# P12879: Vanishing probability of complex phase retrieval with 4M-5 measurements

- ID: `P12879`
- Reference: `randomstrasse-19-phase-retrieval-vanishing-probability`
- Page: https://theoremdb.org/statements/P12879
- 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/randomstrasse-19-phase-retrieval-vanishing-probability?representation=markdown
- Record maturity: Reviewed problem

## The problem

For each integer $M\ge2$, put $N=4M-5$ and let $A\in\mathbb C^{N\times M}$ have independent standard complex Gaussian entries. Let $p_M$ be the probability that $x\mapsto |Ax|^2$ is injective modulo global complex phase: $|Ax|^2=|Ay|^2$ implies $y=\lambda x$ for some $|\lambda|=1$. Does $\lim_{M\to\infty}p_M=0$?

## 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 `randomstrasse-19-phase-retrieval-vanishing-probability`, 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.