MSFCM Paper X — The Modified Friedmann Equation with Torsion in the SGCC Framework: Derivation, Numerical Calibration from ε_pv, and the Non-Singular Cosmological Bounce

Derivation of the modified Friedmann equation H² = (8πG/3)ρ + Λ/3 + T₀ε²_pv(a₀/a)⁶ in the Riemann-Cartan framework of the SGCC. The torsion term is sourced by SMBH spin angular momentum preserved through the cosmological bounce via BHL coupling (Papers I-VI). Numerical calibration table maps ε_pv ∈ [0.55, 1.00] → (a_bounce, ρ_bounce/ρ_Pl, H_bounce/M_Pl) for |T₀| = 10⁻⁴ H₀². For ε_pv > 1/2 the torsion generates a repulsive term preventing the singularity; for ε_pv = 1/2 the equation reduces exactly to ΛCDM. Complete causal chain: LoTSS DR2 jet-filament alignment (z~0.3) → CMB cross-correlations (Papers VIII-IX) → bounce geometry (Paper X). Final paper of the MSFCM series. MNRAS submission: MN-26-1467-P. SHA-256 certified.