Lemma
math, backwards
modular graph
The promise the manifesto made — drawn in real edges.
Lemma claims a modular graph, not a sequence. Today the claim is paid: 16 applications consume 10 modules along 42 edges, and 10 of 10 modules have more than one consumer. Each module gets a colour; every edge into a module inherits it, so the picture below is also the answer to "which math is doing the most work for the most pillars?"
snapshot
16
applications
10/10
modules consumed
42
edges
10/10
multi-consumer modules
the graph
what the graph says today
- The manifesto's modular-graph promise has paid off. 4/4 pillars active, 10/10 modules consumed, 42 edges drawn, 10/10 modules shared by more than one application. The graph is no longer a sketch — it's a count.
- Cross-application module reuse — each module's edge colour traces its consumers in the picture above:
- Vectors — 7 consumers, physics × 2 · graphics × 2 · finance · ml / dl × 2
- The Derivative — 6 consumers, finance · physics × 4 · ml / dl
- Distributions — 5 consumers, graphics · finance · ml / dl × 3
- The Logarithm — 5 consumers, finance × 2 · ml / dl × 3
- The Integral — 4 consumers, finance · physics × 3
- Linearization — 4 consumers, finance · physics × 2 · ml / dl
- Entropy — 3 consumers, graphics × 2 · ml / dl
- Optimization — 3 consumers, finance · ml / dl × 2
- Parametric Curves — 3 consumers, physics × 2 · graphics
- Bezout's Theorem — 2 consumers, graphics · finance
- Glossary terms aren't drawn here on purpose. The application–module structure already carries enough signal to reason from; adding term nodes would dilute the "which math is shared, and how widely?" question this view was built to answer.