alpha_s_prediction
plain-language theorem explainer
alpha_s_prediction defines the strong coupling constant at the Z scale as phi to the power -3 divided by pi, where phi is the self-similar fixed point of the Recognition framework. Gauge theorists and unification model builders would cite it as the structural output of the eight-tick gauge geometry for the strong sector. The definition is a direct algebraic assignment with no reduction steps or lemmas applied.
Claim. $α_s(M_Z) = φ^{-3} / π$, where $φ$ is the golden-ratio fixed point satisfying the Recognition Composition Law and the eight-tick octave structure.
background
The module derives the strong coupling from the RS framework using the 8-tick gauge structure. The three gauge couplings at the unification scale are fixed by cube geometry: electromagnetic from 44π resummation, weak from sin²θ_W = (3-φ)/6, and strong from the remaining degrees of freedom. The key structural claim is that α_s(M_Z) equals φ to an integer power determined by running from the recognition scale. Upstream results supply phi as the T6 self-similar fixed point and the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y).
proof idea
This is a direct definition that assigns the closed-form expression phi ^ (-(3:ℤ)) / Real.pi with no tactics or lemmas invoked.
why it matters
The definition supplies the concrete value used by the downstream theorem alpha_s_positive (which proves positivity via div_pos) and the StrongCouplingCert structure (which adds gauge_sum_prediction = 12π and the 36-to-48 bounds). It realizes the module's Q9 question on deriving α_s(M_Z) from φ-geometry, consistent with the eight-tick octave (T7) and D=3 spatial dimensions (T8). It leaves open the explicit running calculation from the recognition scale to M_Z that would match the PDG interval 0.1180 ± 0.0009.
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