Tests
1) We should test the DNA of the creature before the split of human and chimp. From the chart that you provided below it would be where it points to the common ancestor of human and chimp. That will give us a common DNA map of where we both came from.
2) We should test the DNA of each creature just after separation into different directions to compare to the common ancestor. Your chart shows the human lineage separating from the common ancestor at a point, we should test the DNA of that creature and the DNA of the creature of the chimp just after separation.
3) We should test the DNA of the creature that does not split off from the common ancestor. On your chart there is an arrow moving up between the chimp and human so we should test that creature.
4) We should test the DNA of the creatures along the line of evolution and before the creatures become chimp and human. As they continue to evolve and before they get the chimp and human we should be able to get some valuable DNA maps.
5) We should test the DNA of the creatures that were just before they became human and chimps.
What would falsify our hypothesis:
1) If we fail to find fossil evidence of the creatures that evolved into human and chimps.
2) If we failed to find a mechanism that would cause the behavior differences between chimps and humans. For example, wearing clothes, living in houses, driving cars, burying the dead, praying, using currency, talking, having a self consious, etc.
3) If we fail to observe the human and chimp evolution. If it takes millions of years to produce a human, then millions of years ago when this started we should be seeing it now with some percent of the population.
4) If we fail to find out why humans and chimps don't marry. In some instances there are stories of humans marrying their cousins.
5) If chimps and humans can't reproduce. There should be a great plasticity in the lab between chimps and human reproduction if we are cousins.
What would prove our hypothesis true:
1) If we find concrete proof in the fossil record. We have the common ancestor and we have fossils of every creature along the way of the evolution chain.
2) If we find the mechanism that changes the shapes and usage of bones in hands and feet that are required for this evolution. For example, how could random mutation account for the necessary bone structure for chimps to climb or humans to walk upright.
3) If we observe the common ancestor of chimps and humans producing this split of creatures as they are birthed.
4) Seeing a human and chimp on their honeymoon.
5) Being able to produce offspring between human and chimps.