Beyond Relativity II - Isochron Surfaces and Translation Simultaneity

This foundational work defines simultaneity as a measurable geometry: an isochron surface Στ0={x∣T(x)=τ0}Στ0={x∣T(x)=τ0} derived from accumulated proper time T(x)T(x).It makes the field reconstruction a canonical part of theory via a variational thin-plate-spline formulation and provides a practical, numerically stable center CPCP (Euclidean mean plus orthogonal projection).A weak-field derivation links the mean curvature HH of Στ0Στ0 to mass density through Poisson’s equation H≈(4πGρ)/∥∇Φ∥H≈(4πGρ)/∥∇Φ∥, connecting geometry and gravitation.Applications include GNSS synchronization, satellite imaging, and structural time mapping at centimeter accuracy.The paper builds directly on The Third Observer and underpins Beyond Relativity III – The Proof of Now.