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Analysts have talked about Bitcoin’s four-year halving cycle for years. Most treat it as a simple chart pattern. However, physicist and analyst Giovanni Santostasi went further.
He applied two powerful mathematical tools, the Singular Spectrum Analysis and Dynamic Mode Decomposition, to Bitcoin’s entire price history. And his conclusion is striking.
🧵 THREAD: We just proved Bitcoin's 4-year halving cycle is a fundamental eigenmode of the system
Using eigenvalue decomposition (SSA + DMD), we discovered something remarkable about Bitcoin's price dynamics. Let me explain what we did and why it matters…
1/ What are… pic.twitter.com/5gPpgd3h40
— Giovanni's BTC_POWER_LAW (@Giovann35084111) March 30, 2026
The four-year cycle is not just a repeating pattern. It is a real eigenmode, like a fundamental frequency baked into the system, emerging naturally from the data in the way a musical note rises from a vibrating string. Eigenvalue Analysis is rigorous physics and signal processing applied to Bitcoin’s market behavior. But just as its findings carry real weight, they also come with real limits.
Bitcoin’s price history is like a complex audio signal. Multiple patterns overlap at the same time. Singular Spectrum Analysis (SSA) works like a filter. It separates the signal into distinct components and ranks them by how much of the total price movement each one explains.
Santostasi’s team ran the analysis in log space, an important step, since Bitcoin’s price has grown across six orders of magnitude.
The result was striking. One single component accounted for 98.7% of all price variance.
That component is the power law. It shows Bitcoin’s price growing proportionally to the number of days since the Genesis Block, raised to the power of 5.7. The model fits the data with an R² of 0.9678.
Santostasi developed this approach using tools from his background in gravitational wave physics and neuroscience. He applied principles from physics and biology to Bitcoin’s market behavior. The core relationship mirrors growth patterns seen in complex natural systems, the same scaling laws found in mammalian metabolic rates and the way cities grow.
After removing the dominant power-law trend, 1.3% of the variance remains. This is where the four-year cycle hides. Using Dynamic Mode Decomposition, the team isolated the oscillations around the main trend. They discovered a clear dominant period of 1,530 days, exactly 4.19 years. The eigenvalue for this mode is 0.9985. It is slightly decaying, which means the cycle is stable and persistent rather than growing or fading away.
In physics terms, this matches what renormalization group theory predicts for complex systems near a phase transition: a strong power-law trend with log-periodic oscillations around it. The halving cycle appears not because analysts expect it. It emerges naturally when the mathematics extracts it directly from Bitcoin’s raw price data.
Running the analysis in linear space makes the four-year cycle invisible. It gets buried in noise. Halvings affect price multiplicatively, in percentage terms, not in absolute dollars.
Log space reveals the true underlying geometry. This methodological choice turns the finding from coincidence into something credible.
The findings are mathematically robust within their framework. But the framework has important assumptions.
SSA and DMD assume the system is stationary, that the rules driving Bitcoin’s price behavior remain consistent over time. Financial markets offer no such guarantee.
Unforeseen events can break power-law relationships. The model relies entirely on historical data, so past patterns are not a promise of future ones.
Bitcoin’s market has changed dramatically since 2010. Spot ETFs, institutional treasuries, geopolitical safe-haven flows, and AI-driven mining were never part of the early dataset. Whether the eigenmode persists as Bitcoin matures is a question the model cannot answer. It can only show that this structure has held for the past 15 years.
THE 4-YEAR CYCLE IS DEAD
it is dead for good, whether you believe it or not!
we've been in a consolidation and accumulation phase across $BTC, majors and many altcoins for a while now
soon, they're going to rip aggressively to the upside and make new ATHs
for a long time now,…
— Unipcs (aka 'Bonk Guy') 🎒 (@theunipcs) December 26, 2025
Also, there are many in the cryptosphere who believe the four-year cycle is dead. One of those who share this sentiment is Unipcs, a popular Crypto analyst with 227,000 followers on X. In a lengthy piece in December 2025, he stated that the four-year market cycle had reached a point where it could no longer influence the behavior of Bitcoin and major altcoins. Matt Hougan, author of the Bitwise Asset Management newsletter, also expressed a similar idea in a LinkedIn article.
The four-year cycle is real in the historical data. Whether the data going forward will keep producing it remains the open question.
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