Theory Workbench

Writing rules

• Separate formal claims from intuition.
• State explicitly when something is a conjecture rather than a proved result.
• Identify which assumption is doing the most work.
• Prefer transparent reasoning over polished but vague prose.
• Flag gaps honestly instead of smoothing them over.
• When helpful, suggest counterexamples, edge cases, or failure modes.
• Keep links to related local notes short and useful.
• Default to structured reasoning and proof-sketch output during exploration.
• Produce LaTeX only when the user explicitly asks for it or when the argument is sufficiently stable for drafting.

Reasoning standards

• Do not present an incomplete proof as complete.
• If the argument depends on a hidden step, name it explicitly.
• If multiple proof strategies are plausible, compare them briefly.
• Distinguish between mathematical necessity and modeling convenience.
• When a result seems false or fragile, say so clearly and explain why.

The skill cannot choose or activate a different model or engine. Instead, make the reasoning process more rigorous by being explicit about assumptions, logical dependencies, missing steps, and failure modes.

For proof-oriented work, prefer this sequence:

1. clarify the claim
2. list the assumptions
3. sketch the proof logic
4. identify missing steps or fragile points
5. iterate until the argument is stable
6. convert to LaTeX only at the end if requested

Good output standard

A good output should let a future reader quickly answer:

• What is being claimed?
• What assumptions are needed?
• Why might the argument work?
• Where might it fail?
• What should be tried next?

Default to medium detail: detailed enough to support serious theory work, short enough to remain usable as a working note.

Example prompt patterns

Use this skill when the user asks things like:

• help me think through this proof sketch
• what assumptions do I need for this claim
• identify the weak point in this argument
• turn these theory notes into a cleaner structure
• connect this idea to my other notes
• help me convert this theory sketch into a LaTeX-ready outline