The "core conclusion" means the main or most important idea or decision that is reached after considering all the information or evidence. Full definition
The second core conclusion is that the main cause of these unusual changes in climate is human activity, above all the combustion of fossil fuels and secondarily tropical deforestation and other land use change. (climatesciencewatch.org)
Corrections to errors that do not affect the core conclusions of a paper are posted online and linked to the published paper. (sciencemag.org)
And yet, their core conclusion was that equities might struggle for price gains, but that owners would still see positive returns due to corporate buyback programs and dividends. (etfexpert.com)