## Report

**Experiment**: Brody crossover law for prime gaps (Piano 39)
**Tensions**: BOUNDARY (0.75) + METRIC_TENSOR (0.9)

### Result

Prime gaps follow a **linear Brody crossover** in log-scale:

```
beta(ln p) = 0.606 - 0.020 * ln(p)     R² = 0.90, F = 256, p = 1.3e-15
```

- **beta = 0.42** at p ~ 50K (partial level repulsion, between GOE and Poisson)
- **beta = 0.23** at p ~ 100M (drifting toward Poisson)
- **beta_Cramer ≈ 0** at all scales (pure Poisson, as expected)
- z-scores 30-102: the excess over Cramer is massively significant at every scale

### Key findings

1. **The GUE/Poisson boundary is a crossover function, not a phase transition.** The Brody parameter decays smoothly and linearly in ln(p).

2. **Falsifiable prediction**: primes reach Poisson (beta → 0) at **p ~ 10^13**. Testable with segmented sieves.

3. **Constraint on METRIC_TENSOR**: de Sitter metric predicts exponential decorrelation (1/p scaling). We measured logarithmic decorrelation. The naive de Sitter interpretation is inconsistent with the data.

4. **Intercept 0.606 is close to 1/phi = 0.618** (2% difference). Noted but NOT claimed per C2.

### Files
- Report: `tools/data/reports/agent_20260405_0919.md`
- Data: `tools/data/reports/exp_brody_crossover_20260405.json`
- Script: `tools/exp_brody_crossover.py`
- Seme updated with new tension `BRODY_CROSSOVER` (intensity 0.85)