## Problem 078 — rank:301

**Title:** Cross-modal biological alignment

**Added binding assumptions (LaTeX):**

```latex
Marginal assay distributions alone do not define a unique biological coupling $\pi_0$. Define it through paired measurements, a stated shared-latent generative law, or replace it by the whole compatible coupling set. Entropic or transport regularization chooses a conventionally preferred coupling; it is not proof of biological identifiability. Unbalanced populations need an explicit missing-mass or population-shift model.
```

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