summary
plain-language theorem explainer
Summary assembles five statements on phi-ladder energy scales, QCD asymptotic freedom with beta0 equal to 7, GUT unification at alpha equal to 1/24, Lambda_QCD near 200 MeV, and the proton mass ratio near 5, each labeled proven. A physicist studying renormalization group flow or grand unification would cite it to anchor Recognition Science results on coupling evolution. The body is a direct list literal with no computation or external calls.
Claim. The summary is the list containing the strings: Scales are $phi$-ladder rungs - PROVEN; QCD asymptotic freedom ($beta_0 = 7$) - PROVEN; GUT at $alpha = 1/24 = 1/(8 times 3)$ - PROVEN; $Lambda_{QCD} sim 200$ MeV - PROVEN; and $m_p / Lambda_{QCD} sim 5$ - PROVEN.
background
The module derives running couplings from phi-ladder scaling, where each rung corresponds to a distinct energy scale and J-cost optimization varies across rungs. Couplings run because the Recognition Composition Law and phi-forcing change the effective J-cost at successive ladder steps. The single upstream dependency is the proton mass definition m_p equal to valence mass plus binding energy, which supplies the final ratio entry.
proof idea
The definition is a literal list of five strings. No lemmas are applied; the body directly enumerates the module's claimed results without reduction or tactic steps.
why it matters
It closes the QFT-011 module by listing the concrete outputs that follow from phi-ladder scaling and the positive beta0 for SU(3). The list references the eight-tick octave structure and the phi fixed point that force the GUT value 1/24. No downstream uses exist, so the definition serves only as an internal summary of the running-coupling claims.
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