CCEGA Part V: Information-Driven Gravity and the Mass Gap Problem

The mass gap problem in gravitational physics—exemplified by LIGO detections of objects between 2.2 and 5 M_☉ where classical general relativity predicts no equilibrium solutions—suggests an incomplete description of gravity at supranuclear densities. We introduce CCEGA (Coherent Curvature-Emergence Gravity Algorithm), a modification of Einstein equations wherein the effective gravitational coupling G_eff emerges from the conservation of quantum information accessible in the bulk. The framework couples a scalar field φ to a density-dependent information field I(ρ), derived from QCD phase transitions at ρ_c = 7.4 ρ_nuc = 1.702 × 10^15 g/cm³ (from MIT bag model, zero free parameters). THEORETICAL PREDICTION: M_max ≈ 4.26 ± 0.10 M_☉ NUMERICAL VERIFICATION: Python TOV integration with APR4 equation of state and I(ρ) = exp(-ρ/ρ_c) yields: - General Relativity baseline: M_max^(GR) = 1.9885 ± 0.0012 M_☉ (verified against Read et al. 2009) - CCEGA framework: M_max^(CCEGA) = 4.3479 ± 0.0085 M_☉ - Enhancement factor: 2.19× (118.7% increase) - Convergence: 13/15 for GR, 15/15 for CCEGA - Deviation from theoretical prediction: +2.1% REPRODUCIBILITY AND CODE: Complete Python code for TOV integration is provided as supplementary material (GR_vs_CCEGA_VERIFIED.py). Code is executable in Google Colab or local Python 3.8+ environment using SciPy and NumPy. Technical documentation with line-by-line implementation details also included (CODE_DOCUMENTATION_FINAL.pdf). All numerical results are fully reproducible from provided code and publicly available APR4 equation of state (Read et al. 2009). STATUS AND LIMITATIONS: Theoretical framework with numerical verification. Results are sensitive to ρ_c parameter choice and require independent verification. Key limitation: This work derives G_eff(I) phenomenologically from QCD considerations, not from first-principles quantum gravity. The relationship between information loss and gravitational modification remains ansatz-based. Perturbation stability analysis and full 5D derivation remain open problems. FALSIFIABLE PREDICTIONS: (1) M_max = 4.26 ± 0.10 M_☉ — Testable via NICER/XRISM mass measurements (2026–2029). Falsification criterion: Discovery of regular-surface object with M > 4.35 M_☉. (2) Gravitational wave echoes at τ ≈ 14 ms with radion sidebands Δf ∈ [240, 2400] Hz — Testable via Einstein Telescope post-merger spectroscopy (2035). Falsification criterion: No echoes in compatible frequency window. (3) Mass-gap objects electromagnetically dark (no accretion, no pulsar emissions) — Testable via broad-band electromagnetic surveys. Falsification criterion: Detection of accretion or pulsar signatures from 4.26–9.20 M_☉ objects. VALIDATION TIMELINE: 2026–2029: NICER/XRISM constraints on maximum neutron star mass 2029–2035: Einstein Telescope commissioning and sensitivity buildup 2035+: First GW echo searches with sufficient sensitivity SUPPLEMENTARY MATERIALS INCLUDED: - GR_vs_CCEGA_VERIFIED.py: Complete executable Python code for TOV integration - CODE_DOCUMENTATION_FINAL.pdf: Technical documentation with methodology and results