## Problem 195 — rank:305

**Title:** Predicting trophic cascades

**Added binding assumptions (LaTeX):**

```latex
The inverse-Jacobian derivative is the established implicit-function formula on a smooth invertible equilibrium branch. It does not extend through a bifurcation or approximate removal without a finite-perturbation error bound. Specify feasible pressure directions preserving nonnegative populations, the post-removal initial survivor state and the endpoint convention. Sign robustness requires a nonzero margin throughout the data-compatible parameter set.
```

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