Dark Matter and Dark Energy as Finite-Observer Corrections to Thermodynamic Gravity: A Unified Structural Derivation from the Persistent Uncertainty Law via Global Admissibility Compensation and Jacobson Thermodynamics

This paper proposes that dark matter and dark energy are not independent substances, but two thermodynamic correction channels generated by the same structural constraint: the Persistent Uncertainty Law (Ug > 0) applied to finite observer domains through the Jacobson thermodynamic derivation of gravity. The framework derives: • Shell-localized effective gravitational enhancement Gₑff (C) > G near coherence thresholds, producing dark-matter-like halo structure without additional matter content. • A bounded dynamic dark-energy correction around baseline vacuum energy: rhoDE (z) = rhoL 1 + epsilon W (z) (RC (z) -1) • An emergent phantom crossing in w (z) generated mechanistically from delayed record-memory structure rather than inserted parametrically. Numerical toy-model implementations produce: (i) bounded shell-localized halo corrections, (ii) improved rotation-curve flattening, (iii) small dynamic dark-energy deviations |dw| ~ 0. 01–0. 04, (iv) epoch correlation between structure formation and dark-energy evolution. The paper explicitly separates structural predictions from unresolved derivations and includes a detailed roadmap of open technical problems required for quantitative completion.