As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
HAD A DEPRESSURIZATION DURING A DESCENT AND WE HAD TO DECLARE AN EMERGENCY. WE WERE ORIGINALLY GIVEN A DESCENT TO FL 350 FROM FL410. UPON REDUCING POWER WE LOST PRESSURIZATION. WE DECLARED AN EMERGENCY AND WERE GIVEN 11000' AND PRIORITY HANDLING TO KHPN. WHEN PASSING THROUGH 6000' THE CABIN DEPRESSURIZATION LIGHT EXTINGUISHED. WE DID NOT NEED EMERGENCY VEHICLES AND PERFORMED A NORMAL LANDING.