## Problem 028 — rank:20

**Title:** Portability of polygenic prediction

**Added binding assumptions (LaTeX):**

```latex
For binary outcomes use a proper loss and define $R_a^*$ as the infimum over a fixed comparator class with identical features. Restrict calibration bins to positive-probability groups and account for familywise validation uncertainty. Calibration and prediction-error constraints may be jointly infeasible in some cohorts; the target permits a proved or empirically bounded attainable frontier rather than presuming universal simultaneous success.
```

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