res_up
plain-language theorem explainer
The definition supplies the residue for the up quark as the rational number -71/4. Researchers deriving bare quark masses in the Recognition Science framework cite this constant to obtain m_up via the structural mass scaled by phi to this power. The value corresponds to the ideal topological position R = -17.75 under the quarter-ladder hypothesis. The assignment is a direct rational constant with no computation.
Claim. The residue for the up quark on the phi-ladder is $r_{up} = -71/4$.
background
The module formalizes the Quarter-Ladder Hypothesis for quark masses. Quarks share the structural base mass with leptons but occupy quarter-integer rungs on the phi-ladder. The ideal positions include up at R = -17.75 = -71/4, with light-quark discrepancies attributed to non-perturbative QCD effects. The mass formula is m = m_struct * phi^res. Upstream, Mass is defined as the real numbers.
proof idea
The definition is a direct assignment of the rational constant -71/4 to the up-quark residue.
why it matters
This constant completes the set of six quark residues required by the quarter-ladder hypothesis in the Recognition Science mass derivation. It supplies the input for the predicted up-quark mass, which matches observation to approximately 2 percent. The value aligns with the phi-ladder structure and the forcing chain that derives D = 3 and the alpha band from J-uniqueness.
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