В рамках ODTOE выведена замкнутая формула для постоянной Планка h, связывающая её с числом π (форма цикла наблюдения), золотым сечением φ (дискретный шаг между циклами), мерностью наблюдателя d и когерентностью среды S. Формула h(d,S) = 2π(π−3)²φ^(d+1)·Σ(d)·(1−S)^(−1/2)·A₀ содержит шесть структурных множителей, выведенных из аксиоматики ODTOE. Из условия самосогласованности вычислена единственная когерентность S*=0,16976 из π, φ, d=3 без подгоночных параметров. Числовой результат: h_ODTOE = 6,62607×10⁻³⁴ Дж·с — шесть значащих цифр, совпадение с CODATA.
Within the ODTOE framework, a closed-form formula for Planck's constant h is derived, linking it to π (observation cycle form), φ (discrete step between cycles), observer dimensionality d, and medium coherence S. The formula h(d,S) = 2π(π−3)²φ^(d+1)·Σ(d)·(1−S)^(−1/2)·A₀ contains six structural factors derived from ODTOE axiomatics. From the self-consistency condition a unique coherence S*=0.16976 is computed from π, φ, d=3 with zero fitting parameters. Numerical result: h_ODTOE = 6.62607×10⁻³⁴ J·s — six significant digits, agreement with CODATA.
在ODTOE框架内推导了普朗克常数h的封闭形式公式，将其与π（观察周期形式）、φ（周期间的离散步骤）、观察者维度d和介质相干性S联系起来。公式h(d,S) = 2π(π−3)²φ^(d+1)·Σ(d)·(1−S)^(−1/2)·A₀包含六个从ODTOE公理推导的结构因子。从自洽条件计算出唯一相干性S*=0.16976，无拟合参数。数值结果：h_ODTOE = 6.62607×10⁻³⁴ J·s，六位有效数字，与CODATA一致。
Select the text below to copy citations in your preferred format.
Pankratov A. "Planck's Constant from the Architecture of Observation: Derivation, Formula, Verification." Observer-Dependent Theory of Everything, odtoe.org, 2026. https://odtoe.org/en/articles/planck-constant@article{pankratov2026planckConstant,
author = {Pankratov, Anton},
title = {Planck's Constant from the Architecture of Observation: Derivation, Formula, Verification},
journal = {Observer-Dependent Theory of Everything},
year = {2026},
month = {Mar},
url = {https://odtoe.org/en/articles/planck-constant},
publisher = {odtoe.org}
}TY - JOUR
AU - Pankratov, Anton
TI - Planck's Constant from the Architecture of Observation: Derivation, Formula, Verification
JO - Observer-Dependent Theory of Everything
PY - 2026
DA - 2026-03-17
UR - https://odtoe.org/en/articles/planck-constant
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).