bottom_rung
plain-language theorem explainer
The bottom-quark rung receives the fixed natural-number value 22 on the phi-ladder that organizes the six quark masses. Researchers deriving structural CKM hierarchies from recognition geometry cite this assignment when stating the third-generation down-type position. The declaration is a direct constant assignment that supplies the integer for subsequent ordering and certificate constructions.
Claim. The bottom-quark rung is the natural number 22, locating the b-quark at position 22 on the ladder where quark masses obey $m(k)=m_0·ϕ^k$ with $m_0=ϕ^{-5}/8$.
background
The module places the six quarks on a phi-ladder whose rungs are fixed by the SU(3)×SU(2)×U(1) gauge structure on the third generation: up at 8, down at 9, strange at 14, charm at 17, bottom at 22, top at 30. Masses then satisfy the geometric progression $m(k)=m_0·ϕ^k$ with unit mass $m_0=ϕ^{-5}/8$. Upstream rung maps in anchor and RSBridge modules supply the integer patterns that this assignment follows.
proof idea
The declaration is a direct constant definition that sets the bottom rung to 22. It functions as a one-line assignment supplying the integer for the strict-ordering theorem and the master hierarchy certificate.
why it matters
This definition supplies the rung value required by the CKMHierarchyFromPhiLadderCert structure, which certifies six-quark count, strict ordering u<d<s<c<b<t, and per-rung ratio exactly ϕ. It completes the assignments needed for the one-statement theorem that recovers the top-to-up ratio ϕ^22. The assignment aligns with the Recognition Science mass formula and the phi self-similar fixed point.
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