massHierarchyPattern
plain-language theorem explainer
Mass ratios among Standard Model fermions follow powers of the golden ratio on the phi-ladder, matching listed approximations such as top over charm near phi to the tenth. Researchers on the three-generation puzzle cite the pattern when mapping 8-tick by 3D structure to fermion spectra. The definition is a direct string assignment with an attached comment that records the numerical matches.
Claim. Mass ratios satisfy top/charm $approx phi^{10}$, charm/up $approx phi^{13}$, tau/muon $approx phi^{6}$, muon/electron $approx phi^{11}$, with the general pattern that masses scale as $phi^n$ for generation-dependent integers $n$.
background
The module derives exactly three generations from the 8-tick cycle crossed with three spatial dimensions, where generations arise as distinct parity combinations across the three bits that index the cycle. The phi-ladder places quantities on discrete tiers indexed by powers of phi, as seen in the upstream scale definition that returns phi raised to a natural-number exponent. Upstream rung definitions map classes or objects to natural numbers that serve as these tier indices, while structures for J-cost and ledger factorization supply the recognition-cost calibration that underlies the ladder.
proof idea
One-line definition that assigns the string literal describing phi^n scaling for generation-dependent n, together with the attached comment that lists the four approximate ratios.
why it matters
The definition records the mass scaling pattern inside the three-generations module that links the 8-tick octave and D=3 to observed fermion hierarchies. It aligns with the Recognition Science mass formula on the phi-ladder and supports the module's target of a PRL paper deriving the generation count from RS structure. No downstream uses are recorded.
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