Local Horizon Thermodynamics and Einstein Gravity in a Source–Readout Architecture

This paper reconstructs Ted Jacobson’s thermodynamic derivation of the Einstein equation within Shadow Theory’s source–readout architecture. A single prepared bundle of null generators supplies the boost-energy flux, Unruh temperature, and horizon area change. In the local equilibrium limit, the paper proves that the Clausius relation on a determining set of null directions is equivalent to the Einstein equation, given local stress-energy conservation and the stipulated temperature and area–entropy laws. The derivation recovers the gravitational coupling and leaves the cosmological constant undetermined. The paper gives an explicit nine-direction reconstruction in four spacetime dimensions and identifies the four-dimensional ambiguity left by measurements on a circle of null directions. It also derives the first finite-length correction to the area-based Clausius relation along an equilibrium generator. A boost-weighted expansion prescription cancels the cubic correction and gives a remainder of definite sign under the stated readout assumptions.