As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
DURING TOP OF DESCENT FL410, THE NR 4 ENGINE EXPERIENCED A SURGE AND FLAMED-OUT. A RESTART AT FL340 WAS SUCCESSFUL AND OPERATION WAS NORMAL THE REMAINDER OF THE FLIGHT. THE ENGINE WAS INSPECTED, FUEL PRESSURES WERE CHECKED, AND A BORESCOPE WAS ACCOMPLISHED. THE EVBC WAS REPLACED, AND A PRECISION TRIM WAS ACCOMPLISHED. PROPER ENGINE OPERATION WAS CONFIRMED.