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.

Price is treated as an observable macro-parameter of the system. The upper boundary of the price channel is linearized by the transformation \(P^{1/4} = at + b\), revealing a 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). An observational experiment (February 6, 2026) confirmed the predicted lower boundary touch.

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.

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
- 2026_03_24_Physics_of_Bitcoin_Kinematics_v1_RU.pdf — Russian version
- figures.zip — all figures in high resolution