On the Status of Local Entropy-Current Extensions of the Gravitational Entropy Escrow Framework: A Clarification Note

In dialogue exploring covariant extensions of the Gravitational Entropy Escrow framework (Whitmer 2026), several large-language-model systems independently proposed an equation of the form ∇μ JSμ = (2π kB/ℏ) εbind, designated C8, in which a local entropy 4-current is sourced by the local energy density. We document its resolution. With dimensions accounted for correctly, the standard cosmological-constant energy density εΛ = Λc4/(8πG), and the integration time chosen as the horizon light-crossing time, C8 reproduces both the Bekenstein–Hawking entropy of a Schwarzschild black hole and the Gibbons–Hawking entropy of the de Sitter horizon exactly. This recovery is a consistency check, not a derivation: C8 with t = R/c is algebraically identical to the saturated Bekenstein bound (Bekenstein 1981), so any horizon that saturates that bound is reproduced trivially. The choice t = R/c is post-hoc—other natural horizon time scales give answers spanning many orders of magnitude. C8 therefore reduces to a rate-equation reformulation of a 1981 result rather than new physics. The published framework's interpretive content is unaffected, and its central open problem (the order-unity coefficient α ≈ 1.34 between the bare Λ-form a0 and the empirical Milgrom value) is untouched by C8.