Population is based on the time factor, and 60K years would give a population greater than the world by a ratio of ten with compounding increments. The claim is bogus.
The rate of change in population over time is the result of the ratio of how many people are being born and how many people are dying. If more people are being born than are dying, then the population will increase. If more people are dying than are being born, then the population will decrease. You seem to believe this ratio must be fixed, since you claim a population must increase by a particular set amount over a set time period. A little bit of thought will see that this can't be the case.
Imagine we have a population with a particular birth/death ratio. Suddenly, a new disease appears, which causes approximately 1,000 extra deaths a year. The ratio between births and deaths is thus changed, and the rate of change in population size will also change. Conversely, if somebody invented a cure for a disease that was a common cause of death, the death rate would decrease and the ratio would again change, once more changing the rate of population change.
Given that death rates and birth rates can be contingent on all sorts of different factors, there cannot be one set rate of increase which will apply to all times and all situations.
If the argument doesn't convince you, just look at the actual world around you. According to the estimates used by the CIA World Factbook, the rate of population change (including migration) ranges from an increase of 3.69% per year in Burundi and the UAE, to a decrease of 7.08% per year in the Northern Mariana Islands.
There is clearly no standard rate of change - we can only look at the specifics of a situation to figure out how quickly (and in what direction), we'd expect population to be changing. Australia, without the benefit of modern agriculture and imports from abroad, lacked the resources in food and water to support more than a couple of million people. It doesn't matter how quickly people were born, since they'd just starve to death.
Even if one gives your own figures benefit of the doubt, we have a vacuum for some 30 to 50K years.
The specific figures don't matter. All you need to do is accept the point that birth/death ratios can change, and thus there is no steady rate of growth which we should always expect to apply.
The fact that Australia, before the coming of agriculture, couldn't supply enough food or water to support 5 trillion people is surely obvious. It couldn't do so now. It doesn't matter how high a population's birth rate is; it doesn't matter if every fertile woman spends all her time pumping out babies as fast as she can manage; if there's not enough food or water for all these extra people, they will just die or starvation and thirst. The population will not increase.
What do you mean by 'a vacuum of some 30 to 50k years'?
Nor do you any proof whatsoever the world's population today is not represented by 'historical research and recorded evidence'.
No idea what to make of that sentence. Where are you quoting 'historical research and recorded evidence' from? I didn't write that, nor did anybody else so far in this thread.