ZDV ARTCC RADAR CTLR MISSPOKE AND ISSUED FL310 VICE FL410 TO A GLF2 CREW RESULTING IN A LOSS OF SEPARATION WITH TFC AT FL390.

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A PRETTY CUT AND DRIED CASE. THE 2 ACFT INVOLVED WERE LAS VEGAS ARRS; WHICH ARE REQUIRED TO BE AT FL310 GOING INTO ZLA'S AIRSPACE. THE GLF2 WAS AT FL430 SLIGHTLY AHEAD AND FASTER THAN THE LR60 AT FL390. THE LR60 HAD POSSIBLE TFC AT FL370 SO HE WAS NOT DSNDED RIGHT AWAY. I TOLD THE GLF2 TO DSND AND MAINTAIN FL410 JUST TO GET HIM STARTED DOWN. I HEARD HIM READ BACK 'OUT OF FL430 FOR FL410.' A COUPLE MINS LATER; I SAW HIS MODEL AT FL408 AND I ASKED HIM TO VERIFY AT FL410. HE REPLIED 'AFFIRMATIVE; OUT OF FL410 FOR FL310.' I TOLD HIM TO MAINTAIN FL410. A MIN LATER; HE ASKED IF HE HAD BEEN CLRED TO FL410 OR FL310. I TOLD HIM FL410; AND HE SAID THEY HEARD FL310; READ BACK FL310; AND WROTE DOWN FL310. HE CONFLICTED WITH THE LR60 AT FL390 BEHIND HIM. AFTER LISTENING TO THE PLAYBACK OF THE TAPE; I VERY CLRLY SAID 'DSND AND MAINTAIN FL310.' I ONLY HAD 5 ACFT IN THE SECTOR; AND WAS NOT BUSY AT ALL. I WAS 'SURE' I HAD SAID FL410. I DON'T KNOW HOW YOU CAN CORRECT WHAT WOULD BE CLASSIFIED AS A 'BRAIN FART.' WE'VE ALL DONE IT; WE'RE HUMAN; AND USUALLY IT'S A NON FACTOR; OR YOU CATCH IT. THIS TIME IT WAS AN ERROR. SUPPLEMENTAL INFO FROM ACN 548660: THE PNF READ BACK THE ALT LEAVING. THIS IS A CONFIRMATION BOTH PLTS UNDERSTAND THE NEWLY ASSIGNED ALT. UPON REACHING FL405; THE CTLR STATES 'MAINTAIN FL410.' WE CLBED BACK TO FL410 AND ASKED THE CTLR WHAT ALT WE WERE ORIGINALLY ASSIGNED. THE CTLR SAID FL410. WE DO NOT BELIEVE THIS TO BE TRUE. BOTH PLTS UNDERSTOOD FL310 WAS THE ALT.