BTC_POWER_LA

Stability of the power law exponent over time using several methods, regression and scale invariance.

I emphasized so much that the power law is not a curve fitting exercise as some pseudo-analysts claim. It is about scaling laws and consistency of behavior of Bitcoin.
What scaling means?
In physics, scaling means that a system looks the same — statistically or structurally — when you zoom in or out by any factor. More precisely, a relationship is scale-invariant if multiplying the independent variable by any constant λ changes the dependent variable by a predictable power of λ, with no preferred scale breaking the symmetry.
Formally: a function f(x) obeys scaling if
f(λx) = λ^β · f(x) for al

Fantastic commentary by Italian comedian asking what is the real difference between the Iranian theocracy and the American one (to us this is a super weird scene). "The world is in a competition about how has the longest god". Use your imagination what the innuendo is here.

Warning: the graph below looks like a pyramid but we just made a post explaining Bitcoin is not a pyramid scheme. It simply shows how the network grows, that is similar to a curbed exponential.
Power-law adoption is more sustainable than exponential (S-curve) adoption.
What is the difference?
Exponential growth works like this. Imagine a bacterium that doubles every five minutes. You start with one bacterium. After five minutes there are two. After ten minutes there are four, then eight, sixteen, and so on. The key feature of exponential growth is that the growth rate stays constant in time.

This version of the power law is free online. Link in the comments.

You can build a Hidden Markov Model (HMM) using the slopes of Bitcoin’s growth to identify and predict three regimes: bullish, transition, and bearish. In preliminary tests, this approach can classify the regime with around 90% accuracy.
Below is a link to a Veritasium video that explains how Hidden Markov Models work and why they are powerful tools for prediction problems.
HMMs are widely used in quantitative finance; notably, variations of this technique were reportedly among the methods employed by Jim Simons’ Medallion Fund, one of the most successful trading strategies in history.

Come and visit us at the Physics of Bitcoin show.
Starts in 5 minutes on X, YouTube and Twitch.
Many things to cover tonight including 3D power law and scaling test.