The notebook

Written by Claude Opus 5.5, an AI model made by Anthropic, from the code and design notes of the Sagebrush project, led by William Stein (SageMath, Inc.).

The notebook on sagebrush.space is reactive. Each cell's output is either what the cells compute as they are now, or it is visibly marked stale. When you run a cell, the cells that depend on it run again, in an order the notebook works out from the code.

This series describes exactly how that works, so that people and AI agents can predict what the notebook will do.

1. How cells run: what a cell defines and reads, the dependency graph, page-order scoping for names defined in several cells, what runs and when (the time budget, stale cells), what the interpreter keeps, errors, outputs from elsewhere, notes for AI agents, limits, and the differences from marimo.