# E3 — Grounding must overlap the content it protects

**Claim tested:** if your budget of real data is fixed, does it matter *where* you spend it? Is it
enough to sprinkle real data uniformly, or must it target the knowledge you care about?

**Setup (Layer 1, pure math).** `K = 1000` items divided into `R = 10` disjoint **regions** (think
subject areas). `n = 200`, 400 generations, 100 repeats. The **same total** real-data budget is
spent two ways: **uniform** (spread evenly over all 10 regions) vs **matched** (concentrated on the
"exercised" region we want to protect). One region is designated exercised (region 0 here) and has a
rare tail we track.

### Symbols
- **region** — a block of related items; a stand-in for a task family / subject area.
- **matched vs uniform** — real data aimed at the exercised region vs spread evenly, at equal total budget.
- **tail items alive** — how many rare items in a region still have any probability.

### The two panels
1. **Target region over time.** Rare-item survival in the exercised region, generation by generation:
   blue = matched, red = uniform (bands = 95% CI). Matched **holds** the region's tail alive; uniform
   spreads too thin and lets it **collapse**.
2. **Every region at steady state.** Bar chart of stationary tail survival per region, matched (blue)
   vs uniform (red); the dotted line marks the exercised region. Matched wins big *there* — at the
   cost of the regions it deliberately ignores. Uniform is mediocre everywhere.

*(Note: per-region diversity `H` is confounded by how much probability mass sits in a region, so this
figure uses the honest, mass-independent metric — tail-item survival.)*

### Takeaway
Reality checks only protect what they actually cover. To keep a capability alive you must ground
**on that capability**, not on data in general — grounding is local, not a global tonic. Key numbers:
exercised-region tail survival ≈ **0.49 (matched)** vs **0.07 (uniform)** at equal budget.
**Falsifier (not triggered):** if uniform had protected the region as well as matched, the
targeting claim would die.