BTC_POWER_LA

Who wears it better?
1) Quantile regression that uses linear price and linear time.
2) Quantile regression that uses log price and linear time
3) Quantile regression that uses log price and log time.

This hysteria about the Gold power law being “broken” actually helps clarify things even further about what the power law is really about.
Do you realize what it really implies? Bitcoin is essentially laughing at gold’s attempt to catch up. A 3× move may look impressive in isolation, but it is trivial compared to a system that has grown by a factor of 100,000,000 over 17 years.
That contrast is the whole point—it highlights what a truly scale-invariant system looks like.
Now think in log scale. The apparent “deviation” becomes almost negligible. It’s well within statistical error.
Focus on the

The Gold power law is perfectly fine. What we never claimed is that there exists a fixed floor at 50% of the reference price—that feature is specific to BTC/USD, not to gold.
This distinction is essential, and it’s unclear why it keeps being misunderstood. Gold behaves differently because it moves relative to fiat, not within a self-referential, scale-invariant monetary system like Bitcoin.
What’s actually remarkable is that even after gold’s recent ~3× increase—following decades of stagnation—it still remains within roughly 2σ of its power law trend.
That fluctuation is just noise. The real t

Why the power law is a big deal.

This affine reduction idea is genuinely exciting, it offers yet another lens through which to understand why the power law is so powerful.
It’s one of those insights that, once seen, cannot be unseen, as they once said on What Bitcoin Did.
But what makes it truly compelling is that it’s not just a visual or empirical curiosity. There is deep physics behind it, the same intellectual framework that led to the heliocentric model and, centuries later, to general relativity.

What are affine spaces in physics?
An affine space is where relationships become linear - straight lines instead of curves. In physics, finding the right affine space means discovering the coordinate system where complex, nonlinear behavior simplifies into something you can write as y = a + bx.|
Think of it as finding the "natural viewpoint" for a phenomenon. Earth's orbit looks like a complex curve from one angle, but from the right perspective it's a simple ellipse. Finding the affine space is finding that right perspective where the math becomes clean.
Why log-log is THE affine space for po

People try and try again, but the power law always win, because mathematical truth always wins.
Novozhilov proposes this elegant method (this is where his physics background shows) called affine reduction. I didn't think to use this one. It is a good contribution. But he applies it to only 4 points and he gets a power law of 4.
Well what happens if you apply it to all the data points?
A power law close to 6 is the best result.
Thank you Novozhilov for showing the power law is real using method 2312.

The power law is found by regression but regression is not the end of the story at all. We have said this many times.
Regression Says:
"I assumed a power law, fit the parameters, and got R² = 0.951"
Criticism: "Of course you got a good fit - you can fit almost anything to a power law over a limited range. It's just curve-fitting."
SSA Says:
"I made NO assumptions about functional form. I decomposed the data into its natural modes. ONE mode dominates (99.26%), and that mode IS a power law."
This is fundamentally different.
Key Advantages of SSA Over Regression:
1. Model-Free Discovery
Regressi

Bitcoin is a metanetwork.

A single power law for modelling the long term growth and the oscillations around it.
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