Consider the research work for five in series breakthroughs: 1, 2, 16, 8, 128 each breakthrough doubles your research power.

If you start at 1 research, you get the first breakthrough after 1/1=1 year. Then you get the second breakthrough after 2/2=1 year. Then you get the third breakthrough after 16/4 = 4 years. The fourth breakthrough after 8/8= year. The fifth breakthrough after 128/16 = 8 years.

If it only takes one year for a competitor to learn your breakthrough, they can catch up despite the fact that your research rate is doubling after every breakthrough.