Clock–Dynamics Consistency Test in VER: Separating the Two-Channel Observable (˜g00,φ)

AbstractWithin the framework of Vacuum–Energonic Relativity (VER), we formulate an operational consistency test linking three classes of observations in a stationary gravitational field: (i) gravitationalredshift measured by clocks, (ii) local test-body dynamics, and (iii) the Shapiro/PPN channel. InVER, the physical matter metric ˜gµν and the energonicity field φ(x) > 0, which sets the localcausal speed limit via c(x) = √φ(x), jointly enter the observable redshift. Under the operationaldefinition of physical clock timed˜τ ≡ d˜sc(x) = d˜s√φ(x) ,wich reduced to d˜τ = dt for a locally resting clock, the stationary redshift acquires the exacttwo-channel formln ν1ν2 = 12 ln −˜g00(x2)−˜g00(x1) − 12 ln φ(x2)In the weak-field regime, this reduces toln ν1ν2 ≃∆Φg − 12∆u,φ(x1) .u ≡ δφφ∗.Accordingly, clocks, local dynamics, and the Shapiro/PPN channel generally probe different combinations of the same stationary fields. We show that confronting these three channels yields a directVER consistency test and makes it possible either to reconstruct the profile u(r) or to constrainthe effective Yukawa sector (mφ,∆) already in a non-cosmological regime. The proposed test thusprovides a straightforward route toward the falsifiability of VER on laboratory, geophysical, andnear-planetary scales.