NSS has now provisionally qualified to compete in the Games
Summarizing Space Elevator Feasibility Articles
For a Carbon Nanotube tether that is 30 MYuri [A MYuri is the name we gave the SI equivalent of N/Tex, or GPa-cc/g] strong, and a characteristic time constant (CTC) of 1 year the Feasibility Condition requires that the climbers will have a power density of at least 1.0 kiloWatt/kg.
So where do the competition requirements stand in respect to this?
It is easy to show that when moving straight up, the power density of the climber is directly proportional to its speed (mgv/m), and so a 5 m/s speed in 1 g gravity corresponds to 50 Watt/kg, or about 5% of a real Space Elevator climber.
Today's materials perform at 2.5 – 3 MYuri (GPa-cc/g) at best when built as tethers suitable for the tests.
The Space Elevator will function a lot better with a ~35 MYuri material, but this is the bare minimum that we need. Keep in mind that successive 50% improvements in material strength are very large steps, but that we already know that CNT molecules are measured at ~50 MYuri, and fabricated CNT micro-bundles have been produced by several labs at 10 MYuri, so this challenge is not impossible.
Achieving higher speeds and power density for the climber seems more likely than achieving stronger tethers.