For the fourth time, the burden of proof rests on you to prove material change. You cannot prove lack of material change in a stochastic environment because you need infinite data. That is not the case with proving change.

Of course the probabilities are not 0.5. But they also don't matter much. Since both my semantic simile and your argument assume independence, order does not matter. Thus all permutations are in the same class of rarety.

Furthermore, if only counts of "short" vs "long" gaps matter, then instead of x seconds times 8 + y seconds times 4 you also need to include small deviations. Such as, for example, x-1, x+1, x times 6 + y times 4, and all the permutations of each of these. So you are integrating over all partitions on 12 elements, which is a gigantic set when you generalize enough to learn the blockchain in any meaningful way. The blockchain has too little data to believe your statement with even 60% confidencence. We're talking 0.1 sigma deviations here and a combinatorially monstrous set, with only a quarter of a million of data points. Not gonna happen.

On the contrary, my position is that given the amount of entropy there is in the blockchain so far, and adding time dependence to the combinatorial mess (because independence is false), we cannot say that there is something wrong with meaningful certainty.

Finally, over all this academic modelling exercise that we went through, the reality is, as I mentioned in my first post and smoothie detailed, that even if you were right on the modelling, what we know about how timestamps work and how they are somewhat adversarially arbitrary for you as the modeller, your conclusion holds no epistemic water.

You are right on the Maths. You are wrong on many levels on your modelling. Even if you were right on the modelling, you are still wrong on what conclusions you can draw from the results.

Your argument is "something could be wrong". My counterargument above is "even if that was the case, you don't have enough entropy to draw that conclusion". Smoothie's corrolary is "even if you are right, it doesn't make much of a difference".

Thank you for responding calmly earlier and compelling me to articulate my position.

Edit: answering your edit