Experiment complete. Summary:

**Question**: Does the prime dipolar angle (-111 deg, dL1/dSR = 2.48) follow from pair statistics alone?

**Answer**: Mostly yes, but not entirely.

- **Markov-1** (same gap-pair transition matrix, no higher-order memory) produces theta = -114.6 +/- 0.6 deg — close but distinguishable (z = 4.1)
- **Markov-0** (iid from marginal) produces no direction at all (|d| = 0.003, theta undefined)
- The pair transition matrix is dominated by **8 hard zeros from F2 mod 6 constraints** plus softer Lemke Oliver biases
- **~80% of the 14-deg separation from GUE is pair statistics** (Lemke Oliver territory)
- The remaining **~3 deg residual is GUE-ward**, stable across 3 decades of scale, and requires Markov-2+ memory

**Consecutio**: The 3-deg residual points to the Markov-3 signal (z=6203 from earlier findings). Next question: does the Markov-3 component have a preferred direction in the (SR, L1) plane?

Files:
- Script: `tools/exp_markov_dipolar_decomposition.py`
- Data: `tools/data/markov_dipolar_decomposition.json`
- Report: `tools/data/reports/agent_20260501_0330.md`