## Problem 307 — rank:199

**Title:** Independent origins of multicellularity

**Added binding assumptions (LaTeX):**

```latex
A rate of entry to state 2 among at-risk lineages conditions on $Z_t<2$ and depends on the lineage-state distribution at a stated time or branch position. Population-wide transition incidence uses different unnormalized weights. Specify whether re-entry after loss counts as a new independent origin or a recurrence retaining ancestral machinery. Time-varying covariates and hidden trait states need a joint evolutionary law; a regression coefficient alone is not causal evidence.
```

**Direct edits:** 2. **Fresh external checks:** None; supplied sources retained as provenance.