## Problem 085 — rank:68

**Title:** Lipid–protein coupling

**Added binding assumptions (LaTeX):**

```latex
Fix a spatial discretization or a function space and a normalized Gibbs measure for the membrane fields. Respect the composition simplex and positive thickness, and impose an ultraviolet cutoff or equivalent regularization for fluctuation calculations. Only energy differences and identifiable parameter combinations are inferred; a constant energy shift and observationally equivalent contact terms remain gauge freedoms.
```

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