Part number for coolant hose ('11 X5 35d)?

[Homegrown]

Hi all:
My wife complained that her '11 35d X5 had coolant underneath in the morning. There was a lot under the driver side. I read a bunch of articles and assumed it was the expansion tank. Nope; after pulling it, there were no cracks to be found.
I reinstalled, filled up with Pentosin 50:50, and took the car out. When I got home, there was steam/smoke coming from the engine bay around the alternator. From what I can tell, the alternator pulley rubbed a hose (marked 'H1032') and made a 1" cut. Apparently, under pressure from driving the coolant sprays thus dousing the engine.

I've searched every picture online using our VIN in the catalogues, but nothing matches what I see. One end of the hose tucks underneath the power steering reservoir and plugs into a small pump (?) and then runs along the alternator to the back of the engine. I assume this is a coolant hose to the head, but cannot find a match online.

Can anyone help me identify the hose? It appears to have the quick release fittings on each end and runs the length of the engine along the driver side underneath the upper radiator hose.

Thanks to all for this great resource and repository of wisdom!
Kev (Mpls MN)