From UD Theory to General Relativity: A Complete Derivation of Gravitational Theory

Abstract We establish the foundations of UD theory and derive general relativity as its macroscopic limit. The universe originates from a critical state of dynamic equilibrium (U=D), where two fundamental attributes continuously compete. After symmetry breaking, four aspects emerge as physical fields. Two sequential normalization conditions govern the pre-breakdown (linear sum) and post-breakdown (quadratic integral) phases. The structural constant e^ is obtained through physical image identification at extreme limits: characterizes the balance of radial condensation and isotropic resistance at the black hole limit; e^ characterizes self-driven expansion at the vacuum limit, with e identified as the natural base of U's intrinsic dynamics. Macroscopic background values UU=UD=1/4, DD=DU=1/ (4e^) follow from critical state inheritance and the vacuum rejection mechanism. Four exhaustive mathematical projections emerge: scalar (gravity), spinor (quantum mechanics), vector (electromagnetism), and tensor (spacetime geometry). The tensor projection constructs g_ from the energy-momentum tensor of the four-aspect fields. The scalar projection yields a scalar-tensor theory; when freezes via the intrinsic chameleon mechanism at ₀=8/17, the theory reduces to general relativity. The post-Newtonian parameter -1-6. 510^-6 is consistent with Cassini constraints. All derivations are self-contained. Key Points - UD theory employs **physical image identification** at extreme limits—a legitimate a priori paradigm analogous to Einstein's equivalence principle being identified prior to field equations- Structural constant e^ encodes the inseparability of black hole and vacuum limits under exact U D duality- General relativity emerges as the frozen-scalar limit with intrinsic chameleon screening- -1 is structurally determined and robust across orders of magnitude- UD theory is a metatheory: it reveals GR's origin without replacing it References Will (2014), Living Rev. Rel. 17, 4; Bertotti et al. (2003), Nature 425, 374; Planck Collaboration (2020), A Abbott et al. (2016), PRL 116, 061102; Brans Khoury Damour & Esposito-Farese (1992), CQG 9, 2093.