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ISAT: Quantum Dynamics v10.0: Bridging Information Structural Attraction Theory and Quantum Phenomena through Structural Vectors

SUTIPONG CHANPENGPAD

Published Jun 28, 2026• 0 citations
Publisher

Abstract

ISAT: Quantum Dynamics v10.0 introduces a comprehensive computational verification engine demonstrating that scale-invariant structural vectors ($K^*$) function as a non-trivial, shape-sensitive observer metric. Through systematic multi-dimensional numerical experiments (45 multi-scale tests), this framework bridges Information Structural Attraction Theory (ISAT) and quantum phenomena across diverse regimes. Core Verification Suite Findings (Section 4.11) Exp A (Quantum Revivals): $C_{K^*}$ detects geometric shape revivals under Lindblad dephasing with 0.9999 peak value, while standard Fidelity drops to 0.3908 (a 2.56x robustness gain). Exp B3 (Dicke Transition): Observer dynamics detect the superradiant transition via Critical Slowing Down (CSD), showing a sharp 9.6x peak in convergence steps near the critical point ($\lambda_c = 0.50$). Exp C2 (Dimensionality Tracking): PCA projects a 256D spatial grid collapse path onto an effective 2.7D manifold, capturing 96.1% of the total dynamical variance. Exp D2 (Entanglement Transition): A 12D multi-basis ($X$ & $Z$) moments vector tracks the volume-to-area law transition, establishing a strong monotonic correlation ($r = -0.8142$) with half-chain entanglement entropy. Exp E2 (Error Mitigation Witness): In the density matrix limit, the $K^*$ space Euclidean distance to the ideal state drops from 0.5314 (unmitigated) to 0.0099 (mitigated), yielding a $p\text{-value} = 0.0000$ and 100% separability. Exp F2 (Non-Markovian Memory): Moments space distance expansion tracks open-system information backflow, achieving a perfect correlation ($r = 1.0000$) with the BLP trace-distance measure, proving Bloch-sphere geometric isomorphism. Repository Contents Computational Verification Engine: Source code and scripts for the 45 multi-scale tests across 1D, 2D, 3D, 4D, Time-dependent Dynamics, Many-Body, Open systems, and Closed-loop Active Inference. Official Preprint: The full theoretical and numerical manuscript detailing the mathematical foundations of the $K^*$ metric. Breakthrough Verification Suite: Complete data tables and plotting scripts resolving legacy numerical anomalies.

DOI
10.5281/zenodo.21001096

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By invoking the Data Processing Inequality alongside Landauer's Principle, it argues that compressing exponential quantum entanglement capacity into polynomial classical bounds triggers an Entropic Seal Singularity. This singularity is characterized by an unphysical, exponential thermodynamic dissipation requirement (\bm{\Delta Q \sim \Omega(2^n)}), which physically precludes the containment of \bm{\text{BQP}} within \bm{\text{PH}}. • Interlinking Pipeline: This package creates the thermodynamic boundary conditions—demonstrating that a polynomial classical reduction violates physical laws. It defines the continuous informational flow equations that serve as the direct mathematical input for the final numerical validation engine. Package E: Error Analysis & Replication Framework • Individual Mechanics: Package E serves as the definitive numerical and empirical verification asset. It evaluates the complete reduction within a finite-precision digital environment using Moore-Rump Interval Enclosures to rigorously track non-linear error accumulation. Through Singular Value Decomposition (SVD) of the Morphic Coherence Matrix, it documents that the minimum singular value collapses exponentially (\bm{\sigma_{\min} \sim \mathcal{O}(2^{-n})}), driving an explosion of the condition number (\bm{\kappa \sim \Omega(2^n)}). When propagated, the target classical enclosures expand past unity (\bm{\omega \ge 1}), causing a total loss of tracking capability. • Interlinking Pipeline: Package E closes the entire suite. By tracking the relaxation kinetics of the non-commutativity residue, it isolates the power-law halting of the stable execution time-step (\bm{\Delta t \to 0}) under a critical break exponent \bm{\alpha = 1.0000 \pm 0.0001}. 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Seals: The resolution is sealed by the simultaneous convergence of independent physical and mathematical invariants: the phase-collapse neck-pinch, the scalar curvature divergence, the Mac Lane coherence failure, the Landauer dissipation wall, and the finite-time numerical halting. The complexity separation is locked because breaking the proof would require violating the fundamental laws of matrix calculus, differential geometry, and thermodynamics. 4. Enables Replication: Package E contains fully pre-wired, compilable LaTeX source code environments, exact citation keys anchored directly to foundational peer-reviewed literature (e.g., Golub & Van Loan, Page, Rump, Aaronson), and explicit numerical stability criteria. 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