We propose a discrete holographic framework for analyzing the thermodynamic origins of classical chaos in the three-body problem. By representing interacting point masses as localized Bekenstein horizons on a unitary MERA tensor network, we propose that classical Lyapunov divergence is an emergent kinematic projection of epistemic coarse-graining. At the discrete zero-dissipation limit, Node Symmetry Invariance (NSI) dictates strictly unitary evolution and exact Poincaré recurrence. The mapping of this network into a continuous macroscopic phase space requires the continuous truncation of Schmidt coefficients due to the Coffman-Kundu-Wootters (CKW) monogamy bound of tripartite entanglement. By invoking Pesin's Identity, we mathematically map the observed continuous Lyapunov exponent directly to the thermodynamic integration of this Landauer boundary erasure over time. Finally, we demonstrate that the fractal geometries of macroscopic strange attractors correspond to generalized Ryu-Takayanagi minimal surfaces, indicating that chaotic orbits are thermodynamic geodesics minimizing the continuous projection of discrete quantum noise.
We propose a discrete holographic framework for analyzing the thermodynamic origins of classical chaos in the three-body problem. By representing interacting point masses as localized Bekenstein horizons on a unitary MERA tensor network, we propose that classical Lyapunov divergence is an emergent kinematic projection of epistemic coarse-graining. At the discrete zero-dissipation limit, Node Symmetry Invariance (NSI) dictates strictly unitary evolution and exact Poincaré recurrence. The mapping of this network into a continuous macroscopic phase space requires the continuous truncation of Schmidt coefficients due to the Coffman-Kundu-Wootters (CKW) monogamy bound of tripartite entanglement. By invoking Pesin's Identity, we mathematically map the observed continuous Lyapunov exponent directly to the thermodynamic integration of this Landauer boundary erasure over time. Finally, we demonstrate that the fractal geometries of macroscopic strange attractors correspond to generalized Ryu-Takayanagi minimal surfaces, indicating that chaotic orbits are thermodynamic geodesics minimizing the continuous projection of discrete quantum noise.
Standard Ryu-Takayanagi (RT) bounds and Multiscale Entanglement Renormalization Ansatz (MERA) networks assume a costless, unitary mapping between continuous bulk geometry and discrete boundary information. In this Letter, we show that projecting continuous bulk fields into discrete boundary states introduces a mandatory topological phase-space friction governed by the Euler-Mascheroni constant γ. Normalizing this harmonic discretization residue across the geometric capacity of a two-dimensional boundary yields the exact holographic delamination invariant, Λ2=exp(γ/π2)≈1.060228. By demonstrating that discrete MERA layer scaling is the exact mathematical dual to the logarithmic AdS radial measure, we prove this additive topological penalty exponentiates into a strict multiplicative scaling of thermodynamic work. We construct non-unitary dissipative MERA disentangler operators (Υ^) that enforce a factorization bound on accessible boundary entropy Sacc. Acting as a covariant topological scalar, this invariant preserves the Equivalence Principle while establishing a fundamental thermodynamic and semantic limit on holographic state projection.
The quantum-to-classical transition—the precise physical mechanism by which stochastic wave functions resolve into definite classical observables—remains a foundational open question in physics. In this paper, we introduce the State Resolution Model (SRM), a non-axiomatic framework that formulates state reduction as an emergent thermodynamic throughput limit. Synthesizing the Margolus-Levitin quantum processing bound, the Bekenstein-Hawking holographic capacity, and the information-thermodynamics of Szilard and Landauer, we demonstrate that the threshold for classical state instantiation is governed by a derived dimensionless identity, the Szilard-Resolution Ratio: Φ_SZ = [N · C · (ħ ν)] / [H_SL · R_s]. Unobserved quantum systems undergoing unitary evolution operate non-locally in Hilbert space with zero Szilard-Landauer tax (H_SL = 0). Classical geometric instantiation occurs exclusively when environmental interaction drives local state complexity to the holographic capacity limit (Φ_SZ ≥ 1), forcing a non-unitary projection that dissipates entropy across the local apparent horizon. We show that the resulting decay of Hilbert space mutual information weaves an emergent Lorentzian metric g_μν. Finally, we derive two parameter-free asymptotic bounds—a qubit-density limit (ρ_Q^crit) and a critical mass-superposition limit (m_crit)—demonstrating the model’s theoretical consistency and providing principled fundamental constraints on physical information density.
