The Bitcoin power law: a model that fits fifteen years of price
Signal21 Editorial Desk
Where Bitcoin sits today
Bitcoin traded near $64,961 on Coinbase this morning, slipping back after failing to hold the $66,500 level it briefly broke earlier this week. Day to day, price is noise: a few percent here, a rejection there. That is exactly why a claim to have captured fifteen years of that noise in a single equation is worth examining carefully rather than dismissing or believing on sight.
A power law that fits fifteen years
In June 2026, a paper by Giovanni Santostasi and Stephen Perrenod was published in Elsevier's Nonlinear Science, arguing that Bitcoin's price follows a power law of time: price rising roughly as the number of days since the network began, raised to an exponent of about 5.69, with a coefficient of determination near 0.96 across some 5,700 daily prices from 2010 to early 2026. In plain terms, one curve tracks the entire history — from cents to five figures — to within a couple of percent.
What makes the paper more than a well-chosen chart is that the exponent is derived, not merely fitted. The authors decompose it into two mechanisms: adoption, where the number of users grows fast but decelerates over time — closer to the cube of elapsed time than to a straight line, echoing how epidemics spread through highly connected networks — and value, where a network is worth more than its user count because value grows with the connections between users, a generalized version of Metcalfe's law. Multiply those two forces together and a steep price exponent falls out.
What it does and doesn't say
The honest reading is the paper's own. Its authors deliberately avoid price targets, and it describes a long-run trend on logarithmic scales, not a timing tool — it says nothing about whether this week's rejection at $66,500 resolves up or down. It is directionally consistent with Signal21's long-term Strong Bullish view, but we treat it as context, not confirmation, and certainly not as a promised number. A follow-up article examines where the model is weakest and how you would know if it were breaking. This is market analysis, not a recommendation to buy or sell.