The US needs to provide assurances to the UK court on the following grounds:
1. The extradition is incompatible with Article 10 of the European convention on Human rights which provides the right to freedom of expression and information.
2. Assange might be prejudged because of his nationality
3. Assange might be subject to death penalty
The US has until April 16 (3 weeks) to provide such assurances. If not provided, I belive there will be new court hearings where Assange can appeal the extradition once more.