lambda_QCD
plain-language theorem explainer
Recognition Science sets the QCD scale Λ_QCD to the numerical value 200 MeV as a fixed input for coupling calculations. Researchers deriving asymptotic freedom or proton mass ratios within the φ-ladder framework cite this constant directly. The definition is a one-line numerical assignment that supplies the scale for downstream order-of-magnitude theorems.
Claim. The QCD scale is defined by the assignment Λ_QCD := 200 MeV.
background
The module QFT-011 derives running couplings from φ-ladder scaling, where distinct rungs label energy scales and J-cost optimization changes with rung. Different couplings run differently: α_s decreases with energy (asymptotic freedom) while α_em increases. The setting imports nuclear density structures from NucleosynthesisTiers, ledger factorization from DAlembert, and spectral emergence that forces the SU(3) factor of the gauge group.
proof idea
The definition is a direct numerical assignment of the constant 200 in ℝ with an MeV annotation. No lemmas or tactics are invoked; the body is a primitive input value.
why it matters
This supplies the fixed scale used by lambda_qcd_scale (proving 100 < Λ_QCD < 300) and by protonToQCDRatio (proving the ratio lies between 4 and 6). It anchors the QCD sector inside the running-couplings derivation from φ-ladder scaling, consistent with the framework's T5 J-uniqueness and the eight-tick octave. The assignment leaves open the question of an exact first-principles derivation from the Recognition Composition Law.
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