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Lorentz-Covariant Completion of the Enchan Field and Earth Weak-Field Validation

This work investigates whether the Enchan Field—a finite-tension geometric order field S with a proposed weak-field effective metric—can be embedded consistently in a Lorentz-covariant spacetime description without introducing a fundamental preferred frame.

The scalar Enchan field equation is shown to be Lorentz covariant when its sources are scalars. A scalar-only metric construction is then shown to be insufficient for rotation, motivating a symmetric tensor completion. Using the frozen normalization σvac=c4/(4πG), the weak-field tensor sector reproduces the static Earth potential and generates the rotational g0i sector from the same source equation. The stationary geometry is separated into a scalar clock-rate sector and a synchronization connection, allowing static temporal gradients and rotational temporal circulation to be treated consistently within one covariant framework.

With theory-side Earth inputs frozen before comparison, the framework recovers Newtonian acceleration, gravitational clock redshift, light deflection, Shapiro-type propagation delay, geodetic precession, and frame dragging. For Gravity Probe B, the spherical weak-field calculation predicts a geodetic drift of −6620.97 mas/yr and a frame-dragging drift of −40.93 mas/yr, corresponding to deviations of 1.05σ and 0.52σ from the reported measurements, respectively. No Earth observational value is used to fit the theory coefficients.

The Earth weak-field and slow-rotation completion is therefore closed at the level tested here. The remaining all-regime problem is isolated as an explicit open lemma: construct a diffeomorphism-invariant nonlinear action whose scalar projection reproduces the finite-tension Enchan equation, whose high-acceleration linearization reproduces the tensor equation, and whose matter coupling and metric variation close consistently with stress-energy conservation and the Bianchi identity.