Window balancer parts id

A home owner from New York says:
Please advise the correct balancer for my application.
The shoe is 2"h x 1.25w x .5d.
The metal channel is 32" long, .5" square and not ribbed. It is stamped with 31HD, BS1, and what looks like LG.
I believe the shoe to be a 15-046, but I wasn't able to id the balancer.

User submitted photos of a window balance.
Profile picture of Paul
Paul from SWISCO responded:
Hey, Kevin. As long as the dimensions match, our 15-046 sounds like a great match. As for the balance, see our S770-31.
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