## Problem 251 — rank:39

**Title:** Microbiome control of cancer-treatment response

**Added binding assumptions (LaTeX):**

```latex
Replace the unrestricted class of all host-dependent rules by a prespecified measurable policy class of bounded complexity. Define a safety endpoint and admissible risk bound, with evaluation on data independent of rule selection. Optimize only over policies meeting that constraint. Existence of a beneficial safe policy is a hypothesis to test, not guaranteed by the notation; report infeasibility or an unresolved benefit bound when appropriate.
```

**Direct edits:** 2. **Fresh external checks:** None; supplied sources retained as provenance.