Research · Updates
JSR Decidability Frontier Updates
Project Scope
This page explains what was added to make the switching-stability frontier reproducible.
The key upgrades are the introduction of explicit frontier report objects and the removal of hidden assumptions about primitivity.
Use this page when you want to know why the frontier discussion is now grounded in schemas, witnesses, and finite outputs.
This page records what changed as the robust switching stability viewpoint was strengthened into an artifact-level frontier.
What this page is about
The joint spectral radius viewpoint is a convenient language for “robust switching stability.”
This project does not treat that language as a slogan.
It treats it as a place where the rigidity program can produce finite objects:
- a robust certificate on a face with explicit margins and a stability radius
- a named obstruction witness localizing failure
- a frontier report or atlas tying local behavior to regions in parameter space
Frontier-layer contributions
| Addition | What it adds | Why it matters |
|---|---|---|
| Frontier report schemas | A contract for reporting the frontier in a way that tools can validate | It makes the frontier a reproducible object rather than a narrative |
| Atlas viewpoint for the frontier | A structured way to describe where uniformity fails across a family | It connects switching stability questions to the same cover-or-atlas logic used in global universality |
| Imprimitive and cyclic core support | Explicit representation of periodic decomposition when it occurs at the minimizing core | It prevents hidden assumptions from creeping into frontier claims |
