Thanks for reaching out and welcome to the Bose Community Forums.
It is great to hear that you are now the proud owner of a pair of SoundSport Pulse headphones. For guaranteed authenticity, we always recommend purchasing from an authorized Bose reseller or from our main website.
The fact that the headphones connect to the Bose Connect app is a good indication that they are original Bose headphones. However, there are a few other things that we can try to determine the authenticity of the headphones:
Go to btu.bose.com on a computer and follow the onscreen instructions to try and update your headphones.
Check the box for a serial number and register the headphones online.
Run the DOM code in our product registration form and check the details of your headphones. This can be found underneath the ear tips on the end of the tube and looks like this, for example, 4JAD.