match_down_d
plain-language theorem explainer
The declaration shows that the legacy rung constructor returns 4 for the down quark. Mass-spectrum modelers in Recognition Science cite it when populating the phi-ladder table for first-generation fermions. The proof is a direct reflexivity evaluation of the rung definition on the down-fermion case.
Claim. The legacy rung constructor assigns rung number 4 to the down quark.
background
The rung constructor appears in the Motif module as a legacy definition that applies universal torsion values {0,11,17} to all charged species. Its documentation states it is correct for leptons and neutrinos but recommends compute_rung_sdgt for quarks. The surrounding module supplies matching theorems that place each standard-model fermion and boson on the phi-ladder used for mass formulas.
proof idea
The proof is a one-line wrapper that applies reflexivity to the definition of the rung constructor on the down-fermion species.
why it matters
It supplies the explicit rung value for the down quark inside the mass-matching table. The value feeds the mass formula yardstick times phi to the power of (rung minus 8 plus gap), consistent with the phi-ladder construction that follows from T5 J-uniqueness and T6 self-similar fixed point. No downstream theorems currently reference it.
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