# P11274: Does the greedy unit-vector orbit have the conjectured limiting geometry?

- ID: `P11274`
- Reference: `greedy-complex-unit-vector-limiting-geometry`
- Page: https://theoremdb.org/statements/P11274
- 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/greedy-complex-unit-vector-limiting-geometry?representation=markdown
- Record maturity: Reviewed problem

## The problem

Let \(a_1\)=1 and S_1=1. For n>=2, choose a_n as the least integer greater than a_(n-1) such that |S_(n-1)+exp(-i log a_n)|<|S_(n-1)|, and set S_n=S_(n-1)+exp(-i log a_n). Does this choice exist for every n? If it does, do |S_n| and a_(n+1)/a_n converge, with a positive limit L for the norms and ratio exp(pi-2 arccos(1/(2L)))?

## 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 `greedy-complex-unit-vector-limiting-geometry`, 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.