Power-law corridor · fit live from CoinGecko

Bitcoin Power-Law Corridor

Q: How is the power-law corridor different from the rainbow chart?

The rainbow chart is a hand-drawn logarithmic regression with arbitrary colored bands and no falsifiable mechanism. The power-law corridor is a least-squares fit of P = A·days^n in log-log space, with a corridor of ±1σ and ±2σ derived from residuals. The slope is testable, the corridor is data-driven, and the model can be invalidated — none of which is true for the rainbow chart. Neither is a price prediction.

Price modeled as P = A · (days since genesis)ⁿ, fit by least squares in log-log space.

n = 5.217 A = -14.806 (log₁₀) R² = 0.912 σ = 0.271 fit 2013-04-28 → 2026-06-19 (4,800 days)

The corridor

log price vs log time · both axes log

fair value (trend)±1σ corridor±2σspot todayyour date

Value any date

Pick a date — past or future — to read the model's fair value and corridor for that day.

Date

−1σ floor

$59,180

Fair value

$110,431

+1σ ceiling

$206,068

Days since genesis

6,378

extrapolated 0.0 yr past the data — treat the band as a floor on uncertainty, not a forecast.

Read it honestly

Window-sensitive. This fit uses CoinGecko data from 2013 on, so n lands near 5.2 — below the canonical ~5.8 that includes 2009–2012. Where you start the clock changes the answer.
Log-log flatters. Compressing nine orders of magnitude makes most monotonic series look linear. A high R² is partly the transform, not proof of a law.
No mechanism. A and n are fit to data with a plausible story (adoption ∝ t³, value ∝ users²) attached — not derived from first principles.
Trend, not timing. The corridor says roughly where the climate sits. It says nothing about next week's weather, and the bands widen the further you extrapolate.

FAQ

How is the power-law corridor different from the rainbow chart?

The colors are the least of it. The real difference is the functional form each one commits to, and that drives everything downstream.

The rainbow chart is a logarithmic regression: log price against linear time. The fit line is price = a·ln(time) + b, and the colored bands are placed above and below it at arbitrary offsets, tagged with sentiment labels ("fire sale," "FOMO," "maximum bubble"). The bands aren't derived from anything — they're hand-set to widths that happen to have bracketed past tops and bottoms, and they get recalibrated as new highs print.

The power law plots log price against log time, where time is network age. Under a power law, price ∝ timeⁿ, so log(price) = n·log(time) + c — a straight line on a log-log axis. The exponent comes out around 5–6 empirically. The corridor is two power laws sharing that same exponent: support and resistance are parallel lines on the log-log plot, both falling out of the same equation rather than drawn on by hand.

The mechanical tell is the geometry. On a log-log chart, the power law is a straight line while the rainbow's log-linear fit is a curve that keeps bending — because they assume different things about how price relates to time.

Why the power law is taken more seriously — four reasons:

Derived bands, not decorated ones — same slope, different intercept, no manual tuning.
Stable and parsimonious — two parameters over the entire history; new data barely moves it. The rainbow visibly gets redrawn each cycle, which is the giveaway that it's fit to history rather than forecasting from it.
A claimed mechanism — Santostasi ties the exponent to a feedback loop among adoption, price, and hashrate/security. An actual attempt to explain why a power law would show up. The rainbow offers none.
Falsifiable — a straight log-log line makes a specific out-of-sample claim you can measure deviation against. Arbitrary bands that get redrawn can't really be wrong.

Where both fail the same way

Each is a single curve fit to one asset's one surviving timeline with roughly fifteen years of data. Log-log linearity is suggestive, not proof of the mechanism — power laws are famously easy to eyeball and overfit across a limited range, and the exponent shifts depending on which genesis date you anchor to. Taken literally, the power law implies smooth, decelerating growth forever, with no adoption ceiling and no path to the regime break that eventually kills most assets. The rainbow at least wears its unseriousness openly. The power law's real danger is the opposite: the straight line and the physics analogy make an empirical regularity feel like a law of nature.

One nuance: many newer "rainbow" charts have quietly rebased themselves on the power law underneath — what's labeled a rainbow is sometimes a power-law corridor with sentiment colors painted over it. The original distinction is log-linear regression with drawn-on bands versus a log-log power law with a corridor derived from the fit.

The honest framing: the power law is the more disciplined model — derived corridor, falsifiable slope, a stated mechanism — and still not a promise.

Methodology

Fits a log-log linear regression of BTC price against time since genesis and renders a multiplicative corridor around the central trend.

Power-Law Fit: log₁₀(P) = a · log₁₀(t) + b
Equivalent Form: P ≈ 10^b · t^a (a ≈ 5.8)
OLS Objective: min Σ (log₁₀(P_i) − ŷ_i)²
Residual Standard Deviation: σ = √(Σ r_i² ÷ (N − 2))
Upper / Lower Bands (log scale): ŷ ± k · σ (k ≈ 1.5–2)
Position in Corridor: pos = (log₁₀(P_spot) − log₁₀(P_lower)) ÷ (log₁₀(P_upper) − log₁₀(P_lower)) × 100%

Readings near 0% have historically clustered at cycle bottoms; readings near 100% at cycle tops. It is a regime gauge, not a forecast.

Data source: CoinGecko spot APILast updated: —

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