Minimum System Science
Minimum System Science is the approximate amount of science that a system needs to break even with its tech penalty.
Notes
Minimum System Science assumes that the system has an equivalent amount of each type of science. i.e. 1/3 is physics, 1/3 society and 1/3 engineering.
The minimum is chosen based on the combined research rate. You can use "Add a System" to get an idea of the minimum science necessary for each category.
Science Rates
This number is the actual value of your science weighted against your empire's tech penalties.
Notes
The number next to Research Rate is the combined research rate for all technologies as a sort of average. An increase in this number means that the average rate is improved (even if some specific rates might decrease).
This number could be used as a comparative tool. For instance, if your empire's research rate is twice that of another empire's research rate, it means that you will, on average, research technologies exactly twice as quickly as they do.
Tier 5 Research Times
How long it would take to research the tier 5 technologies at the current research rate. Tier 5 technologies are mostly repeatables and a few rare techs like Gateway Construction and Mega-Engineering.
Notes
Increases and decreases in direct proportion to Research Rate.
I added this because I thought a clearer visualization/obviously applicable example of the Research Rate values might be helpful to players but really they might as well be the same number.