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Bibliographic Details
Main Author:	Rambold, Gerhard
Format:	Recurso digital
Language:	English
Published:	Zenodo 2025
Online Access:	https://doi.org/10.5281/zenodo.17753472
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Table of Contents:

This preprint introduces an information-geometric holographic boundary framework in which coarse bulk information is encoded on a finite-capacity, expanding boundary through diffusion, compact projection, saturation, and geometric scaling. The formulation presented here is complete at the level defined in the manuscript. Extended derivations and the full stepwise construction (S1–S3) will appear in the forthcoming Version 1.1. Although cosmological analogies are used for illustration, the framework is scale-independent and produces temporal ordering whenever the boundary grows and records information irreversibly. The boundary stores coarse, time-ordered traces without reconstructing the bulk. The present version develops the general mathematical structure; specific instantiations or applications to physical systems are intentionally deferred. No external datasets were generated or analysed. Conceptual Clarification (Version 1.0). Terms such as coarse information, capacity, record, and trace are used in a structural, information-geometric sense. “Coarse” denotes the boundary-stable components of bulk fields that survive smoothing, compact projection, and saturation—that is, persistent low-frequency modes detectable under finite resolution. The boundary is treated as an expanding surface with finite distinguishable states per unit area, not as a physical phase interface. Irreversibility arises because the boundary update is non-invertible, and the resulting sequence of boundary configurations provides an emergent temporal ordering. A record is any persistent boundary state; a trace is the ordered collection of such states. These definitions fix terminology in advance of the detailed derivations that will be provided in Version 1.1. Open Conceptual Points (to be fully resolved in Version 1.1). Several notions are defined structurally but not yet formalised quantitatively. (A) Finite distinguishable states per unit area is specified conceptually but awaits a precise quantitative realisation (e.g., explicit discretisation scale, metric resolution, or information measure). (B) The boundary update is described compositionally (smoothing → projection → scaling → saturation) but its functional form and domain will be formalised in the supplementary derivations. (C) References to low-frequency modes describe the effect of compact projection; the choice of decomposition basis (e.g., Laplace–Beltrami eigenmodes on Σ(t)) will be made explicit in Version 1.1. (D) Boundary stability of components is defined operationally (survival under the boundary update), and a formal stability criterion will be provided when the operator structure is given rigorously. These open points do not affect the structural results presented in the preprint but will be addressed systematically in the forthcoming supplements.

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