Add regime gate walk-forward test (EVIDENCE#050)

- 3 detector types (dispersion/vol/HMM) × 14 configs across 5 years
- Dispersion gates: 0% trip rate everywhere (dead)
- Vol gates: trip differential +32-47pp but destroy returns in good years
- HMM gates: +6pp differential, hmm_0.7 improves 2023/2025 but kills 2026
- Guard candidate regime gate REFUTED (ch 11)
- Script: book/scripts/regime_gate_bt.py
- Results: book/data/regime_gate/regime_gate_trip_rates.csv

book/CLAIMS.md

@@ -70,6 +70,7 @@ The running scoreboard of every quantitative claim in the book. Updated per chap
 | Shorter training windows (1y/2y) recover the edge | REFUTED (every test year negative; only the growing window ever goes positive; mean annual excess ≈ −13% for every window length) | EVIDENCE#046 → exp 55 |
 | The edge concentrates in fresh (low-staleness) predictions | REFUTED (every 90-day staleness bucket negative; freshest bucket most negative; 2025 gains are late-year at 336–397d staleness) | EVIDENCE#047 → exp 56 |
 | The 2026 edge is a 2025–2026 regime artifact; no guard candidate recovers it out-of-sample | PROVEN | EVIDENCE#043–048 → exp 52–56 |
+| A regime gate (dispersion/vol/HMM detector) selectively trades in profitable years | REFUTED (dispersion 0% trip everywhere; vol gates close on profitable days; HMM 37% trip in 2026 vs 31% in bad years — too weak to protect) | EVIDENCE#050 → ad-hoc simulation `book/scripts/regime_gate_bt.py` |
 | Live capital should be sized for the mean (≈ −13% annual excess), not the 2026 tail | PROVEN (walk-forward) + HYPOTHESIS (forward-looking) | EVIDENCE#043–047 → exp 52–56 |
 
 ## Data & reproducibility