Physics of Bitcoin: Kinematics of the Price Channel Defined by Adoption Diffusion and the Emission Protocol

This paper presents a structural model of Bitcoin's price dynamics based on affine reduction and protocol constants.

Bitcoin is treated as a Commercial Decentralized Distributed Computing Network (CDDCN) — a distributed computing system in which computational resources are provided by independent participants, coordinated without a central authority, and compensated through a protocol-defined economic mechanism. Its price is treated as an observable macro-parameter of this system.

The model starts from measurements of the real system. The author first searches for stable empirical regularities in the observed dynamics, validates them against the entire available history (including out-of-sample periods and subsequent observations), and only after passing these validation points proceeds to theoretical justification.

The upper boundary of the price channel is linearized by the transformation \(P^{1/4} = at + b\), revealing an empirical structural invariant with exponent \(k = 4\). The lower boundary is derived directly from the Bitcoin protocol: \(P_{\min} = P_{\max} / (1 + 50 \cdot 2^{-n})\), where 50 is the initial block reward and \(n\) is the halving number.

The model achieves 96.1% coverage of historical data (2009–2026) and a channel \(R^2 = 0.9992\). It passes stress tests (leave-one-out, leave-two-out) and out-of-sample checks on pre-market data (2009–2010), COVID dump (2020), and FTX crash (2022). The ongoing observational experiment showed that in early February 2026 the price reached the lower boundary previously calculated by the model and has remained near it in the following months (relevant as of August 2026).

Potential practical applications include structural risk management, position trading, ASIC demand forecasting, energy grid load estimation, and carbon footprint assessment.

This preprint is the first article in a series of four. It lays the kinematic foundation for subsequent studies on phase dynamics, external factors, and the theoretical derivation of the model.

Public discussion on LinkedIn.

The code for reproducing the results will be published in early 2027, following the release of Article II.

Contents:
- 2026_03_24_Physics_of_Bitcoin_Kinematics_v1_EN.pdf — English version (translation)
- 2026_03_24_Physics_of_Bitcoin_Kinematics_v1_RU.pdf — Russian version (original)
- figures.zip — all figures in high resolution

A popular science introduction to this research program is available as a separate booklet:

📘 The Engineer-Physicist's View: What is Bitcoin and Why Does It Have This Price?
doi.org/10.5281/zenodo.21774320

Learn more about the author:
igornovozhilov.ru

Research program:
cryptoeconophysics.com (under development)