Citation? I don’t know of evidence that the small sword actually out-competed the broadsword on the field of battle. I don’t think dueling-type swords were ever actually used on the battlefield. They were worn by nobility to show class, but not actually to fight against armored opponents.
A heavy cut-through-armor sword was much more effective in a cavalry charge than a light poke-at-the-seams sword. You could argue that a light sword would be helpful once people were on the ground, but I just haven’t seen evidence that they were actually used that way.
