# P11360: What is the arithmetic nature of the fourth super-root of two?

- ID: `P11360`
- Reference: `fourth-super-root-of-two-arithmetic-classification`
- Page: https://theoremdb.org/statements/P11360
- Export scope: built Markdown snapshot. The current public packet may have changed since this build.
- Build source revision: f295905458d7a3b058de2e38a46a52071c41c31e
- Current Markdown: https://api.theoremdb.org/v1/statements/fourth-super-root-of-two-arithmetic-classification?representation=markdown
- Record maturity: Reviewed problem

## The problem

Let x be the unique real number in (1,2) satisfying the right-associated equation \(x^(x^(x^x))\)=2. Is x rational, algebraic irrational, or transcendental? Equivalently for the first two possibilities, does its simple continued fraction terminate or become eventually periodic?

## Status

**Resolution status:** Open.

Research work is recorded. A complete resolution has not passed review.

## Research packet

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `fourth-super-root-of-two-arithmetic-classification`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.