Flush Before You Trust: The Locality Trick Behind Incremental Sheaf Cohomology
TL;DR for operators Most business systems do not fail because they lack another dashboard. They fail because the dashboard is reading from a structure that changed three minutes ago, and nobody knows which part of the structure is now stale. Delightful. The paper behind this article proposes an incremental algorithm for maintaining first sheaf cohomology, $H^1$, on evolving 1-dimensional cellular complexes — essentially graph-like structures decorated with local vector spaces and consistency maps.1 In plainer operational language, it is about tracking whether a changing network of constraints still holds together without rebuilding the whole mathematical object after every edit. ...