Library · Document
Appendix Suite
Project Scope
This page answers a question that serious readers always ask:
If the theorem has “boundary cases” where it can fail, are those boundary cases real or are they artifacts of the method.
The appendix suite is where that question is treated with respect.
What “sharpness” means here
Sharpness is the difference between:
- “We proved something, but we do not know whether the assumptions are necessary,” and
- “Every obstruction we list can actually happen, and if you remove an assumption you really do lose the conclusion.”
Why this matters
The main program claims that minimality forces structure.
A skeptic will naturally ask:
- Could the conclusion be stronger.
- Could the assumptions be weaker.
- Are the failure modes just uninteresting corner cases.
This appendix suite is where those questions are answered in a disciplined way.
How to read it
- Read it after you know the main theorem statement.
- Use it to understand what is genuinely necessary.
- Treat it as an integrity check: it shows the method is not built on hidden conveniences.
Project Scope
This is a set of supporting appendices that strengthen the main theorem by showing the “gates” are real and necessary.
- What it proves: when the program says “either the contract holds or a specific obstruction happens,” those obstructions are not artificial.
- What that buys you: referee confidence, because each failure mode is shown to be genuinely realizable.
- How it is used: as a reference when someone asks “could this assumption be removed” or “is that obstruction really needed.”
| Added credibility | Why it matters |
|---|---|
| Sharpness | The conditions are not cosmetic, they align with true boundary cases |
| Realizability | Each obstruction class can actually occur in an admissible example |
| Clean separation | Structural theorem stays clean, appendices carry the edge-case weight |
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