Strict Locality and the Emergence of Linearity: An Information-Theoretic Account of Directional Observability
Year: 2026
Type: preprint
Abstract: This paper investigates why strict locality—the principle that each elementary cell accesses only its own instantaneous state—should hold at all, and what structural consequences follow from it. Using a minimal discrete model (a periodic ring carrying one localized pattern observed by a coarse observer), the analysis derives three exact closed-form relations with no fitting parameters: position smoothness Delta_obs = v/L, zero-neighbor directional sufficiency S = 2(d-1)v/L, and a critical threshold at (d-1)v/L = 1/2 whose one-half value is the geometric signature of bilateral symmetry. Below the threshold the description is exactly linear; the threshold itself marks where directional information from opposing boundaries first overlaps. A conserved quantity S(L/ell) = 2(d-1)v/ell survives coarse-graining: although the sufficiency fraction vanishes macroscopically, its product with the coarse-graining width remains invariant, instantiating a two-scale (renormalization-like) structure in which the microscopic level is concealed from—not abolished by—a coarse observer. Every result is confirmed three independent ways (model, hand count, closed form), with a computational appendix and a public code repository. The work is the second in a classical-language series leading toward a probabilistic ontological framework, referenced only as an independent proposal; the derivations here are entirely self-contained.
Author: Bohamd, Ossama Anes
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166535942
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