My current understanding is that it's generally expected (and has been predicted) that antimatter will fall down and not up in earth's gravity. But I haven't been able to locate any definitive experimental results, much less independent verification.
What is the current status of reported experimental results, and of ongoing experiments? Is there currently one particular aspect of the measurement that is currently the limiting factor? Also, which is the most likely to give unambiguous results - antiprotons, atomic anti-hydrogen, or molecular anti-hydrogen?
edit: Based on the comment, I've looked at these questions:
Has the gravitational interaction of antimatter ever been examined experimentally?,
Do particles and anti-particles attract each other?, and
Why would Antimatter behave differently via Gravity?,
saw this
The GBAR antimatter gravity experiment paper,
and in this table found websites for the AEGIS experiment and the GBAR experiment as well as this post and video about ALPHA-2.
But I'm a bit overwhelmed by all of this. I get the feeling that there is great interest, but no conclusive measurement of even the sign of the gravitational mass of (atomic?) antihydrogen, much less any independent verification, but I am not sure I'm interpreting this correctly.
The Nature paper is dated January 2013 and includes this figure - the red circles are data - measured decays, while the green dots and both black line are simulations. Thus my question in March, 2016: "What is the Current Status of Measurement of the Gravitational Mass of Antimatter?"
Figure 2 from: "Description and first application of a new technique to measure the gravitational mass of antihydrogen" The ALPHA Collaboration & A. E. Charman, Nature Communications 4, Article number: 1785 doi:10.1038/ncomms2787