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I see that you are consulting sources, which is a great way to get information. It is important to consult as many sources as possible, and to consider how they get their information, so that one can reasonably assess the reliability of that information.

"There seems to be no way out but to cut down the age of Neanderthal man at Combe Grenal from some 60,000 to some 60 years. "

I have been unable to find other sources that have pulled this particular number out of their posterior orifice, and suggest you replace it from whence it came.

I, in short, do not find the evidence presented in the link you provided compelling, and the technique he used to arrive at his conclusion is best described as 'completely making it up'.

Rather than ignoring all other sources of information and settling for the one that is least convincing, I do suggest you seek out more sources, at least if you want to be able to make arguments that have the potential to convince me of anything other than your ignorance.