Differential Time as an Upstream Generative Framework Containing Special and General Relativity

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The paper directly extends the full Differential-Time model from the primitive comparison ΔT(λ)=S(λ)−C(λ) to a complete relativistic construction containing. Special Relativity as its flat inertial branch and General Relativity as its curved covariant branch. The upstream temporal structure is fixed operationally through a calibrated difference-selective comparator that receives external and observer clock signals and produces a direct beat, phase-difference, subtraction, or null record. From this measured differential output, the observer-side clock rate and temporal coframe are reconstructed. Directional null-exchange measurements supply the spatial coframe and shift, completing the spacetime metric. Within this construction, the paper derives the Lorentz factor and Lorentz transformation, invariant interval, relativity of simultaneity, time dilation, length contraction, velocity composition, rapidity, four-momentum, free-particle action, and the mass-shell relation. The curved branch proceeds from the generated coframe to the Lorentzian metric, Levi-Civita connection, geodesic motion, curvature tensors, Bianchi identity, Einstein tensor, Einstein-Hilbert variation, and the Einstein field equation with Newtonian normalization. The original Differential-Time cross, cross-window, temporal-information-weight, and admissibility structures are retained and connected to the same direct differential measurement channel. Weak-field, Schwarzschild, FLRW, and linearized gravitational-wave branches are developed as explicit consistency checks. The central result is a constructive containment relation: Differential-Time readout architecture⊃{SR,GR}.\text{Differential-Time readout architecture}\supset\{\mathrm{SR},\mathrm{GR}\}.Differential-Time readout architecture⊃{SR,GR}. SR and GR are therefore not rejected, replaced, or treated as incorrect. They appear as downstream relativistic sectors generated within the broader Differential-Time framework.

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