## Problem 275 — rank:312

**Title:** Biosensor specificity–sensitivity frontier

**Added binding assumptions (LaTeX):**

```latex
Fix the concentration and nuisance distributions within positive and negative classes; sensitivity and specificity can change when those distributions change, even at the same prevalence. Optimize only over designs and thresholds selected under a complexity-controlled protocol and use simultaneous bands after selection. Report the intermediate concentration region separately. A finite known response-family frontier is an optimization object, not a claim of a universal biological detection limit.
```

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