Strong coupling constant α_s
The strong coupling constant α_s is, in the τ-framework, the τ-effective dimensionless coupling of the strong (C) sector — derived as α_s = 2 κ(C; 3) = 2 ι_τ³/(1 − ι_τ). It is a Layer-1 dimensionless readout of the master constant; the τ-prediction agrees with PDG (at M_Z) to ∼2.4%.
τ-Definition
The strong coupling constant α_s is, in the τ-framework, the τ-effective dimensionless coupling of the strong (C) sector — derived as α_s = 2 κ(C; 3) = 2 ι_τ³/(1 − ι_τ). It is a Layer-1 dimensionless readout of the master constant; the τ-prediction agrees with PDG (at M_Z) to ∼2.4%.
Categorical invariant. α_s = 2 · κ(C; 3) = 2 ι_τ³ / (1 − ι_τ) — the strong-sector readout, twice the depth-3 κ-coupling.
Primary registry anchor:
IV.D182
τ-Derivation Chain
-
I.K0— Universe Postulate -
IV.D255— Master constant ι_τ -
IV.D182— τ-strong coupling constant α_s — strong sector readout -
IV.T76— Uniqueness of the strong coupling — α_s = 2κ(C) is the unique τ-form -
V.T142— E₁ Completeness — α_s = 2 ι_τ³/(1 − ι_τ) ≈ 0.1206 (∼2.4%)
Lean modules referenced:
TauLib.BookIV.Calibration.DimensionlessCouplings,
TauLib.BookV.Coda.ConstantsLedger
SI Translation
Numerical value: 0.1206 ± 0.0029 dimensionless
Calibration anchor: PG-P01-neutron
Calibration chain:
- Layer 0: ι_τ = 2/(π + e_math)
- Layer 1: κ(C; 3) = ι_τ³/(1 − ι_τ) ≈ 0.0603
- Layer 1: α_s = 2 κ(C; 3) ≈ 0.1206
- PDG α_s(M_Z) ≈ 0.1179(9); deviation ∼2.4%
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex