Has Tim Stolte debunked
the power law?

This is rhetorically the punchiest line and technically the weakest. A power law is price = a · t^b. Taking the log of both axes — log price = log a + b·log t — is simply the standard, correct way to fit and view any power law, exactly as a log-linear chart is the standard way to view an exponential. It implies nothing whatsoever about time "passing exponentially." Allometric scaling, Kleiber's law, earthquake frequencies and gravitation are all fit in log–log. The legitimate question is why price should be a power of time at all (a descriptive choice, not a mechanistic one) — but that's not the objection he makes. Verdict: a misunderstanding of what a power law is, not a refutation of one.

There's a real point buried here and an overstatement on top of it. The real point: the time origin t₀ is a genuine free parameter, and power laws of the form (t − t₀)^b are sensitive to it — fair. The overstatement: in practice t₀ is fixed at the genesis block (3 Jan 2009), a real, non-arbitrary event — Bitcoin did not exist before it — which removes most of the "pick any integer" freedom he describes. And window-sensitivity cuts the other way too: the fit estimated on early data has continued to track years of out-of-sample price added since, which is the robustness that actually matters and which the piece doesn't weigh. Verdict: t₀ is a fair caveat; "arbitrary guesswork" is too strong.

The substance is correct and important. If Bitcoin's log-price is a random walk with drift, then fitting any smooth rising curve to it yields a gorgeous R² and tiny-looking residuals that are largely an artifact — and the OLS "corridor," the ±2σ confidence bands, has no valid statistical justification. That is a genuine, well-aimed hit on how the model is usually sold.

But three things keep it short of a knockout. (a) The cointegration test is the wrong instrument. Spurious regression (Granger–Newbold) is about regressing one stochastic I(1) process on another. Here the regressor is log(time) — a deterministic, monotonic variable, not a random process. Testing "cointegration" between price and the clock is a category error; the honest framing is whether log-price is trend-stationary around a deterministic trend or difference-stationary. (b) Unit-root tests have notoriously low power on short, strongly-trending samples — with ~12 years of data, ADF simply cannot separate "trend-stationary with high persistence" (which would vindicate a deterministic power-law trend) from "random walk." Failing to reject a unit root is not proof of one. (c) No out-of-sample test. Debunking a predictive model means showing it has no skill beyond a naive benchmark out-of-sample — which the article never attempts. Verdict: it correctly demolishes the "R²-proves-it" claim; it does not establish that the regularity is noise.

This is the piece's internal inconsistency. Extrapolating a constant growth rate is itself a deterministic-trend model — an exponential, price = a·e^gt — fitted to the very same non-stationary series he just declared off-limits. It is subject to precisely the spurious-trend critique he levelled one section earlier. You cannot wield non-stationarity to kill the power law and then propose another deterministic trend as the cure. Verdict: the alternative inherits the same disease it was meant to treat.

But he hasn't debunked the thing itself. A descriptive regularity that has held across fifteen years and out-of-sample data is still standing after his critique. "Not rigorously proven" is not the same as "shown to be false," and his article only establishes the former.