## Problem 090 — rank:135

**Title:** Thermodynamics of biomolecular phase separation

**Added binding assumptions (LaTeX):**

```latex
Equal chemical potentials and osmotic pressure are necessary but not sufficient for stable coexistence. Impose global supporting-hyperplane inequalities and lever-rule mass balance with nonnegative phase fractions summing to one. Specify the overall composition and ensemble, account for absent species through appropriate boundary conditions, and report degenerate phase sets rather than selecting arbitrary stationary solutions.
```

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