Liquidambar acalycina, which iNaturalist calls Chang’s Sweetgum. These are the Burgundy Flush variety, but this has been such a rotten year for foliage. Compared to American Sweetgum, Liquidambar styraciflua, the leaves here are different, but the smaller, longer-horned seedpod is the quickest way to tell them apart.
Backyard and Beyond 
Thank you for the excellent detailed photos. They are very helpful in identifying the tree.
the difference in horn length gives rise to the function of the horns. I can’t imagine their purpose, but would like to know.