massRatio
plain-language theorem explainer
Recognition Science sets the mass ratio between successive fermion generations to the golden ratio phi. This supplies the scaling for approximate hierarchies such as top/charm ≈ φ^10 and muon/electron ≈ φ^11. Particle physicists addressing the three-generation puzzle cite it when linking the 8-tick cycle to Standard Model structure. The definition is a direct one-line assignment to the self-similar fixed point.
Claim. The mass ratio between successive generations satisfies $m_3/m_2 ≈ m_2/m_1 ≈ φ$, where $φ$ is the golden ratio fixed point of the J-function.
background
The module derives three generations from the 8-tick cycle (period 2^3) crossed with three spatial dimensions, where each generation corresponds to a distinct parity combination across the three bits indexing the cycle. The golden ratio phi enters as the self-similar fixed point forced in the upstream chain (T6). Upstream results include the generation torsion tau from Masses.Anchor, which maps generations 0,1,2 to torsion values 0,11,17, and the Model structure from LawOfExistence that supplies positive constants for defect mass and energy gap.
proof idea
The declaration is a one-line definition that assigns the mass ratio directly to phi.
why it matters
This definition supplies the scaling factor used in GaugeBosonMassCert to certify boson mass ratios and in WZBosonRatioScoreCardCert for empirical bracket checks. It connects the phi-ladder mass formula to the eight-tick octave (T7) and D=3 (T8), filling the mass hierarchy pattern in the module's derivation of exactly three generations. It touches the open question of why the Standard Model exhibits precisely three families.
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