A Lattice Quantum Field Theory Test of the Static Escrow Postulate: 1+1D and 3+1D Falsification with Modular-Hamiltonian Partial Survival

We test the static gravitational entropy escrow postulate Sₙₘ = |Ugrav|/TUnruh of Whitmer 1 using lattice quantum field theory. In 1+1 dimensions, a 295-point parameter scan of a free massless scalar at lattice sizes up to N = 3000 finds that the dimensionless ratio R = Sₑnt/Sₙₘ spans 10. 56 orders of magnitude across the (L, m) grid; the mass-induced entanglement ΔS = Sₑnt − Sᵥac is uniformly negative; and the result is N-converged to four decimal places. In 3+1 dimensions, an N³-site scan over N ∈ 10, 12, 14, 16, 18, 20 confirms the Bombelli–Srednicki area law (Sᵥac/N² → 0. 0228) and shows that R has no finite continuum limit because the bipartition entropy is dominated by the area-law vacuum term, while the mass-induced ratio R_Δ = ΔS/Sₙₘ is bounded by 10⁻³ across the grid. Two independent code paths agree to five decimals, ruling out implementation artifacts. Mutual information I (M₁: M₂) between regions surrounding the masses decays as L⁻⁴, opposite to the linear growth required by the postulate. The modular Hamiltonian content ΔK, evaluated under the Bisognano–Wichmann conjecture, exhibits the right sign and approximately recovers the BW linear asymptote ΔK ∝ d1 in 1+1D within a small-d1 window (d1 ∈ 2, 6 at m=1), with prefactor approximately 1/30 of the literal BW value. At larger d1 the local exponent decreases smoothly into a sublinear decay tail; the previously-published v0. 4/v0. 5 figure of "ΔK ∝ L^0. 7" is here corrected to a regime-dependent characterization, with the single-power-law exponent identified as a fitting artifact across a smooth crossover. The literal bipartition-entropy reading of the postulate is ruled out in both 1+1D and 3+1D; the modular-content interpretation is approximately correct in 1+1D within the small-d1 BW regime, with a calculable suppression factor as the remaining open question. A companion paper 11 reports that the 3+1D modular content does not recover the BW asymptote within the d1 range the lattice can resolve, with ΔK peaked at d1 ≈ 2 and decaying as d1^−2 to −3 for larger d1, indicating that BW recovery is dimension-dependent or, equivalently, that the rate of approach to the continuum BW asymptote is substantially slower in 3+1D than in 1+1D. The framework's horizon-limit recoveries (Bekenstein–Hawking entropy via surface gravity) are independent of these flat-space tests.