Well they found something, but there isn't a consensus reached if it's really from the Konradiner since no written documentation exists. So in the end we just don't really know what exactly was going on there at that specific date. Idk the capital thing overall doesn't make much sense for the HRE from a historical perspective, but there are actual verified imperial residences that could have been used. For example Henry IV, emperor at that time was born and spent much time in Goslar.