pith. sign in
def

rs_alpha_s_anchor

definition
show as:
module
IndisputableMonolith.Physics.RunningCouplings
domain
Physics
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plain-language theorem explainer

RS α_s anchor supplies the numerical value of the strong coupling at the Recognition Science stationarity scale μ* as 0.1181. A physicist computing one-loop QCD running from the φ-ladder to the Z scale would cite this constant when evaluating α_s(M_Z). The declaration is a direct numerical assignment with no internal derivation or lemma applications.

Claim. The strong coupling constant at the Recognition Science anchor scale is defined by $α_s(μ^*) := 0.1181$.

background

The module develops renormalization group evolution of couplings from the RS φ-ladder. The anchor scale μ* = 182.201 GeV is a stationarity point of the RG flow. Asymptotic freedom in QCD follows from the SU(3) color structure forced by Q₃, with the β-function sign determined by the φ-ladder derivative of the coupling. Key results include β(g) = (1/ln φ) dg/dr and the one-loop running formula for α_s(μ).

proof idea

Direct definition that assigns the constant 0.1181. No lemmas or tactics are invoked; the value functions as an empirical input for downstream running calculations.

why it matters

This anchor feeds rs_alpha_s_MZ and the range theorem rs_alpha_s_MZ_range that confirm the perturbative regime at M_Z. It supplies the starting point for the RS renormalization group flow whose β-function sign is fixed by the φ-ladder derivative, realizing asymptotic freedom for n_f ≤ 16 flavors inside the Recognition Science framework.

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