The quoted CO2 levels from ice core samples remained fairly constant through this period of ten thousand years yet we had two periods of much warmer temps. (illconsidered.blogspot.ru)
By taking core samples and estimating age and growth using tree rings, they came up with a trend of how trees grew, going back about 150 years. (sciencemag.org)
Beyond philosophical debates about proving a negative, contamination in core samples has been a chronic problem. (sciencemag.org)