mass_ratio_top_up
plain-language theorem explainer
The definition assigns the top-to-up quark mass ratio the explicit value φ²². Quark mass hierarchy researchers cite it when deriving the CKM structure from the φ-ladder geometry. The assignment follows directly from the rung difference between top at rung 30 and up at rung 8.
Claim. The top-to-up quark mass ratio equals φ²², where φ is the golden ratio and the exponent is the difference between the assigned φ-ladder rungs for the top quark (30) and the up quark (8).
background
In the CKM Quark Mass Hierarchy from φ-Ladder module, quark masses sit on the φ-ladder via m_quark(k) = m_unit · φ^k with m_unit = φ^{-5}/8. The six quarks receive fixed rungs: up at 8, down at 9, strange at 14, charm at 17, bottom at 22, top at 30. These rungs are forced by the SU(3)×SU(2)×U(1) gauge structure on Q₃. The module states the structural prediction m_t / m_u = φ^{30-8} = φ^{22}.
proof idea
One-line definition that sets the ratio equal to phi raised to the power 22, using the rung difference top minus up.
why it matters
This definition supplies the explicit top-to-up ratio used inside the CKMHierarchyFromPhiLadderCert structure and the one-statement theorem ckm_hierarchy_one_statement. It realizes the Track F7 structural prediction that places the observed five-order mass span on the φ-ladder with per-rung factor exactly φ. The result sits inside the Recognition Science derivation of quark masses from the self-similar fixed point φ.
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