Giovanni Santostasi's "Bitcoin Power Law Theory"
Read the Original Article
You can read the original article by Giovanni Santostasi: https://giovannisantostasi.medium.com/the-bitcoin-power-law-theory-962dfaf99ee9
My main discovery was that Bitcoin is ruled by power laws. Its regularities show that it behaves more like a physical system than an asset. This intuition was based on observing a striking power law over many orders of magnitude in the Price of bitcoin vs time.
Overview
Giovanni Santostasi's "The Bitcoin Power Law Theory" posits that Bitcoin behaves less like a traditional financial asset and more like a natural phenomenon or a growing city, with its dynamics governed by power laws. This comprehensive theory, developed over twelve years, suggests that key on-chain parameters like Price, Hash-Rate, and Address growth are all mathematically linked and driven by a continuous feedback loop that is rooted in principles of logic and physics. A central and astonishing consequence of the theory is Scale Invariance, which implies that Bitcoin’s long-term growth trajectory and cycles, including the necessary bubbles, are predictable and established, remaining unchanged across different scales of magnitude. Crucially, the author emphasizes that his model entirely excludes the concept of scarcity, supply, and demand as explanatory factors for Bitcoin's behavior.
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Manifestation of Determinism: The Bitcoin Power Law Theory (PLT)
Under the unfiltered lens of Codex Umbra, the analysis of Giovanni Santostasi's Bitcoin Power Law Theory (PLT) reveals a stark reality: Bitcoin operates not as a capricious financial asset subject to fleeting human sentiment, but as a deterministic, physical system governed by immutable, amplifying feedback loops. Conventional economic metrics are rendered obsolete by the sheer, predictable chaos inherent in this digital entity.
The PLT is a scientific framework detailing the growth and dynamics of Bitcoin, positing that its behavior aligns with natural phenomena and the growth patterns of cities or biological organisms. Santostasi, operating as a physicist and neuroscientist, formulated this theory based on the shocking regularity observed across multiple orders of magnitude in Bitcoin's key parameters.
Deciphering the Power Law Structure
A Power Law is a mathematical expression of fundamental importance, defined by the formula y = A x^n. These relations are not accidental anomalies but are ubiquitous across natural and social systems—from the growth metrics of cities and nations to complex phenomena in physics.
Power laws are the direct computational output of an iterative, recursive process where the product of the system immediately becomes the new input for the next cycle, creating a continuous feedback loop. In the dark machinery of Bitcoin, this principle dictates that the instantaneous hash rate, for example, influences the subsequent hash rate in an endless iteration. The patterns that emerge from this colossal network of agents, despite the illusion of individual free will, exhibit a universality that allows them to be modeled precisely like physical systems.
The Unfiltered Reality of the Bitcoin Power Law Theory
The PLT serves as a mathematical expression, rooted in logic, physics, and mathematics, of the causative feedback loop that drives Bitcoin. It proposes that three core on-chain parameters—Price, Hash Rate, and Addresses—are bound to each other and to time by definitive power laws.
I. The Core Power Law Relationships
The raw data extracted from the Bitcoin network yields the following deterministic relationships, which describe the long-term, predictable trajectory of the system:
II. The Causal Feedback Loop (The Engine of Inevitability)
The observed power laws are generated by a continuous cycle of positive feedback:
- Adoption and Value Initialization: The cycle begins with the adoption of users.
- Price Ascent: The perceived "value" (Price) is amplified according to the square of the users, as predicted by Metcalfe’s law.
- Resource Influx: The soaring Price attracts massive resources, specifically mining power and computational capability.
- Security Escalation: This influx of resources elevates the Hash Rate, dramatically increasing the security and computational intractability of the system. The system's difficulty adjustment ensures that miners operate at the very edge of profitability, denying any "free lunch" and linking energy expenditure directly to value.
- User Attraction: The manifest security of the system (the raw truth of its computational integrity) then attracts new users, commencing the adoption phase anew.
- Infinite Iteration: This process repeats indefinitely, driving the system along its established power law curve.
III. The Brutal Truth of Scale Invariance and Bubbles
A central consequence of the PLT, and a doctrine that defies conventional financial thought, is Scale Invariance. Scale invariance dictates that the long-term, underlying behavior of Bitcoin is unchanging regardless of the scale of growth. The system will continue to follow the same predictable trend as it scales through additional orders of magnitude.
- Prediction as Inevitability: Because the system is governed by power laws, everything essential—price, adoption, hash rate—is predictable in the long term. The established trajectory is fixed; technological breakthroughs (like ETFs) are merely critical events necessary for the system to continue its predetermined path, not influences capable of changing the fundamental growth slope. The path is set: NO MORE, NO LESS.
- The Nullification of Scarcity: In a provocative divergence from prevailing cryptocurrency narratives, Santostasi claims that scarcity plays absolutely zero role in the PLT, possessing neither mechanism nor explanatory power for the observed dynamics.
- Bubbles as Punctuated Evolution: The manic "bubble" periods are not random fluctuations but a necessary and inherent component of this self-organized system, described as a form of "punctuated equilibrium". They are triggered when escalating security attracts users (a period of "excitement") leading to rapid, nearly exponential price overshooting, which is then swiftly corrected by a symmetric burst back down to the fundamental power law equilibrium line. This violent, necessary volatility is interwoven with the underlying four-year cycles tied to Moore's Law and the programmed halving schedule.
The PLT thus frames Bitcoin as a singular, technologically enforced truth, resistant to political power and human caprice, marching along a mathematically predetermined path.