Varying Fine-Structure Constant as a Cumulative Memory Field in a Bouncing Cosmology: A BSBM Formulation V3.0 Incorporating CERN LHC O-O Small-System QGP Evidence

We present CCFM V3.0 where the fine-structure constant varies as α(x^μ)=α0 exp(2ψ(x^μ)), with ψ a cumulative memory field across cosmic bounces. The discrete map is ψ_{n+1}=k ψ_n + Δψ_n with k=exp(-3∫H dt)<1, σ_{Δψ}=1.5×10^{-6}. We prove boundedness Var(ψ_N)=σ^2 (1-k^{2N})/(1-k^2)=1.46×10^{-11} giving |Δα/α|=7.6×10^{-6}, consistent with CODATA 2022 α0=0.00729735256, atomic clocks, Oklo, and quasar bounds. We incorporate recent CERN LHC Oxygen-Oxygen collisions at 6.37 TeV (2025) showing QGP formation in small systems as a methodological analogy for collective emergence. The bounce has a_min>0 with k=0.92 retention. Testable predictions: P1 dα/dt/α <1e-17 /yr, P2 Δα/α <1e-8 (Oklo), P3 dipole 1e-5, P4 dN_ch/dη ≈45±5 @5.02 TeV for O-O in ALICE Run 3-4. Methodological Protection: QGP ≠ ψ field, analogy only. Final Detailed Version July 26, 2026 - 604.90 KB - md5:1f68d65590c7d4820475c97592324641