I would suggest that, by using proved statistical theory regarding atypical distribution of data it may be possible to determine a rough understanding of the minimum time frame of human occupation of the Americas.
Lithic artifact distribution in the Americas is probably related to population density.
To do this, we must ignore the arbitrary classifications of historic and prehistoric so that we can understand the distribution of population, and therefore artifact, density.
The density of artifact distribution is probably going to be a left skewed distribution where the distribution falls off suddenly when lithic technology is replaced with newer iron age technologies brought over from Europe, or when population density is decimated by European diseases.
We can assume that the modality of the distribution of lithic artifacts will be around the period of highest population density. When did Native Americans first encounter Europeans and European diseases? Vikings? Columbus? When did the population of the Americas begin to drop?
We can further assume that the farther left of the modality the less probable the discovery of artifacts is.
The farther we move from the mean, or the modality, the less probable it will be that we will find an artifact.
This implies that, if we find an artifact, the artifact is within the higher probabilities of the distribution of artifacts. In the case of a skewed distribution a discovered prehistoric artifact is probably between the mean, which will be on the left of the data point which the artifact represents, and the modality, which will be to the right of the data point the artifact represents.
This has some interesting implications. Some data points have been discovered as far back as 30-35 thousand years before present. Do we assume that these data points are to the right or the left of the mean? Chebychev’s Theorum describes the minimum probabilities of finding a data point in non-Gaussian distributions, however, it is not as easy to determine the probability of discovering a specific data point within the distribution without understanding the shape of the distribution.
Chebychev’s Theorum allows us to say, for example, that the highest possible probability of finding a data point between 2 and 3 standard deviations on either side of the mean is about 14%. However, with a left skewed distribution the probability of finding a data point to the right of the mean is higher than the probability of finding an artifact to the left of the mean.