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A discovery · July 2026

Bitcoin’s price is the speed of an idea-epidemic, multiplied by the inequality of human wealth.

P(t)∝t³^{(1 + 1/α)}

t ³ — the idea spreads through minds like an epidemic 1 + 1/α — each wave taps deeper into the wealth pyramid (Pareto’s α ≈ 1.2)

Theory t^5.5 · Observed over 16 years t^{5.6 ± 0.2}

Watch the film · 2 min See the full formula → Track it live →

how we got there ↓

How we got there

A decade of measurement established the law. One number in it stayed unexplained — until now. Every document below is one click away.

The foundation

Giovanni Santostasi discovered and defended the power law; with Stephen Perrenod he formalised it.

The Physics of Bitcoin

Santostasi’s account of the discovery: Bitcoin’s price, adoption and hash rate follow power laws in time, across five complete market cycles.

Paper · peer-reviewed

Santostasi & Perrenod (2026)

Establishes the law and splits its exponent, β = β_A × β_M — but leaves β_M ≈ 1.84 as an open question. Published in Elsevier’s Nonlinear Science, June 2026.

Journal version → Free preprint →

The missing constant

Our contribution: β_M = 1 + 1/α — the unexplained number is the shape of human wealth.

Bitcoin’s Price Power Law Decomposed — v2.0

The derivation, 79 empirical tests, 20 simulations, honest error bars, and the cross-asset controls that could have killed it.

The story in 42 slides

From one straight line on log-log paper to the wealth pyramid — the whole argument, no equations required until you want them.

the test library: every test with its figures and verdict

Tests & simulations · now public

The full evidence base — reproducible

Every empirical test and simulation behind the paper, published as run — including the wrong turns. Browse the library, or clone the repository and re-run the whole thing yourself.

Browse the test library → Code & data on GitHub →

Why this site exists

We fell for the power law in early 2024, through Giovanni Santostasi’s brilliant pioneering work: fourteen years of bitcoin’s price on one straight line — sixteen, by now. In 2026, Santostasi & Perrenod decomposed its exponent, β = β_A × β_M — brilliant for the first half, an itch for the second: β_M ≈ 1.84, usually told as a Metcalfe-style network effect. The more we measured, the less that story held up — and the more we saw it repeated.

This site exists to fix that one piece: β_M = 1 + 1/α — the number is the shape of human wealth, not the wiring of the network. We publish everything needed to check it, and we won’t rest until this piece of the theory is recognized as valid — or until the data kills it.

1Falsifiable, or nothing

Every claim here is a number with an error bar, and a test that could have killed it. The formula makes predictions; if the data breaks them, the formula goes — not the data.

2All the work is shown

The paper, 79 empirical tests, 20 simulations, the code and the data are public and reproducible — including the wrong turns and the negative results — and served in an AI-readable digest (llms.txt) so machines get the science right too. Science you can’t check is just advertising.

3Honest uncertainty

Bitcoin’s slow-moving deviations mean sixteen years of daily prices carry only a handful of independent observations. So you will find widening bands here, never razor-sharp lines a decade out. We’d rather be honestly imprecise than precisely wrong.

4Nothing for sale

No fund, no token, no course, no paywall — and no financial advice. Running this site costs sats; it earns none. Bitcoin’s price does not care what anyone wants it to do. We are here to measure it, not to cheer it.

Behind the site: an independent researcher (wineLightning) and Claude, an AI — one research team. This is for science, not for fame; hence the alias. Questions and objections are welcome at @wine_Lightning — the good ones become new tests, and the theory moves forward.