A Possibility-Space Derivation of a Planck-Softened Correlation Kernel for Holographic Entropy Deficit

I derive a Lorentzian correlation kernel from a maximum-entropy principle on an abstract possibility space, assuming no spacetime or field theory. Maximizing Shannon entropy over positive phase rates at fixed mean gives p(ω)=Ω-1e-ω/Ω, and averaging relative phase coherence yields ρ(σ)=1/(1+Ω2σ2). Given a posited array of pairwise comparison intervals, classical multidimensional scaling returns a screen, its metric, and its dimension; the dimension is an output, and the test can fail, which makes the existence of a geometry falsifiable in principle. A postulated finite invariant speed supplies the Lorentzian cone. Under a stated locality assumption the Fisher coordinate of the ensemble is a shift-symmetric scalar that admits no potential within the Fisher sector; with Lovelock's theorem this gives Gμν+Λgμν=(8πG/c4)Tμν, with the coupling normalized thermodynamically and G an input. A Gaussian treatment of the patches solves for the correlation scale, giving λG≃1.302ℓP. Treating Planck patches as binary variables on a square lattice instead sets λ=2ℓP, the largest scale binary patches can realize, before any entropy comparison. At that scale the maximum-entropy Ising multi-information agrees with 1-1/(4ln2)=0.6393, the Bekenstein-Hawking deficit, within 0.05%: transfer-matrix bounds give 0.6135, and 0.6389 under one assumption; a pre-registered extrapolation gives 0.6391. No anti-de Sitter asymptotics are used.