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.