ebitdang · research instrument

The Bitcoin Power Law

One claim — price = A × daysn since the genesis block — and everything that follows from taking it seriously. Pick a published fit or make your own, choose how the corridor is drawn, and read the fine print below.

BTC spot
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daily close
Model fair value
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Deviation
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Time vs trend
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where the trend says this price belongs
Time vs floor
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Band position
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of all days since 2010 were cheaper vs trend
last 90 days · daily closes
BTC price model corridor
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Model

Corridor

Date → price

Pick a date.
Uses the selected model and corridor.

Price → date

Type a price.
When the trend line — and the corridor edges — cross that price.
What this is

The model in four sentences

Plot Bitcoin's price against its age on log-log axes and the sixteen-year history hugs a straight line: price ≈ A × (days since Jan 3, 2009)n, with n around 5.7. The proposed mechanism is that adoption spreads like an epidemic (users ∝ t³) while network value scales super-linearly with users (a generalized Metcalfe's law, value ∝ users1.8) — multiply the two and price grows as roughly the sixth power of time. The idea has a clear lineage: astrophysicist Giovanni Santostasi proposed it in 2014 and has championed it ever since; Harold Christopher Burger drew the corridor form in 2019. In June 2026 the argument, and the fit behind it, passed peer review (Santostasi & Perrenod, Nonlinear Science); R² is about 0.96 and typical deviation from the line is a factor of two in either direction, which is what the corridor bands measure.

Every readout above derives from the one formula. "Deviation" is how far today's price sits from the line — in percent and in σ (standard deviations of the historical log-residuals). "Time vs trend" solves the model backwards: the date at which the trend line passes through today's price. "Time vs floor" asks the same of the corridor's lower edge — how long price could drift sideways before the floor rises to meet it (negative once price is already beneath it) — and follows whichever corridor is selected. The band-position tile ranks today against every day since 2010: at 0% Bitcoin has never been cheaper relative to its trend; at 100%, never more expensive.

How the floor is drawn matters more than it looks. Four of the five corridors slide the trend line down by a constant factor — a parallel line on log-log axes — and differ only in how that factor is chosen. Percentile bands take the actual historical distribution of deviations (which is skewed — manias overshoot more than crashes undershoot), so the floor is the 5th percentile. σ bands assume that distribution is a bell curve and use −2σ. Fixed multiples are the folk convention (0.42× has roughly marked every major low since 2011, though Aug 2015 slipped through it). The Burger corridor is the 2019 original: a support line shifted down to hug the all-time lows, and a resistance line fitted through the cycle tops — its flatter slope is why each mania overshoots the trend less than the last.

The fit through the lows is different in kind: a power law of its own through the cycle bottoms, with its own exponent. It exists because the lows are the most regular thing about Bitcoin — every cycle bottom since 2010 sits at roughly 0.3–0.6× the trend, while the tops fell from 16× to 1.2× — which is why Santostasi has long argued that the bottoms, not the bubbles, carry the law. Regular in hindsight is not the same as predictive, though: the line through the lows known in 2016 put the 2022 floor near $26,000, and the bottom printed at $15,760, forty percent through it. The same test on the tops misses by far more, so "more predictable than the tops" is true; "a hard floor" is not.

Fine print

Why this might be nonsense

A model this seductive deserves its strongest objections, stated plainly:

  • The regression may be spurious. Price is a wandering process, time is not; regressing one on the other can manufacture impressive R² from nothing. Critics have called the corridor "falsified" on exactly these grounds. Perrenod's follow-up analysis (June 2026) answers with a cointegration test — deviations from the line do appear to mean-revert (p = 0.026) — but the argument is genuinely unsettled.
  • The daily points are not 5,800 independent observations. Residuals are enormously autocorrelated (price spends years on one side of the line), so the tiny quoted uncertainties on n are overconfident, and the bands here should be read as historical envelopes — not statistical prediction intervals.
  • The exponent is not a constant of nature. It has drifted from 5.85 (2019 fit) to about 5.65 (fit on this page, today) as below-trend years accumulated — watch it move in the exhibit below. And it depends heavily on the choice of day zero, which is a convention, not a measurement.
  • Survivorship. The law is fit to the one asset that survived and compounded. Assets that died never get power-law papers. Extrapolating to 2040 assumes the adoption curve keeps this exact shape through saturation, regulation, and competition — the model cannot see a regime change until it has already broken. Stock-to-flow looked this good once.

Exhibit A — the origin is a choice

The "universal constant n ≈ 5.7" assumes day zero is the genesis block. Slide the origin and refit — same data, same method:
genesis
exponent n → 5.65R² → 0.962

Exhibit B — the exponent drifts

n refit each year using only the data available at the time. A law of nature would be a flat line.

Falsification, on the record

The 2026 paper names its own break conditions. The relevant one: price more than 3σ below trend, sustained for over a year, kills the model.
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Sources: Santostasi & Perrenod 2026 (paper, preprint) · Santostasi's The Physics of Bitcoin · Burger 2019 (corridor) · the critique (M. Burger 2019, Baquero & Menezes 2026). Price data: Coin Metrics community data (CC BY-NC 4.0) + Kraken daily closes. Independent of, and not endorsed by, any of the people, sites or companies named.