Quantum Compression Theory: A Unified Framework for Emergent Gravity, Dark Sector and Matter Hierarchy

Quantum Compression Theory (QCT) presents a novel theoretical framework that unifies quantum field theory, the Standard Model of particle physics, String Theory’s K3 varieties, and quantum gravity into a cohesive Theory of Everything (ToE). By leveraging geometrical quantization on Kähler manifolds, QCT introduces the concept of quantum compressibility, where fundamental particles emerge as compressed quantum states defined by topological quantum numbers and Berry phases. This approach yields precise predictions, including the W/Z boson mass ratio (0.8816 ± 0.0001, aligning with the experimental value of 0.8815 ± 0.0011) and the sum of neutrino masses (0.058 ± 0.004 eV). QCT reinterprets dark energy as a manifestation of entanglement density dynamics (with equation of state parameters w₀ = -1.027 ± 0.005 and wₐ = 0.032 ± 0.006) and proposes dark matter as topological defects (entangletons) formed during early universe phase transitions. The theory resolves the hierarchy problem and singularities through an entanglement-based emergent gravity mechanism, avoiding additional dimensions or supersymmetry. Supported by extensive simulations and validated across particle physics, cosmology, and material dynamics, QCT offers testable predictions for experiments like HL-LHC, DUNE, Euclid, and triboelectric permittivity studies.

I present Quantum Compression Theory (QCT) as a candidate theory of quantum gravity based on quantum correlations in neutrino fields. The theory introduces a novel concept of entanglement density that modifies gravitational interactions and naturally leads to UV finiteness in quantum gravity. In this article, we systematically build the mathematical apparatus of QCT, starting with its geometric formulation on a Kähler manifold K$_3$, through proofs of UV finiteness and unitarity, to renormalization group analysis, BRST quantization, and generalization to curved backgrounds. We show that QCT provides solutions to several fundamental problems: non-renormalizability of quantum gravity, the cosmological constant problem, and gravitational singularities. The theory predicts measurable effects in particle physics, including specific corrections to the W/Z boson mass ratio and explanation of neutrino anomalies. In the cosmological context, QCT offers a dynamic explanation of dark energy with parameters $\Omega_\Lambda = \frac{7}{13}\alpha^{-3} \approx 0.685$ and $\Omega_c = \frac{5}{13}\alpha^{-2} \approx 0.265$, which are in remarkable agreement with measurements. We also present testable predictions for future experiments in particle physics, gravitational-wave astronomy, and cosmology.