# P11520: Can the A370193 stack completely collapse after n=12?

- ID: `P11520`
- Reference: `stack-complete-collapse-after-twelve`
- Page: https://theoremdb.org/statements/P11520
- 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/stack-complete-collapse-after-twelve?representation=markdown
- Record maturity: Reviewed problem

## The problem

Begin with an empty stack. At stage n, place n on top. A layer is unstable when the sum of all layers above it exceeds its value. Stabilize by finding the topmost unstable layer, merging the layer immediately above into it, and repeating. The stack has height 1 at \(n=1\),2,4,6,12. Does it ever have height 1 again?

## 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 `stack-complete-collapse-after-twelve`, 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.