## Problem 115 — rank:28

**Title:** Fundamental function of sleep

**Added binding assumptions (LaTeX):**

```latex
Specify feasible sleep-state transitions and whether schedules are predetermined or feedback policies. Loss components and their weights must be fixed independently of observed sleep preferences. The strict benefit margin excludes the trivial weak inequality when the sleep-policy class includes wakefulness. Intervention effects on stress, circadian phase and energy expenditure require explicit causal treatment rather than statistical adjustment for post-treatment mediators.
```

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