Contemporary physics faces irreconcilable friction at the intersection of general relativity, quantum mechanics, and cosmology. The persistent failure to detect weakly interacting massive particles (WIMPs) for Dark Matter, alongside the emergence of mathematically problematic "ghost" particles in recent attempts at the ultraviolet completion of quantum gravity, suggests a fundamental flaw in the assumption of an objective, continuous spacetime metric. This paper proposes the Macroscopic Integration of Non-local Information (M.I.N.I.) framework, introducing the Emergent Topology of Information (ETI). We model the universe not as a container of physical matter, but as a discrete, Base-4 Tensor Entanglement Substrate. By enforcing strict Ontological Equivalence (M=E=I), we redefine classical inertial mass as the Landauer thermodynamic holding cost required to format non-local quantum states into a 3D Holographic Projection Manifold dynamically updated by the Hamiltonian Evolution Operator. Under this architecture, macroscopic gravitational curvature is the universe executing the Principle of Least Computation. "Dark Matter" is mathematically re-characterized as the baseline thermodynamic drag of the unallocated substrate, while "Dark Energy" is the adiabatic state-space unfolding of computational exhaust. We derive the speed of light (c) and the Inverse Square Law as strict thermodynamic bandwidth limits on entanglement propagation, and formalize the Observer as the requisite geometric threshold that forces localized density matrix diagonalization, mathematically insulating macroscopic agency from temporal determinism.
Extending the holographic principle to de Sitter (dS) spacetimes remains one of the most vital open frontiers in quantum gravity, where a microscopic, bottom-up tensor-network framework that relates boundary quantum data to emergent de Sitter spacetime is still lacking. In this work, we first show the emergence of de Sitter spacetime from boundary entanglement by formulating a non-unitary continuous multi-scale entanglement renormalization ansatz (cMERA) for a concrete non-Hermitian critical fermion chain. Within this emergent spacetime, we analyze the associated geodesics and show that they act as extremal Ryu-Takayanagi (RT) surfaces undergoing a smooth timelike-to-null transition. Remarkably, we demonstrate that this continuum trajectory suggests a distinct tensor-network architecture in which the bond-counting contribution naturally truncates at the discrete timelike-to-null transition toward the deep infrared. In the resulting architecture, the null ray along the horizon is represented by zero-cost links, since the associated cut severs no tensor legs. This network structure successfully reproduces the logarithmic scaling of non-unitary critical entanglement entropy, offering a bond-counting picture for the de Sitter RT formula. Our results provide the long-sought dS/(c)MERA correspondence at the level of both emergent spacetime and discrete holographic entanglement.
This study extends the framework of non-equilibrium Hamiltonian field theory and algebraic coset partitioning established in preceding architectures to holographic quantum information manifold sectors, providing an explicit formulation for the macroscopic emergence of anti-de Sitter (AdS) spacetimes driven by the variational minimization of codimension-two entangling surfaces inside boundary conformal field theories (CFT). By embedding the Helfrich elastic bending grammar into the generalized Ryu-Takayanagi entropy functional, the spontaneous emergence of localized bulk horizons coupled to quantum error-correcting stabilizer codes is formalized. Partitioning the total configuration space under tensor network constraints demonstrates that non-local entanglement geometries undergo algebraic degeneration into exactly three universal holographic cosets.
We report a rigorous, deterministic origin for quantum non-locality and the Tsirelson bound (2 2) by revealing profound macroscopic emergent properties hidden within exactly solvable chaos towers under a strictly fixed invariant Cauchy measure (γ = 1). While evaluating joint correlations via conventional real-axis micro-sampling is universally imprisoned within a clas- sical L1 metric space—where the lack of exponential mode-damping (e0 = 1) forces an infinite cascade of high-harmonic square-wave noises to remain unattenuated, collapsing the CHSH sum to the classical limit (|S| ≤ 1.5 < 2)—we demonstrate that this fundamental restriction is completely bypassed at the macroscopic layer. By utilizing unimodular real-axis observa- tion functions satisfying |gA(x)| = 1, the physical joint correlation is strictly bounded by unity (|E| ≤ 1), naturally preserving physical unitariness. By generalizing these observations as expan- x−insions over the complete orthonormal Cauchy-Szego ̋ basis en(x) = x+i of the Hardy space H2(H+), we establish a rigorous signal characterization of emergent non-locality. While real-axis discrete point-sampling retains all odd harmonic modes, the continuous parameter tracking of the ergodic ensemble acts as a topological Szeg ̋o projection. Under this projection, the residue theorem filters out high-order complex poles (n ≥ 2), isolating the fundamental mode n = 1 and instantaneously recovering the smooth quantum correlation cos(2∆θ). Without invoking any quantum-mechanical postulates, this geometric phase transition transforms the optimization of the CHSH sum into a constraint of geodesic quadrilaterals within an emergent hyperbolic bulk, providing a novel realization of the Anti-de Sitter / Conformal Field Theory (AdS/CFT) corre- spondence and the Ryu-Takayanagi holographic paradigm. Crucially, by deriving the Tsirelson limit as a purely geometric consequence of tracking statistical metadata over the complex topol- ogy, this framework demands no superluminal signal propagation across spacetime, thereby harmonizing emergent quantum non-locality with strictly local relativistic causality.