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\title{The Abstract of the Holographic Alaya–Field Framework}

\author{
  Sidong Liu, PhD \\
  iBioStratix Ltd \\
  \texttt{sidongliu@hotmail.com}
}

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\section*{Abstract}

This volume develops a structural framework for understanding the emergence of spacetime, locality, and classicality within quantum theory, without assuming any preferred subsystem decomposition or fundamental spacetime background.

The central claim is that many features traditionally treated as primitive---such as spatial separation, temporal ordering, and observer--system distinctions---are instead consequences of how a single global quantum structure is coarse-grained into physically accessible subalgebras. Building on insights from algebraic quantum theory, quantum information, and holography \cite{Haag1996,Zanardi2001,Zanardi2004,RyuTakayanagi2006,VanRaamsdonk2010}, the framework treats observable algebras, rather than states or tensor factorizations, as the primary carriers of physical structure.

Within this approach, subsystems are not assumed but induced by stable patterns of accessibility, constrained by interaction structure, information-theoretic robustness, and environmental redundancy \cite{Zurek2009}. Geometry, time, and measurement arise only in regimes where such structures persist, and are shown to be contingent, emergent, and structurally bounded. Different coarse-graining schemes can give rise to inequivalent effective geometries, even when defined on the same underlying quantum state, without modifying the underlying dynamics.

The framework does not propose new fundamental laws or cosmological dynamics. Instead, it reorganizes explanatory priority, clarifying the conditions under which physical descriptions are possible at all. By identifying the structural limits of locality, temporality, and observation, this work aims to delineate the narrow domain in which spacetime physics, classical records, and intelligible experience can arise, and beyond which no further physical description is well-defined.

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\noindent\textbf{Keywords}: emergent geometry, accessible algebras, coarse-graining, quantum foundations, algebraic quantum theory, structural realism

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\begin{thebibliography}{99}

\bibitem{Haag1996}
R. Haag, \emph{Local Quantum Physics: Fields, Particles, Algebras}, Springer-Verlag (1996).

\bibitem{Zanardi2001}
P. Zanardi, \emph{Virtual Quantum Subsystems}, Phys. Rev. Lett. \textbf{87}, 077901 (2001).

\bibitem{Zanardi2004}
P. Zanardi, D. A. Lidar, and S. Lloyd, \emph{Quantum Tensor Product Structures are Observable Induced}, Phys. Rev. Lett. \textbf{92}, 060402 (2004).

\bibitem{RyuTakayanagi2006}
S. Ryu and T. Takayanagi, \emph{Holographic Derivation of Entanglement Entropy from AdS/CFT}, Phys. Rev. Lett. \textbf{96}, 181602 (2006).

\bibitem{VanRaamsdonk2010}
M. Van Raamsdonk, \emph{Building up spacetime with quantum entanglement}, Gen. Relativ. Gravit. \textbf{42}, 2323 (2010).

\bibitem{Zurek2009}
W. H. Zurek, \emph{Quantum Darwinism}, Nature Physics \textbf{5}, 181 (2009).

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