torsion_diff_31
plain-language theorem explainer
The torsion difference between the third and first generations equals 17. Researchers computing fermion mass hierarchies on the φ-ladder in Recognition Science cite this when fixing generation offsets for ratio calculations. The proof is a one-line simplification that unfolds the torsion difference definition.
Claim. The torsion difference between the third and first generations satisfies $τ_3 - τ_1 = 17$.
background
The RSLedger module equips Recognition Science with a rich ledger that derives particle masses from generation torsion offsets on the φ-ladder rather than from direct φ-formulas. Torsion values arise from D=3 cube combinatorics: the ground generation carries offset 0, the edge-dressed generation carries 11, and the face-plus-edge generation carries 17. The upstream definition states that the torsion difference between two generations is the integer subtraction of their respective generation torsions.
proof idea
The proof is a one-line wrapper that applies simplification to the definition of torsion difference.
why it matters
This lemma supplies the numerical offset 17 required for the Gen 3 to Gen 1 mass ratio φ^{17} inside the Recognition Science mass formula. It completes the torsion triple {0, 11, 17} that produces the inter-generation ratios φ^{11}, φ^{17}, and φ^6 from D=3 cube geometry. The result anchors the RSLedger structure that feeds downstream mass derivations for fermion sectors.
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