Finite-Observer Corrections to Jacobson Thermodynamics: Record Entropy, Coherence Thresholds, and Stochastic Geometry

This work presents a finite-observer extension of Jacobson’s thermodynamic derivation of the Einstein equations. Instead of ideal point-like observers, observers are modeled as finite coherence-bounded domains with horizon-limited access, accumulated records, and residual fluctuations. Three correction structures emerge: a covariant record entropy contribution, a coherence-dependent operational temperature, and a stochastic geometric correction term. Standard general relativity is recovered in the high-coherence limit, while structured deviations appear near coherence thresholds. The formulation is explicitly scoped: correction terms are structural and require derivation from first principles. The paper establishes what modifications necessarily arise when observer finiteness is taken as a physical constraint.