canonical_massRatio_32
plain-language theorem explainer
The theorem establishes that the mass ratio between third and second generation fermions equals phi to the sixth power in the canonical recognition ledger, for any sector. Researchers deriving particle mass hierarchies from geometric torsion in Recognition Science cite this when linking cube combinatorics to the phi-ladder. The proof is a one-line term application of the general massRatio_32_canonical lemma on the canonical ledger and its torsion offsets.
Claim. For the canonical rich ledger and any fermion sector, the ratio of third-generation mass to second-generation mass equals $phi^6$.
background
Recognition Science places fermion masses on a phi-ladder where the full rung equals base rung plus generation torsion offset, and the mass ratio between generations is phi raised to their rung difference. The RSLedger module defines the rich ledger whose torsion values come from D=3 cube geometry: generation 1 offset 0, generation 2 offset 11, generation 3 offset 17. FermionSector is the inductive type with constructors leptons (base rung 2), upQuarks (base rung 4), and downQuarks (base rung 4).
proof idea
The proof is a one-line term wrapper that applies the lemma massRatio_32_canonical to the canonical ledger, the real parameter phi, the given sector, and the torsion structure of that ledger.
why it matters
This supplies the explicit inter-generation ratio Gen 3 over Gen 2 equals phi^6, completing the derivation of mass ratios from torsion structure rather than ad hoc formulas. It realizes the key result stated in the RSLedger module that connects cube combinatorics in three dimensions to the phi-ladder. The declaration supports the broader Recognition Science claim that mass hierarchies emerge from recognition geometry with torsion offsets as the only input.
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