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On March 12, 2026, David, a quantitative analyst with engineering and MBA credentials from USC, CSU, and Stanford, published a statistical deep dive into Bitcoin’s long-run price structure. The response from Giovanni Santostasi, the astrophysicist who created the Bitcoin Power Law theory, was brief but telling: “Long term scale invariance.”
That response carries weight. Santostasi has spent around 14 years developing a quantitative theory linking Bitcoin’s price, hash rate, and network adoption through recursive, self-reinforcing feedback loops. He is the original discoverer of Bitcoin’s power law in time, a framework that treats Bitcoin’s long-run price behavior as a structural property of the network, not just a market outcome.
Long term scale invariance. https://t.co/gIPTQBducZ
— Giovanni's BTC_POWER_LAW (@Giovann35084111) March 13, 2026
David’s analysis is built on 5,718 daily price observations spanning roughly 17 years of Bitcoin data. The model he derived is simple:
ln(P) = 5.686 × ln(time) – 37.99
This single equation explains 96% of Bitcoin’s long-run log-price variation, reflected in an R² of 0.961. The HAC t-statistic, a measure adjusted for noise and serial correlation, comes in at 103, far above the conventional significance threshold of 2.
Bitcoin’s Most Bullish Proof Is Engineering: Long-Term Scale Invariance
Bitcoin’s strongest signal is not short-term momentum.
It is structural integrity.
Using 5,718 daily observations across ~17 years, Bitcoin still fits:
ln(P) = [5.686 × ln(time) − 37.99]
Exponent: 5.686… pic.twitter.com/jzSehvfVkL
— David (@david_eng_mba) March 12, 2026
The exponent of 5.686 closely aligns with Santostasi’s theoretical framework. Under the Bitcoin Power Law Theory, user adoption scales roughly with time³, while network value scales with users² through Metcalfe-style effects, leading to a theoretical price exponent near 6.
David’s observed value lands squarely in that range.
David also tested the power law against a simple random walk model across different time horizons. At 90 and 180 days, the random walk performs better. At 365 days, the power law dominates.
In the short term, Bitcoin behaves like noise. In the long term, it behaves like structure.
He further tested the model’s stability using residual stationarity. An ADF p-value of 0.022 confirms that deviations from the power law trend revert over time rather than drift indefinitely. Overshoots tend to decay, and undershoots tend to recover. The system oscillates around its structural trend rather than diverging from it.
David also showed that when time is rescaled by factors between 1.25× and 4×, the exponent remains constant. This satisfies the mathematical definition of scale invariance – the growth law holds regardless of the time scale used.
Interpretation
The figure shows that when time is rescaled by factors from 1.25× to 4×, the estimated exponent remains constant and the scaling identity holds.This confirms that the power-law model itself satisfies the mathematical conditions required for scale invariance.
In… pic.twitter.com/RH7bNCqnLq
— David (@david_eng_mba) March 12, 2026
Santostasi’s theory helps explain this durability. Bitcoin has passed through early hobbyist adoption, China mining dominance, retail speculation, institutional balance sheets, and the ETF era. Each phase introduced different participants, liquidity conditions, and market structures, yet the same scaling law has held throughout. Even institutional ETF inflows did not disrupt the trajectory; they aligned with the expectations of scale-invariant growth.
After four halvings, multiple 70% drawdowns, and nearly 17 years of market evolution, the structural law remains intact. That is the bull case David is making – not that Bitcoin will do something extraordinary next week, but that the mathematical backbone governing its long-run behavior has not broken yet.
Noise changes – the structure persists.
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