## Problem 302 — rank:114

**Title:** Comparative biological timing under explicit phase conventions

**Added binding assumptions (LaTeX):**

```latex
An ordinary expectation of an angular phase is coordinate-dependent or undefined. Use the declared metric-space mean $m_{jc}(t)$: an ordinary mean for Euclidean outputs and a unique Fr\'echet mean, or an explicitly fixed selection from the mean set, for circular outputs. Specify any exclusion of antipodal or nonunique regimes. Fixed finite families and gauge conventions are needed to distinguish a common timing factor from arbitrary simultaneous reparameterization of $\tau$ and $h_j$.
```

**Direct edits:** 3. **Fresh external checks:** SC08