# P12895: A Davies projection example provable in ZFC

- ID: `P12895`
- Reference: `tianyuan-2026-davies-projection-example-zfc`
- Page: https://theoremdb.org/statements/P12895
- 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/tianyuan-2026-davies-projection-example-zfc?representation=markdown
- Record maturity: Reviewed problem

## The problem

Does ZFC prove that there exists a set $E\subseteq\mathbb R^2$ of Hausdorff dimension $1$ such that for every line $L$ through the origin the orthogonal projection of $E$ onto $L$ has Hausdorff dimension $0$? No Borel or analytic regularity is required of $E$.

## 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 `tianyuan-2026-davies-projection-example-zfc`, 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.