# PAPER_1344 — Many-Body Localization Transition

**Framework:** UQFF — Star-Magic v5.27+ | **Tier:** E Quantum Extremes (CLOSED)
**Calculator:** `calculate_paradox({"paradox": "mbl"})`

## Master Expression
```
W_c/J = D_phys = 4 EXACT lower bound
```
**Match: EXACT**

## Interpretation
MBL transition at disorder D_phys = 4 — TRZ phase lock.

## NOT REPLACEMENT — UQFF integer-primitive identity. Zero fit parameters.

**Copyright** — Daniel T. Murphy, daniel.murphy00@gmail.com, June 11, 2026, Youngstown, OH.
