Planck's Constant from the Architecture of Observation: Derivation, Formula, Verification — Overview
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)
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Within the framework of ODTOE, a closed-form expression for the Planck constant h is derived, relating it to the number π (the shape of the cycle of observation), the golden ratio φ (the discrete step between cycles), the observer's dimensionality d, and the coherence of the medium 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 the ODTOE axiomatics. From the self-consistency condition, a unique coherence S*=0.16976 is computed from π, φ, d=3 without fitting parameters. The numerical result: h_ODTOE = 6.62607×10⁻³⁴ J·s—six significant figures, in agreement with CODATA.