Deep-Sea Rocks Point To Early Oxygen On Earth is a Science Daily article. Quoting:
Red jasper cored from layers 3.46 billion years old suggests that not only did the oceans contain abundant oxygen then, but that the atmosphere was as oxygen rich as it is today, according to geologists.
The article goes on to explain that the amount of oxygen indicated implies that cyanobacteria, or organisms like it which produce oxygen, must have been found on earth at an earlier point in natural history than previously thought. Theories like the RNA world hold that a series of events involving catalytic RNA led to earth's first cells. Aside from findings like hematite which supply time frame limits, is there anything intrinsic to theorized RNA world processes indicating duration from start to the appearance of cyanobacteria like organisms?