You haven't gotten credit for doing all 6 ascendant challenges though. The triumph tracker on Bnet is giving you credit for duplicates.
https://bray.tech/3/4611686018467393947/2305843009309045706/triumphs/node/3483405511/1296857362/3424890260
https://imgur.com/a/Vemk8SE
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I tracked it on braytech too. What I'm saying is I've literally done them all, including the Keep of Honed Edges buggy crap, but getting nada.
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Right, but you're still missing credit for one of them. Bungie tracker is saying 6 yet there are other posts of it counting incorrectly. Braytech is telling you 5 - which explains why you still dont have the emblem. Go and check you actually have the triumph claimed in game, if not then you haven't gotten credit for all 6 and need to redo them.