"conclusively confirm" is a correct and usable phrase in written English.
You can use it when you are trying to affirm something definitively or decisively. For example: "The results of the study conclusively confirmed that the new drug is effective in treating this condition."
"Without empirical evidence, we cannot conclusively confirm or deny the effectiveness of the programme.
Facebook could not conclusively confirm that Russia was behind the campaign, but evidence points strongly to the Kremlin.
In order to conclusively confirm that wood does show NPR, we have used a combination of geometric modelling, finite element analysis (FEA) and off-axis compression testing.
But Pew researchers said the increases in the 2012 census data — the latest available — were too small for them to conclusively confirm the recent rise.
The authors acknowledged that their findings do not conclusively confirm that antibiotic use is a cause of asthma, and that further work would be required to sort out the associations between the composition of normal intestinal bacteria, antibiotic use, childhood allergies and the development of the illness.
Optical images of flame particles collected by an independent sampling method conclusively confirm the presence of the micron sized PAH-containing particles in the flame and strongly suggest that mature soot aggregates are formed directly from the micron-sized PAH-containing particles.
But Whewell often used these terms in a way which connotes a conclusion which is simply not conclusively confirmed.
They announced their discovery – which is yet to be conclusively confirmed – on 4 July.
Our article broke this important public interest story, and it has been independently and conclusively confirmed.
Although inflation is not yet conclusively confirmed, it is now in better shape than ever, many astronomers said, and many models can be eliminated.
Two weeks ago the FSA published research by the University of Southampton which for the first time conclusively confirmed a link between specified additives and hyperactive behaviour.
