Second Account has stuff from first account.
I saw that Seatin started a new account, just to have fun seeing what it was like to start the game over from scratch. I decided to do that, too. So I logged out, signed up again, and started over.
The first time I checked my inventory, I found something odd. I was halfway to a Tier 4 basic catalyst! On a brand new account where I hadn't earned a single T4b shard! So I looked through the inventory, and I only had one T1b and one T2b as complete shards (which I did earn), but I also had shards for every catalyst. I looked at the numbers and realized they were familiar.
I logged out and checked my original account. They were exactly the same. All the catalyst shards I'd earned in the first account were not zeroed out when I started the new account. The number of catalysts was reset to zero, but not the shards.