## Problem 131 — rank:144

**Title:** Positional information encoding

**Added binding assumptions (LaTeX):**

```latex
Fix the spatial prior and a finite positional resolution or continuous distortion loss. For $M$ position bins, $I(X;S)\leq\log_2 M$; mutual information alone does not determine the error of a particular positional decoder. State the admissible decoder and its achievable risk, and distinguish a molecule-number budget from an energy or entropy-production budget. Any bound depends on the specified sensing and noise family.
```

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