In May 2026 two researchers at the University of Porto, Carlos Baquero and Raquel Menezes, did to the bitcoin power law what almost nobody promoting it had bothered to do. They ran the proper statistical test, end to end, then ran a second one to be sure. Their preprint reaches the same conclusion I argued in an earlier piece months before, and it catches me in an overstatement I should have caught myself.
The overstatement was about a tail. The tail of a distribution is its extreme end: for daily returns, the rare days when bitcoin moves enormously, the crashes and the violent rallies that sit far out from an ordinary session. I claimed that this tail, unlike the price chart, was a genuine power law. The new paper, running a test I skipped, shows it is not.
Both halves of that result matter, the confirmation and the correction, and the second matters more.
The Argument, Recapped
I have taken apart the "Bitcoin Power Law" twice here. The first piece argued that the famous straight line on log-log axes is a power trendline, a fitted regression of price on time, and not a power law in the sense physics uses the term: a scale-invariant structural property with a derived, fixed exponent. The second engaged the most rigorous version of the claim, Giovanni Santostasi's causal model, and located its load-bearing weakness in a single fitted exponent. My throughline was one idea. Log-log linearity is necessary for a power law and nowhere near sufficient, and most claimed power laws fail the moment someone runs the formal test.
Someone Ran the Test
Baquero and Menezes ran it. Their paper applies the Clauset-Shalizi-Newman protocol, the standard method for testing power-law claims, together with three time-domain adaptations and a nine-asset comparison. On the central question, whether bitcoin's price-versus-time curve is a structural power law, their verdict matches mine, and the evidence is sharper than anything I published.
The cleanest result is the shift test. A structural power law has one exponent, and the data should return it regardless of where the clock starts. Baquero and Menezes move the time origin across a reasonable range and watch the fitted exponent climb from 5.65 to 16.49. An exponent that depends on a free choice of origin is not a property of the data; it is a property of the specification. That single table does more damage to the law claim than any amount of prose.
They go further and reproduce the four scale-invariance tests that the power law's proponents offer as proof. Every test passes on real bitcoin. Every test also passes on a three-component sigmoid stack fabricated to match the same prices. A sigmoid stack: three S-shaped adoption-wave curves (slow start, surge, plateau) glued end to end and tuned to mimic bitcoin's price history, a shape everyone agrees is not a power law. A test that a known non-power-law passes cannot be evidence for a power law. And a flexible multi-sigmoid model fits the price history better than the power law does to begin with. The structure the proponents see is real as a stable long-run slope, and a stable slope does not single out a power law as the form that generates it.
None of this is new to anyone who read those earlier pieces. What is new is the rigor and the source: an independent academic team, no stake in the dashboard, reaching the conclusion through the canonical protocol. Confirmation of that kind is worth more than being first.
And They Caught the Error
Here is the part worth dwelling on. I did not only debunk. I made a positive claim: that bitcoin does contain a genuine power law, not in the price chart but in the tails of the daily return distribution, the extreme up and down days. I fitted a Pareto tail (the classic power-law shape, the pattern behind the 80/20 rule) to those extremes, reported a clean goodness-of-fit, and called the result a power law "by any reasonable statistical standard."
Baquero and Menezes tested that distribution properly, and it does not hold. The Clauset-Shalizi-Newman protocol has a final step I skipped: a likelihood-ratio test against the lognormal, the distribution that most often masquerades as a power law over a finite range. A lognormal is the shape a multiplicative process produces, the natural baseline for returns that compound as percentages, and it looks heavy and runs straight on log-log axes just as a power law does, which is why the two are so easily confused. They part company only in the far extreme: a power law stays scale-free and lets its largest moments (the summary numbers, like the average size of the extremes) run to infinity, while a lognormal, though still far heavier than a bell curve, eventually thins out and keeps every moment finite. Run on bitcoin's daily absolute returns, the power law is rejected and the lognormal is preferred, decisively, on the full sample and on the recent sub-periods. The tail is heavy and decidedly non-Gaussian. A normal distribution fitted to bitcoin's own daily volatility puts a 20% one-day move at roughly once a century; bitcoin has them about twice a year, and its worst single day, a near-50% drop, sits past ten standard deviations, which a bell curve rates at less than once in the age of the universe. For price the lesson is about expectation, not insurance: moves like these are ordinary features of the series, not rare disasters bolted on from outside, so any position-sizing or risk model that reads a calm stretch as safety is mispriced from the start. "Heavy-tailed" is the claim the data supports. "A power law" was a reach.
The uncomfortable symmetry is the lesson. I criticised the price-law crowd for exactly this move: take a curve that looks right on log-log axes, fit it, and declare a law without running the comparison that separates a law from a look-alike. Then I made a quieter version of the same move with the return tail. A good Pareto fit, reported as a power law, with the lognormal test never run. Being right about the price bought me no license to be loose about the tail.
Why This Is the Whole Point
A website that exists to hold confident claims to the data does not get to exempt its own, and that includes mine. The protocol that vindicates the main argument, the one the price law fails, is the same protocol that the return-tail claim fails. A standard cuts both ways or it is not a standard. And the right response to a better paper finding the thing I missed is to say so, in public, with the authors' names attached.
So: credit to Carlos Baquero and Raquel Menezes. Their paper is the rigorous version of an argument I made loosely, and it is the correction I needed on the one claim I advanced without finishing the test. The 2.9 tail index I quoted stands as a description of the extreme moves; the word "law" attached to it does not.
That tail was the last place I had claimed a real power law in bitcoin. With it reclassified, none is left: not in the price curve, not in the daily returns. The asset is heavy-tailed and its long-run trend is strong, and neither of those is a power law. There is, in fact, no power law in bitcoin at all.
Weak Structure, Strong Forecasts
The paper's title carries its deepest finding, and it settles a tension a careful reader might have noticed in the dashboard. If the power law is not a law, why does the dashboard weight Power Law Position at 17% and lean on it more than any other indicator?
Because descriptive truth and predictive value are different things. Baquero and Menezes run a walk-forward forecasting test, and the simple power law produces the lowest error at horizons of 12 to 24 months, beating every flexible model and every standard time-series baseline. The flexible model that traces every past swing forecasts worst of all: it is like memorising the exact path of last year's storm and expecting the next one to follow the same line. The power law wins long horizons precisely because it commits to nothing but the broad long-run band. At one to three months a no-skill baseline beats everything, which is the same coin-flip result a foundation-model test on this website reported for daily direction.
That is the honest case for the indicator. Power Law Position is not a law and not a price target. It is a steady long-range marker. The dashboard leans on it because it is good at saying roughly where price should sit a year or two out, not because the line is destiny. Weak as a law, useful as a forecast. The dashboard treats it as nothing more than that.
A power law that cannot be reproduced is not a law. A claim that was never tested is not a finding. The difference between this website and the laser-eye charts is supposed to be that the tests get run. When someone runs them better and reports both what I got right and what I got wrong, the only honest move is to publish their names and the verdict, and update.