higgsYukawaBridgeCert_inhabited
plain-language theorem explainer
The theorem asserts that the Higgs-Yukawa bridge certificate is inhabited by exhibiting an explicit construction. Researchers modeling fermion masses via the Recognition Science phi-ladder would reference it to guarantee that all derived Yukawa couplings remain positive and obey the required scaling. The proof proceeds as a direct term that packages the pre-built certificate structure.
Claim. The type of the master certificate for the Higgs-Yukawa bridge is inhabited: there exists a structure $C$ such that for all species $s$, rung $r$, atomic number $Z$, and electroweak scale $v>0$, the Yukawa coupling $y_f=√2 m_f/v$ is positive, satisfies adjacent-rung scaling $y_f(s,r+1,Z,v)=φ·y_f(s,r,Z,v)$, obeys integer-rung scaling by $φ^n$, and has ratios independent of $v$.
background
In the Higgs-Yukawa bridge module the Yukawa coupling for a fermion is expressed as $y_f=√2 m_f/v$, where $m_f$ is supplied by the mass law on the phi-ladder. The master certificate collects four theorems: positivity for $v>0$, adjacent-rung scaling by $φ$, integer-rung scaling by $φ^n$, and independence of Yukawa ratios from $v$. This setting translates the standard-model extraction convention into the Recognition Science ladder structure while preserving phi-rung scaling across generations.
proof idea
The proof is a one-line term-mode wrapper that supplies the pre-constructed higgsYukawaBridgeCert definition as the inhabitant of the Nonempty type.
why it matters
This declaration confirms the existence of the complete Higgs-Yukawa bridge certificate, closing the construction begun in the module's main definition. It supports the claim that no Yukawa coupling needs independent fitting, as each is determined by the fermion's rung on the phi-ladder and the electroweak scale. The result aligns with the Recognition Science forcing chain by ensuring consistency with J-uniqueness and self-similar scaling, though the explicit rung map for each SM species remains an open task.
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