Theory of Generated Space — Particle-sector closure: a TGP-structured derivation of charged-lepton masses, the Koide relation, and the Cabibbo angle

Preprint and supporting numerical material for the TGP particle-sector closure paper, a companion to the TGP core paper (Zenodo DOI: 10. 5281/zenodo. 19670324). Starting from the substrate-field framework fixed by the core paper, we derive, from the same soliton ODE: (i) the charged-lepton mass law mₙ = cM · Aₜail, n⁴, with m_μ/mₑ = 206. 74 vs PDG 206. 768 (0. 013%) ; (ii) the Koide relation K = 2/3 as a theorem of the Brannen ratio B = b/a = √2; (iii) the integer N = 3 generation count from a metric-singularity barrier g0crit = 2. 206 with g0^τ safely inside the well; (iv) the Cabibbo angle λC via a Z₃ self-energy subtraction on GL (3, 𝔽₂), reducing PDG tension from 4. 8σ to 0. 75σ. The perturbative coefficient α₃ = π²/128 + Pcos is decomposed, with Pcos = 0. 0126159… shown at 40-digit precision to have no relation to any 24-element polylog/Clausen basis at max-coef 10¹4; it is promoted to a TGP-named constant. Quark Koide is shown to be RG-invariant under 2-loop QCD γₘ with Kᵤ = 0. 8746 and Kd = 0. 7398, and the neutrino Brannen-√2 ansatz is falsified by Δm² oscillation data (max K_ν = 0. 553 in NO), establishing that Koide K = 2/3 is a charged-lepton signature of the soliton ODE, not a universal law. The repository contains the paper source, compiled PDF, and the numerical folders that are directly cited: particleₛectorclosure/, brannenₛqrt2/, whyₙ3/, massₛcalingₖ4/, cabibbocorrection/, and neutrinoₘsw/.