dimensionalTransmutationDescription
plain-language theorem explainer
Dimensional transmutation in Recognition Science is expressed by the relation in which the proton mass emerges from the QCD scale generated by the running strong coupling. A physicist examining scale generation in gauge theories via φ-ladder rungs would cite this string when linking J-cost optimization to RG flow. The definition is a direct string literal with no computation or lemma applications.
Claim. Dimensional transmutation is described by the relation $m_p sim Lambda_QCD sim M_Pl exp(-c/alpha_s)$, where a dimensionless gauge coupling generates the mass scale $Lambda$ through renormalization-group evolution.
background
The module sets running couplings as the variation of J-cost with φ-ladder rung, where each rung labels an energy scale. The module doc states that α_s decreases with energy (asymptotic freedom) while α_em increases, all arising from φ-scaling of the Recognition Composition Law. Upstream, SpectralEmergence.of supplies the SU(3) gauge sector whose beta function drives the running, and PhiForcingDerived.of encodes the J-cost whose optimization produces the exponential suppression.
proof idea
One-line definition that directly assigns the string literal describing the transmutation formula. No lemmas or tactics are invoked.
why it matters
The definition supplies the textual anchor for QFT-011, the target of deriving running couplings from φ-scaling. It connects the mass formula (yardstick times phi to a rung offset) to the exponential dependence on 1/α_s that appears in the eight-tick octave and D=3 spatial structure. Although no downstream uses are recorded, it supports the sibling definitions alpha_s_Z and betaFunction that quantify the same running.
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