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 Gₑff 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 ρc = 7. 4 ρₙuc = 1. 702 × 10¹5 g/cm³ (from MIT bag model, zero free parameters). THEORETICAL PREDICTION: Mₘax ≈ 4. 26 ± 0. 10 M_☉ NUMERICAL VERIFICATION: Python TOV integration with APR4 equation of state and I (ρ) = exp (-ρ/ρc) yields: - General Relativity baseline: Mₘax^ (GR) = 1. 9885 ± 0. 0012 M_☉ (verified against Read et al. 2009) - CCEGA framework: Mₘax^ (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 (GRᵥsCCEGAVERIFIED. 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 (CODEDOCUMENTATIONFINAL. 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 ρc parameter choice and require independent verification. Key limitation: This work derives Gₑff (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) Mₘax = 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: - GRᵥsCCEGAVERIFIED. py: Complete executable Python code for TOV integration - CODEDOCUMENTATIONFINAL. pdf: Technical documentation with methodology and results