m_u_contrib
plain-language theorem explainer
The definition sets the up-quark valence contribution to the proton mass equal to the mass function evaluated at rung 4 on the phi-ladder. Researchers decomposing the proton mass into valence and binding parts within Recognition Science cite this term when isolating the small quark component. It is realized as a direct one-line substitution of rung 4 into the general mass-on-rung construction.
Claim. The up-quark contribution is defined by $m_{u,contrib} = E_{coh} phi^4$, where $E_{coh}$ is the anchor coherence energy and $phi$ is the golden ratio.
background
In the mass hierarchy module, mass on rung is defined as the product of the anchor energy and phi raised to the rung index. This places particle masses on the phi-ladder with rung 4 assigned to the up quark. The ProtonMass module decomposes the proton mass into valence quarks at rung 4 and binding energy at a higher confinement rung, as stated in the module documentation: valence quarks contribute about 1 percent while binding supplies the rest. Upstream result mass on rung states: Mass in RS units: E_coh · φ^r where r is the rung.
proof idea
This definition is a one-line wrapper that applies mass_on_rung to the integer 4.
why it matters
It supplies the up-quark term required by m_valence and by the theorem binding_dominates, which shows binding energy exceeds valence mass by more than a factor of 40. The term fills the valence slot in the C-008 proton mass derivation, where rung 14 for confinement lies ten steps above rung 4 and produces the phi^10 separation. The placement rests on the phi-ladder structure with phi as the self-similar fixed point.
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