massRatio_32_canonical
plain-language theorem explainer
The theorem establishes that any rich ledger with canonical generation torsion yields a third-to-second generation fermion mass ratio of phi to the sixth power, independent of sector. Recognition Science researchers assembling generational mass hierarchies from the phi-ladder would cite this when closing the ratio triple. The term proof reduces the ratio via the rung difference lemma under the torsion hypothesis and simplifies the offset.
Claim. For any rich ledger $L$ with torsion equal to the canonical generation torsion function and any fermion sector $s$, the rung-derived mass ratio of third to second generation equals $m_3/m_2 = phi^6$.
background
A rich ledger augments a base ledger with a torsion map from generations to integers and base rungs per fermion sector. Fermion sectors are leptons, up quarks, and down quarks, each with a base rung from charge structure. The full rung is base plus torsion, so mass ratios are phi to the rung difference. Torsion values derive from D=3 cube combinatorics: generation 1 has offset 0, generation 2 has 11, generation 3 has 17. The module states that these produce the ratios phi^11, phi^17, and phi^6. The result depends on the rung difference lemma for canonical torsion.
proof idea
The term proof first simplifies the mass ratio definition, rewrites the rung difference using the canonical torsion hypothesis on the ledger, then simplifies the torsion difference expression.
why it matters
This supplies the Gen 3/Gen 2 ratio that completes the mass ratio triple in the downstream theorem massRatiosFromTiers_canonical. It realizes the key result in the module documentation that torsion from cube geometry yields phi^6 for the third-to-second ratio. The construction supports the Recognition Science derivation of masses on the phi-ladder with eight-tick octave structure.
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