Formalization roadmap

The formula bridge shows what is proven. This page rates every operator on the map by what a Lean theorem about its formula would take: a closed-form definition, a formula that needs analysis, or an external code's output with nothing to prove. A definition gets no theorem that restates it. A theorem about one must state a property, such as a limit, a bound or a reduction to another model.

Counts by difficulty

The rows marked "Needs analysis" hold Brillouin-zone sums, correlation-function integrals and occupation-number factors. Each is a well-posed formalization project. A row is marked proven when a compiled bridge in lean/bridge proves a statement about its formula, under the conditions the bridge page lists. If one of the open rows is a problem you work on, the repository is open, and lean/bridge builds against Physlib with lake exe cache get and lake build.

All operators