Unified Scalar-Tensor Theory of Erflett Spacetime: The Shiodome Tensor and Geometric-Temporal Coupling

We present a complete unified field theory for the Erflett spacetime, combining Brans-Dicke scalar-tensor gravity with a novel geometric boundary tensor—the Shiodome tensor $S_{\mu\nu}$—that encodes the unique inverted pyramid geometry and north-south asymmetry inherent to Erflett. The tensor is rigorously derived from an extended Gibbons-Hawking-York boundary action. The theory is formulated through a modified Lagrangian density incorporating (i) a dynamical scalar field X representing temporalspatial coupling strength, (ii) the Shiodome tensor implementing boundary constraints and anisotropic spatial structure, and (iii) a multi-well potential $U(X, \phi, z)$ generating phase-dependent equilibria. We derive the complete field equations and implement finite difference method (FDM) numerical solutions on the pyramid domain $\Omega$, achieving sub-percent agreement (< 1% error) in proper time ratio τ with empirical measurements
from the Al'bina Institute Erflett Temporal-gravitational Calculation System (AISU-ETCS) API. The scalar field X shows up to 6% deviation near the vertex singularity, which we attribute to a known limitation of the API reference model rather than the theory itself. The north-south time flow asymmetry ratio $\tau_{North} / \tau{South} = 4.10$ is shown to be a mathematical necessity of the temporal chirality structure, independent of parameter values. Our results provide the first ab initio theoretical foundation for Erflett spacetime phenomena and establish a framework for future quantum field theory extensions.