Предлагает интерпретацию броуновского движения как проявления архитектуры наблюдения в рамках ODTOE. Устанавливает связь между показателем Херста H и когерентностью S: H(S)=(1+S)/2. Формула воспроизводит два экспериментальных предела: при S=0 (полная декогеренция) H=1/2—классическое броуновское движение; при S=1 (полная когерентность) H=1—баллистический детерминизм. Масштабный коэффициент между уровнями наблюдения равен φᴴ, где φ—золотое сечение. Выявлена шестая роль спирального зазора (π−3)²: управляет переходом стохастичность-дрейф. Численная проверка на синтетических траекториях показывает ошибку 0.55%.
Proposes interpretation of Brownian motion as manifestation of observational architecture within ODTOE. Establishes relation between Hurst exponent H and coherence S: H(S)=(1+S)/2. Formula reproduces two experimental limits: at S=0 (complete decoherence) H=1/2—classical Brownian motion; at S=1 (complete coherence) H=1—ballistic determinism. Scaling factor between observation levels equals φᴴ, where φ is golden ratio. Sixth role of spiral gap (π−3)² identified: governs stochasticity-drift transition. Numerical verification on synthetic trajectories shows 0.55% mean error.
在ODTOE框架内提出布朗运动作为观察架构体现��解释。建立赫斯特指数H与相干性S的关系：H(S)=(1+S)/2。公式再现两个实验极限：在S=0（完全退相干）时H=1/2—经典布朗运动；在S=1（完全相干）时H=1—弹道确定论。观察级之间的尺度因子等于φᴴ，其中φ为黄金比。确定螺旋间隙(π−3)²的第六个角色：管控随机性-漂移转变。数值验证合成轨迹显示平均误差0.55%。
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Pankratov A. "Brownian Motion as a Manifestation of Observational Architecture: Hurst Exponent, Coherence, and the Golden Ratio." Observer-Dependent Theory of Everything, odtoe.org, 2026. https://odtoe.org/en/articles/brownian-motion@article{pankratov2026brownianMotion,
author = {Pankratov, Anton},
title = {Brownian Motion as a Manifestation of Observational Architecture: Hurst Exponent, Coherence, and the Golden Ratio},
journal = {Observer-Dependent Theory of Everything},
year = {2026},
month = {Apr},
url = {https://odtoe.org/en/articles/brownian-motion},
publisher = {odtoe.org}
}TY - JOUR
AU - Pankratov, Anton
TI - Brownian Motion as a Manifestation of Observational Architecture: Hurst Exponent, Coherence, and the Golden Ratio
JO - Observer-Dependent Theory of Everything
PY - 2026
DA - 2026-04-30
UR - https://odtoe.org/en/articles/brownian-motion
PB - odtoe.org
ER - Proton = observed R, neutron = observer O, electron = observation operator. Wheeler-Feynman single electron hypothesis. Neutrino as spiral gap.
Five mechanisms: coherence channel S to 1, resonance with H modes, Casimir effect, recursive amplification, collective observation.
Charge = orientation in self-observation cycle. Maxwell equations as self-consistency conditions. Coherent conductivity resonator (KRP).