The Complex Numbers and Unitarity of the Self-Referential Universe 3; The Self-Referential Consistency Principle and the Emergence of Quantum Spacetime

Based on the complex-number self-referential framework established in previous work, this paper proposes the ”Self-Referential Consistency Principle” aimedat unifying quantum mechanics and spacetime geometry. This principle assertsthat a fundamental physical theory must allow quantum superposition states tobe compatible with logical self-referential structures, and its mathematical form isexpressed as a fixed-point equation of self-referential operators. To implement thisprinciple, we construct a ”quantum self-referential network” model, whose states exist in the direct sum of hierarchical complex Hilbert spaces, with the physical stateof the system constrained by a global self-referential consistency condition. Weprove that the macroscopic coarse-graining limit of this network naturally yields afour-dimensional pseudo-Riemannian manifold from the second moment of information entropy. Its metric structure satisfies a covariant relation with the informationdensity field; the free energy extremum principle of the system further derives theEinstein-Hilbert action, reducing gravitational dynamics to a balance between information entropy and energy. Furthermore, this framework derives, from first principles, the microscopic definitions of interlayer map characteristic time and criticalcurvature, thereby obtaining the phase correction formula for the dispersion effectof gravitational wave propagation. Under Planck-scale parameters, this correctionis far below the sensitivity of current detectors, but as a unique fingerprint beyondgeneral relativity, it provides a clear theoretical prediction and testable target forfuture ultra-high-precision gravitational wave experiments.