The strongest evidence $BTC 's Power Law is real is not the ~96% R²
It fails where noise should win.
Then wins where structure should matter.
The fit is strong:
R² = 0.961
Exponent ≈ 5.67
But that is not the proof.
Anything can fit the past.
The real test is out-of-sample.
Leak-free walk-forward vs random walk:
At every date, the model only sees data available at that date.
90d: -97.3%
180d: -3.2%
1Y: +49.1%
2Y: +76.5%
Median across the defensible window, 90d–2Y:
+23% OOS R²
At 90 days, it gets destroyed.
At 180 days, it is noise.
At 1 year, it cuts squared error roughly in half.
At 2 years, it cuts squared error by more than three-quarters.
That is not what a fake curve-fit usually looks like.
That is the signature of a long-duration adoption curve.
Short term:
liquidity, leverage, headlines, forced selling.
Long term:
fixed supply, adoption, network effects.
Residuals pass the sanity test too:
ADF p = 0.021
Deviations from trend have historically mean-reverted instead of wandering away.
Not a perfect law.
Not a trading signal.
A scale-invariant adoption structure that only shows up when time beats noise.
90 days is chaos.
1+ years is signal.