## Problem 070 — rank:223

**Title:** Single-cell batch correction without erasing biology

**Added binding assumptions (LaTeX):**

```latex
Define $R_C$ using a fixed loss and the deployment distribution; it is Bayes risk under the given representation. The guarantee preserves only the chosen biological target $C$, not all biological information. A constant embedding may pass when $C$ is uninformative, so require a nontrivial target benchmark or a family of biological tasks. Perfect batch--biology confounding is an identification obstruction, not a batch-correction algorithm failure alone.
```

**Direct edits:** 0. **Fresh external checks:** None; supplied sources retained as provenance.