hbar_RS
plain-language theorem explainer
The definition supplies the reduced Planck constant in Recognition Science native units as the reciprocal of the golden ratio raised to the coherence exponent. Researchers deriving physical constants from the Recognition framework cite this when establishing unit conversions or verifying positivity. It is realized as a direct abbreviation that applies the fixed exponent value of 5.
Claim. $h_{RS} := (phi)^{-5}$ where $phi$ is the golden ratio and the exponent equals the coherence exponent fixed at 5.
background
The module derives the key constants of the Standard Model from Recognition Science, with the coherence exponent defined as 5. This value is forced at spatial dimension 3 by the Fibonacci route $k_{fib}(D) = 2^D - D = 5$ and the integration route $k_{int}(D) = D + 2 = 5$. Upstream results establish the coherence exponent as 5 and the native reduced Planck constant as $phi$ to the negative fifth power.
proof idea
This is a direct definition that inverts $phi$ raised to the coherence exponent. The definition substitutes the fixed value 5 for the exponent and applies the reciprocal operation.
why it matters
It supplies the value of $h$ used in the positivity theorem $h_{RS pos}$ and the certification structure PlanckConstantCert. This completes the algebraic derivation of $h = phi^{-5}$ once the exponent is pinned at 5 by the uniqueness result. It anchors the RS-native units where $c=1$, $h=phi^{-5}$, $G=phi^5/pi$, consistent with the eight-tick octave and $D=3$.
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