Wow. You haven't understood a thing I said. Which doesn't surprise me.
Since the Hurst phenomenon drives global temperatures through (amongst other things) a GHG far more powerful than CO2 is, if I falsified the concept of GHGs, then I would be falsifying one of the most important mechanisms through which LTP gets into the global temperature measurement.
If you understood Koutsoyiannis' maximum entropy work, you would understand that global temperature does not meet the constraints he uses to analytically derive LTP behaviour from first principles. I would have expected a scientist to raise this quite early on when understanding Koutsoyiannis' work (it was one of my first questions when I read his analysis). From your answers, it is pretty much self-evident that you are making no effort whatsoever to understand the reasoning. You can call that what you want, but it isn't science.
However, many aspects of the hydrological cycle do meet these constraints, and these in turn affect global temperature through indirect mechanisms such as the greenhouse effect.
The problem is, the magnitude of the effect on temperature from the Hurst phenomenon via these mechanisms is greater than the direct effect of CO2 forcing, especially on longer scales - in fact, as scale increases (decadal, centennial etc.) the Hurst phenomenon increasingly dominates temperature changes. The effect of CO2 is, quite simply, lost in the noise of the 20th century natural variability.
The work also creates huge problems for the idea of feedbacks, although the reasons for these are more subtle.
Oh, and seriously. You should try to learn from Randi's work. He's pretty good at what he does.