The Nesc Recipe: A Cross-Regime Observation of Bekenstein-Bound Saturation from the Static Escrow Construction |U |/T

We propose a static escrow framework for gravitational entropy in which the basic ratio Sesc = |U|/T — gravitational binding energy divided by characteristic temperature — produces the Bekenstein-bound saturation form 𝒩esc(E, L) ≡ 2πEL/(ℏc) across three distinct regimes: (i) a test mass in Schwarzschild geometry at the horizon limit, (ii) the Bekenstein–Hawking entropy of a black-hole horizon via the Smarr formula, and (iii) the entanglement-entropy change of a localized matter configuration in a Rindler wedge. The dimensionless count 𝒩esc(E, L) is identical in form to the Bekenstein-bound saturation value; what the framework names is the recipe by which (E, L) are extracted from |U|/T in each gravitational regime. The same one-function recipe, applied across three qualitatively distinct settings, evaluates to the Bekenstein form in each. For regime (iii), we identify the framework's prediction with Casini's quantum-field-theoretic derivation of the Bekenstein bound. We provide a lattice check consistent with the Rindler-wedge inequality (Compton-wavepacket and mass-perturbation protocols), together with a moment-concentration check of the boost-generator step across lattice sizes N ∈ 200, 1200 and perturbation strengths mpert2 ∈ 0.5, 5.0 spanning one order of magnitude. The maximum observed saturation is 5.4% at the Compton scale. The framework is an organizing observation, not a derivation: each regime's prediction follows from a standard continuum result (Bisognano–Wichmann theorem, Smarr formula, Bekenstein bound), while the framework's contribution is the unifying observation that the same recipe |U|/T generates the Bekenstein form in all three. The present work is the fifth deposit in the Windstorm Institute gravitational entropy escrow series and formalizes the cross-regime 𝒩esc notation introduced in the preceding translation paper.