This analysis computes the Wolfenstein ρ parameter using the inter-type torsion operator, indicating new findings in particle physics.
We compute the complete Wolfenstein ρ̄ parameter from the inter-type torsion operator on the truncated octahedron's 14-face graph. The operator O = [(C_A−1)P_sq + P_hx]·T, restricted to the two T₁u irreducible representations, yields a 2×2 effective generation matrix H with four Schur scalars. We discover three exact algebraic identities: tr(H) = 1/3, det(H) = −8, and the characteristic polynomial 3μ²−μ−24 = 0 whose discriminant is 289 = 17² = Δ² — the square of the master discriminant. The eigenvalues are μ₁ = C_A = 3 and μ₂ = −r₁r₂/(2C_A) = −8/3, tying the generation matrix directly to the colour number and master equation product. The CKM CP phase δ = arg(λ₁₂) = 66.36° was established in Paper #39. We derive R_b = r₁²/(r₁r₂−1) = (49−9√17)/30, an NLO correction to the tree-level ratio r₁/r₂ with factor 16/15 = r₁r₂/(r₁r₂−1), interpretable as a self-energy vertex renormalisation. This yields ρ̄ = 0.1590 (−0.002σ from PDG 2024), resolving the previous 1.0σ tension. The companion prediction η̄ = 0.363 sits at +1.5σ, attributable to the 0.91° offset in δ from the experimental central value. The combined CKM unitarity triangle is determined by cell integers alone, with no free parameters. We also report the first computation of the off-diagonal Schur scalar λ₂₁ = 0.004 − 2.252i, not previously published, completing the full 2×2 block structure.
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Luke Martin (2026) studied this question.
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