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World Scientific
Abstract
We propose a candidate theory of quantum gravity founded on the entropic projection of a
complex operator de¯ned in a Diagram Hilbert Space. This operator uni¯es mass–energy and
charge within a single microscopic entity whose spectral structure encodes the physical content
of both gravitational and gauge interactions. Embedding the microscopic dynamics within
partition functions - most notably QCD - provides spectral data for the operator, while
entropy maximization under energy and charge constraints yields Einstein's and Maxwell's
equations from its real and imaginary projections, respectively. Both ¯eld systems thus arise
from one statistical–variational principle. Hidden eigenstates of the operator naturally form
dark-matter halos with isothermal equilibrium pro¯les explaining °at galactic rotation curves.
Dark energy and black holes acquire consistent operator–entropic interpretations. The frame-
work therefore o®ers a testable route toward a uni¯ed quantum-gravitational theory in which
spacetime and gauge ¯elds emerge as macroscopic thermodynamic constructs of an underlying
operator algebra.
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