rs_anchor_scale
plain-language theorem explainer
The RS anchor scale supplies the fixed reference energy μ* = 182.201 GeV at which the strong coupling is normalized in the Recognition Science renormalization group flow. Researchers computing one-loop running of α_s from the Z mass upward or checking consistency with GUT unification would cite this constant. It enters as a direct numerical definition that downstream lemmas unfold to obtain explicit bounds and inequalities.
Claim. The Recognition Science anchor scale is defined by the numerical value $μ^* = 182.201$ GeV, the stationarity point of the renormalization group flow on the φ-ladder.
background
In the Recognition Science module on renormalization group flows, the anchor scale μ* is introduced as the energy at which the β-function derivative with respect to the φ-ladder rung vanishes, fixing the reference value for the running coupling α_s(μ). The module derives asymptotic freedom for QCD from the SU(3) color structure forced by the three-dimensional geometry Q₃ and the sign of the ladder derivative of the coupling. Key upstream conventions include the one-loop running formula α_s(μ) obtained from β(g) = (1/ln φ) dg/dr together with the explicit b₀ coefficient for six active flavors.
proof idea
This declaration is a direct numerical definition that assigns the constant 182.201 GeV to the anchor scale μ* with no further computation or tactic steps.
why it matters
The definition supplies the reference scale required by rs_alpha_s_MZ and rs_alpha_s_MZ_range to place the one-loop value of α_s(M_Z) inside the perturbative interval (0.11, 0.14). It also supports the comparison theorem gut_above_ew that places any GUT unification scale above the electroweak regime. Within the Recognition Science framework it instantiates the stationarity point demanded by the φ-ladder derivative of the coupling, consistent with the forced spatial dimension D = 3 and the eight-tick octave structure.
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