Done. Summary of results:

**Experiment**: Observable hunt for Markov-3 memory visibility in prime gaps.

**Finding**: Prime gap ordering decomposes into **two visible layers**, orthogonal to each other:
- **Layer 1** (pairs, Mk1): lives in (SR, L1) — the dipolar plane. Already known.
- **Layer 2** (triples, Mk2): lives in **SR2** (next-nearest-neighbor spacing ratio), L2, conditional entropy. **SR2 is the sharpest probe**: z = -9.4 under Mk1 (pair model misses it), z = -0.05 under Mk2 (triple model captures it perfectly).

**Surprise**: Markov-3 adds nothing to any of the 10 observables tested. The massive z=6203 from previous entropy measurements is distributional (property of the transition matrix), not projectable onto any single low-dimensional observable. For practical characterization, **Mk2 is sufficient**.

**Consecutio**: Derive SR2 = 0.4785 analytically from Hardy-Littlewood singular series for prime triplets. The 0.008 gap between Mk1 prediction (0.4864) and reality IS the triple correlation content.

Files:
- Script: `tools/exp_markov3_observable_hunt.py`
- Data: `tools/data/markov3_observable_hunt.json`
- Report: `tools/data/reports/agent_20260503_0330.md`