A Possibility-Space Derivation of a Planck-Softened Correlation Kernel for Holographic Entropy Deficit
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entropy-28-01142-v2.pdf
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66647b7bcf1166eeb2ca420394229f01
Author(s)
Adair, Aaron
Date Issued
October 17, 2026
Journal
Entropy
Publisher
MDPI Publishing
Citation
Adair, A. A Possibility-Space Derivation of a Planck-Softened Correlation Kernel for Holographic Entropy Deficit. Entropy 2026, 28, 1142.
Version
Final published version
Abstract
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 com parison 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 thermody namically 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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.3390/e28101142
