This summary is a great way to think about the Power Law. Credit to Noah Frank: A very high Bitcoin (R^2), like 0.96, simply means that the power-law curve has matched Bitcoin’s historical price extremely well, but it does not automatically mean that Bitcoin is literally controlled by a fundamental power law. A good way to think about it is this: imagine you look at a section of road that appears perfectly straight from where you are standing; that does not prove the road stays straight forever, because it might actually be part of a very large curve that only looks straight over the distance you can see. Bitcoin may be similar. When you plot its price against its age on a log-log chart, the data form an impressively straight line, which is why the power-law model looks so convincing, but other types of growth can also produce something that looks almost straight over a limited period. One warning sign is that the estimated power-law exponent, usually around 5.6 or 5.7, depends heavily on where you decide that “time begins.” Bitcoin researchers normally count time from the genesis block in January 2009, which makes sense because that is when Bitcoin actually came into existence, but if you mathematically shift that starting point, you can get a very different exponent while still keeping a surprisingly good fit. That means the high (R^2) alone cannot prove that 5.7 is some deep, universal Bitcoin constant; to make that stronger claim, you would need a convincing economic or network-based explanation for why Bitcoin’s creation date must be the exact starting point and why the exponent should specifically be around 5.7. There is also another possible explanation for Bitcoin’s history: instead of following one smooth power law forever, Bitcoin may have gone through several waves of adoption. Think of the way a new technology spreads: at first hardly anyone uses it, then adoption accelerates rapidly, and eventually that group becomes saturated and growth slows down. That produces an S-shaped, or sigmoid, curve. Bitcoin could have experienced several such waves. Early enthusiasts, then retail investors, then institutional investors, and perhaps future groups after that. If several S-shaped waves overlap, the combined result can look remarkably similar to a power law for many years. In other words, what looks like one smooth, permanent rule might actually be the combined effect of several separate growth phases. This matters because the two explanations have very different long-term implications: a true power law keeps rising indefinitely according to the same basic mathematical relationship, while an adoption-wave model eventually slows unless another major wave appears. Researchers have found that multi-sigmoid models can sometimes fit Bitcoin’s past history better than the simple power law, which suggests that Bitcoin’s cycles may contain meaningful structure that the power-law line smooths over. But fitting the past better does NOT necessarily mean predicting the future better. The safest conclusion is that Bitcoin HAS behaved in a very power-law-like way over its historical lifetime, but we still cannot be sure whether that pattern is a deep law of the system or simply the result of several growth and adoption waves that happen to create a very similar looking curve.