to date as code is written. No spec survives first contact with the enemy (implementation in the real world). "Huh, there are TWO statuses for Missing orders, but we wrote this assuming just one. How do we display them? Which are we setting or is it configurable?" etc. Implementer finds things the specifier got wrong about reality, things the specifier missed that need to be specified/decided, and testing finds what they both missed.
I have a colleague working on saving architecture decisions, and his description of it feels like a higher-abstraction version of my saving and maintaining requirements.
My recursive-mode workflow handles all of that and more and gives you full traceability: https://recursive-mode.dev/introduction