massHierarchyPattern
plain-language theorem explainer
The massHierarchyPattern definition encodes the observation that Standard Model fermion masses follow scaling as powers of the golden ratio φ on the phi-ladder, matching ratios such as top/charm near φ^10 and muon/electron near φ^11. Particle physicists examining fermion generation structure would cite this when connecting empirical hierarchies to Recognition Science's 8-tick cycle in three dimensions. It is implemented as a direct string literal assignment with no computation.
Claim. Fermion masses satisfy approximate relations $m_t/m_c ≈ φ^{10}$, $m_c/m_u ≈ φ^{13}$, $m_τ/m_μ ≈ φ^6$, and $m_μ/m_e ≈ φ^{11}$, where the exponents arise from distinct rungs on the phi-ladder.
background
Recognition Science places physical quantities on discrete tiers of the phi-ladder, with masses given by yardstick times φ raised to a rung-dependent power. The module derives exactly three generations from the 8-tick cycle (period 2^3) crossed with three spatial dimensions, indexing the eight phases by three bits each tied to one dimension. Upstream results supply rung as a natural number indexing tiers and scale functions returning φ^k, drawn from Cosmology.LargeScaleStructureFromRS.scale and Compat.Constants.rung.
proof idea
This definition is a one-line wrapper that directly assigns the descriptive string summarizing the phi-ladder mass scaling pattern for generations.
why it matters
This definition supplies the concrete mass hierarchy pattern that accompanies the module's derivation of three generations from the 8-tick by 3D structure. It fills the paper proposition of a PRL derivation of generation number. It touches the open question of the origin of three generations by linking to framework landmarks T7 eight-tick octave and T8 D=3.
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