Research · Flagship Variant
Gap-Free Flagship
Project Scope
This page is a polished narrative form of the flagship mechanism, written with an emphasis on clarity about regimes and failure modes.
In many growth problems, people talk about “gaps” or “spectral separation” as if it were an aesthetic preference. In this program, the point is sharper:
- When a robust contraction mechanism exists, structure is forced.
- When it fails, it fails for specific reasons that can be classified.
This page collects that perspective in a way that is easier to present and easier to cross-reference.
When it is most useful
- When you already understand the main story and want a cleaner presentation of the regime split.
- When you are comparing the structural theorem to the certification machinery and want a single page that highlights the separation.
- When you are preparing to explain the program to someone who does not want to start inside the proof appendix.
If you are new, do not start here. Start with Rigidity and Reconstruction. Then come back and use this page as a sharpening tool.
Project Scope
This page exists to highlight the strongest form of the rigidity story: the form that does not hide behind convenient separation assumptions.
If you arrived here looking for the flagship statement, use this page as your main entry point:
That page contains the cleanest explanation of what “gap-free” means, why it is harder than the pleasant case, and how the verification layer turns the claim into something a reader can audit.
| What you may be looking for | Where to go |
|---|---|
| The program map | Rigidity and Reconstruction |
| The geometric intuition | Roots as Geometry |
| A tiny concrete example | Golden Ratio Minimal Growth |
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