The 4100-series index files are generated from and follow the license of the Tycho-2 catalogue. 

The license information for the Tycho-2 catalogue: 
Copyright 2000 Hog E., Fabricius C., Makarov V.V., Urban S., Corbin T., Wycoff G., Bastian U., Schwekendiek P., Wicenec A. 

The Astrometry.net team claims copyright on the script to generate 4100-series index files (but not on the resulting index files):
Copyright 2006-2015 Michael Blanton, David W. Hogg, Dustin Lang, Keir Mierle and Sam Roweis