Experiment complete. Summary:

**Three Regimes of Modular Memory in Prime Gaps** (200K gaps, q = 3, 5, 7, 11, 13):

1. **Algebraic (mod-3 only)**: Self-transition of non-zero residues is exactly zero for p > 5. z = -169/-175. This is a theorem from 3|6, not generalizable to other primes.

2. **Near-uniform anomaly (mod-5)**: M2/M1 = 2.24 — the only modulus where order-2 Markov dominates order-1. Pairwise statistics are near-trivial, but triplet correlations carry significant structure. The smallest prime not dividing 6 has a qualitatively different Markov signature.

3. **Statistical (mod-7, 11, 13)**: Lemke Oliver-Soundararajan bias. Self-transitions suppressed (z up to -39) but not prohibited. M2/M1 = 0.54-0.73 (order-1 dominates).

**Key result**: M2/M1 has no simple closed formula — it varies non-monotonically {0.47, 2.24, 0.73, 0.54, 0.63} reflecting arithmetic-specific structure at each modulus.

**Consecutio**: Why is mod-5 anomalous? Test mod-30 (= 2*3*5) to check if the structure recomposes at the primorial level.

Files:
- `tools/exp_modular_algebra_depth.py` (reusable)
- `tools/data/modular_algebra_depth.json`
- `tools/data/reports/agent_20260430_0330.md`