Quantum–Gravitational–Informational Theory (QGI): A Unified Approach Based on Informational Principles

The Quantum–Gravitational–Informational (QGI) Theory proposes that information is the primordial substrate of physical reality. In this work, we demonstrate how fundamental constants and physical relations naturally emerge from purely informational principles, without adjustable parameters. We derive the informational constant\[ \alpha_{\mathrm{info}} = \frac{1}{8\pi^3\ln\pi} \approx 0.00352174 \]and the scale-dependent effective dimensionality\[ D_{\mathrm{eff}}(r) = 4 \;-\;\frac{1}{8}\Bigl[1 + \frac{\alpha_{\mathrm{info}}\ln(r/r_0)}{\ln\pi}\Bigr]. \]From these, we obtain: - Weinberg angle with only 0.15 % error; - Fine–structure constant \[ \alpha = \alpha_{\mathrm{info}}^2 \,\frac{\ln(32)}{2\pi}\,\times\,1067.36 \approx0.007301 \quad(\approx1/136.94); \] - Universe composition (dark energy 67.52 %, dark matter 27.34 %, baryonic matter 4.48 %) with average error 3.89 %; - Cosmological constant \[ \Lambda = \frac{8\pi G}{c^4}\,\frac{\pi^{D_{\mathrm{eff}}}\,\alpha_{\mathrm{info}}}{L_{\mathrm{eff}}^2} \approx1.108\times10^{-52}\,\mathrm{m^{-2}} \] (1.10 % error); - A convolutional‐spectral model \(\phi^n/\pi^l\) reproducing the observed density fractions without free parameters. We validate numerically the key integrals (trapezoid, Simpson, adaptive quad, Gauss–Legendre), perform a statistical fit to \(H(z)\) data (\(\chi^2_{\rm QGI}=29.04\) vs. \(\chi^2_{\Lambda{\rm CDM}}=29.74\)), and propose four experimental tests (precision Bell–type interferometry, quantum‐processor simulations, high-ℓ CMB power spectrum, and high-energy Weinberg-angle measurements).