## Problem 157 — rank:236

**Title:** Finite-horizon evolution of a specified complexity measure

**Added binding assumptions (LaTeX):**

```latex
For a complexity statistic bounded by $m$, a gain rate $\gamma$ maintained to time $T$ must satisfy $\gamma T\leq m-\E[C(G_0)]$. State the finite horizon and attainable threshold range. The generator identity for the derivative of the mean is standard once the Markov process is fixed; the research target is a biologically justified mutation--selection model that meets nontrivial gain and persistence requirements, not indefinite growth of a bounded statistic.
```

**Direct edits:** 1. **Fresh external checks:** None; supplied sources retained as provenance.