CCEGA Part VI: Critical Density Resolution via CFL Quark Matter

The CCEGA modified gravity framework predicts maximum neutron star masses of Mₘax ≈ 4. 26 M☉ using a critical density parameter ρc = 7. 4 ρₙuc derived from the MIT bag model. However, recent observations of massive neutron stars—specifically PSR J0740+6620 (2. 17 ± 0. 10 M☉) and PSR J0952-0607 (2. 35 ± 0. 17 M☉) —impose constraints that require ρc ≥ 10 ρₙuc for consistency with CCEGA predictions. We provide a semi-rigorous derivation of the critical density by combining two well-established models: (1) the APR (Akmal-Pandharipande-Ravenhall) nuclear equation of state for hadrons (fitted to nuclear saturation data), and (2) the Alford et al. color-flavor-locked (CFL) quark matter model (from high-density QCD). By applying the Gibbs thermodynamic condition Pₕadron (ρ) = PCFL (ρ) at the phase transition, numerical evaluation yields: ρc = 10. 0 ± 0. 1 ρₙuc (range: 9. 9-10. 2 ρₙuc) This result is consistent with observational requirements and demonstrates that the critical density emerges naturally from combining MIT bag model deconfinement with CFL stabilization physics, without arbitrary parameter tuning. The information field I (ρ) in CCEGA acquires a physical interpretation as the saturation fraction of CFL quark-pair condensates. We clearly distinguish between heuristic estimates and semi-rigorous derivations, identify assumptions and limitations, and propose future work (lattice QCD at finite density) needed for full first-principles calculation. METADATA FIELDS: Publication date: 2026-04-13 Version: 2. 0 Language: English Publication type: Preprint License: Creative Commons Attribution 4. 0 International (CC-BY-4. 0) charvel. neo@gmail. com / charvel112@gmail. com ================================================================================ 1. P46CCEGAFINALWITHDERIVATION. pdf Descripción: "Main manuscript (12 pages) " 2. P46CCEGAFINALWITHDERIVATION. tex Descripción: "LaTeX source code" 3. rhocderivacionₛemiᵣigorous. png Descripción: "Figure 1: Semi-rigorous derivation showing Gibbs condition" 4. ccegaᵣhocₐnalysis. py Descripción: "Python code for numerical verification" 5. ccegacolabₛimple. py Descripción: "Simplified Python version