I spent some time today analyzing the Bitcoin Power Law Quantile model by @TheRealPlanC, and I believe I’m successfully reproducing his results. 

However, I have significant reservations about the model's underlying assumptions and its implications when represented in a log-log graph.

Observations and Criticisms

Multiple Power Laws in the Log-Log Graph: 

When plotted on a log-log graph, the model suggests the presence of multiple power laws — one at the bottom quantile and another at the top quantile for example. 

This raises questions about the logical interpretation of these trends.

This idea of a distinct power law for the tops is not new; @hcburger1 proposed something similar years ago when he first popularized the Bitcoin power law. However, his approach didn’t involve quantile regression — he simply drew a power law through the market tops.

Flawed Interpretation of the Top Power Law: 

The concept of a power law that tracks the market tops is problematic. Unlike the power law at the bottom (which provides a clear support trend for Bitcoin’s long-term growth), the "top power law" is neither consistent nor meaningful. 

For example:
As it stands, the quantile regression model implies that the top quantile (e.g., the 99% quantile) will eventually intersect with the bottom power law. What could this possibly mean in practical or theoretical terms? There’s no logical interpretation for such an event as far as I can see.

A Better Perspective: 
It’s more coherent to treat Bitcoin’s price movements as two separate signals:

A general power law that defines the long-term trend and is best represented by the bottom quantile or support levels.

Exponential deviations from this trend that occur during market bubbles and corrections. 

These deviations reflect the cyclical nature of Bitcoin’s price behavior and are better explained by exponential growth and decay processes, rather than an arbitrary "top power law."

Conclusion:
The Quantile model, while visually appealing, seems to overcomplicate Bitcoin’s behavior by introducing a second, unjustified power law for the tops. A simpler and more robust approach is to focus on the primary power law trend and analyze the deviations around it as distinct exponential phenomena. 

This not only aligns better with Bitcoin's observed market cycles but also avoids the interpretative issues associated with intersecting power laws.