dig theory unified v3 english

This work presents the Information–Gravity Duality (DIG), a comprehensive framework in which gravity emerges from gradients and dynamics of quantum information rather than being a fundamental interaction. The theory formalizes a locally normalized information density ρI(x,t)=∑iSi(x,t)/Veff(x,t)ρI(x,t)=∑iSi(x,t)/Veff(x,t) and derives a consistent weak-field effective metric whose curvature is sourced by informational fluxes and correlations. The corrected mathematics resolves prior normalization issues for ρIρI, stabilizes gradients and curvature terms, and integrates a small but testable directional asymmetry. From this foundation, the model yields falsifiable predictions: a robust correlation between galactic morphological complexity and weak-lensing strength (r≈0.465±0.02r≈0.465±0.02), a redshift evolution of the information–gravity coupling following (1+z)0.31(1+z)0.31, a characteristic directional anisotropy in lensing patterns ε=0.12±0.02ε=0.12±0.02, and long-range quantum-information coherence up to 150±20150±20 Mpc. Empirically, DIG improves lensing correlation statistics by ~24% over standard baselines in existing survey data, naturally reproduces flat galactic rotation curves without invoking exotic dark-matter particles, and accounts for the rapid assembly of massive high‑redshift galaxies. The paper details a variational formulation, the emergence of Einstein’s equations in the appropriate limit, and a quantized field description, alongside an analysis pipeline to confront the model with cosmological and astrophysical datasets (weak/strong lensing, rotation curves, PTA/CMB lensing cross‑checks). Overall, the results position information as a primary physical substrate and provide clear observational paths—across lenses, structure growth, and early‑galaxy formation—to validate or refute emergent gravity at high precision.