Given that Smith, bassist John Lindberg and drummer Pheeroan akLaff all are long-established, well-respected performers in the field of creative improvised music, and pianist Vijay Iyer is one of the most talked-about jazz musicians of recent years, it's tempting, though perhaps a bit glib, to call the Golden Quartet an "avant-jazz supergroup." But don't call their music "free jazz."
Smith makes that clear in a short quote seen at the beginning of the first clip up above, part of a film called Eclipse recorded in 2004 at Festival Banlieues Bleues in Paris. Though this version of the group included Ronald Shannon Jackson on drums instead of akLaff, what the trumpeter says in the introduction about their modus operandi - that the music is based on systems, and therefore cannot been considered free - presumably still applies.
Indeed, if you look closely, you'll see that all the musicians have music stands in front of them, and there are even a couple of quick glimpses of the score they're working from, which appears to contain a mix of standard notated passages, graphic scoring, and written instructions. You can also see Smith giving cues in a couple of these clips, another signpost of a structured improvisation in which the musicians have a great deal of freedom to improvise and invent, but do their improvising within a predetermined form or sequence of events.
Down below, the second clip, which features the current lineup of the Golden Quartet including akLaff, was recorded in 2009 at a Festival in Sardinia, Italy. Below that, there's an excerpt from the band's performance this past July in San Sebastián, Spain. (The music kicks in after a short introduction from an on-camera presenter.)
Batting cleanup is a video recorded in 2008 at the Vision Festival in NYC, in which the Golden Quartet is expanded to a quintet with the addition of drummer Famoudou Don Moye of the Art Ensemble of Chicago. They're performing an excerpt of "Al-Shadhili's Litany of the Sea: Sunrise," from the 2009 CD Spiritual Dimensions.