Research · Companion Note
Golden Ratio Minimal Growth
Project Scope
This is the simplest concrete example in the whole library.
- What it shows: in a very explicit 2×2 positive matrix family, growth cannot drop below a fixed baseline.
- What the baseline is: the golden ratio shows up as the unavoidable minimum, and the equality case is the most uniform choice.
- Why it is included: it gives a hand-computable model of the larger theme: constraints force structure.
| Practical takeaway | Why it matters |
|---|---|
| A clean worked example | You can compute the bound by hand and see the equality case |
| A sanity check | The larger program reduces to this same kind of rigidity mechanism |
| A teaching tool | Useful for explaining the ideas without heavy machinery |
Where to go next
- If you want the full-strength theorem-and-certificate story beyond this toy example, read Gap-Free Rigidity and Robust Certificates.
- If you want the hub that explains how the whole program fits together, read Rigidity and Reconstruction.
Books by Drew Higgins
