Paper 7 of the Field of Resonance (FoR) series, version 2. This version substantially extends v1a (DOI: 10. 5281/zenodo. 19246232) with three new results and a new section situating the work within the Asymptotic Safety programme. The gravitational damping coefficient cₗin is derived from first principles via the Wetterich functional renormalisation group trace for the dimension-6 Skyrme operator in the curved SU (2) TEGR background. Using the Barvinsky-Vilkovisky heat kernel ratio a₄ (□²) /a₄ (□) = 1/2 for biharmonic operators, the result is cₗin (g̃, λ̃) = 5g̃/12π (1−2λ̃) ², replacing the placeholder estimate of v1a. The three-coupling stability matrix of the fully coupled gravity-Skyrme system yields a new critical exponent θₑ ≈ −1. 74. Since θₑ < 0, the Skyrme direction is UV-irrelevant: e* is uniquely fixed by the gravitational fixed point with no additional free parameter. The theory has exactly two UV-relevant directions, as required by Asymptotic Safety predictivity. The structural prediction G·MSk² = K·ħc is expressed in terms of the scheme-independent critical exponents θ₁ and θ₂ as K ≈ 0. 054·θ₁³·⁹³·θ₂⁻⁵·²⁹. Using the Padé-resummed result θ₁ = 2. 49 ± 0. 03, θ₂ = 1. 54 ± 0. 05 (Falls-Litim-Platania 2020), this gives K ≈ 0. 20–0. 36 and MSk ≈ 0. 45–0. 60 × MPl — the preon Skyrmion mass is predicted to be slightly sub-Planckian. This is a factor of ten improvement in predictive range over v1a (which had K ∈ 28–800).
Bruce Hunter (Fri,) studied this question.