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Given that they were hunter/gatherers i find it unlikely they should have crossed on ice where they knew they couldn't gather or Hunt anything enough to be sure to feed them across. They did not even know it was something worth coming to on the other side. Or if it was anything but ice. We do know the Bringing landbridge existed and that people could have walked into America that way and would have had animals to Hunt during their crossing. For all we know the spearhead could be a result of barter, trade between people. The tradition on spearhead was probably rather wide spread. The culture (Soon after the Cromagnon i suppose) was rather common over large areas and to trade eastwards nothing strange about that. Just an alternative idea.You're right, it's just what I call the frozen ice areas that could have been crossed between Asia/Europe and America.