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Soft Spaces: Exploring Hidden Structures in Low-Qubit Hilbert Spaces

Tom Stevns

Published Aug 6, 2026• 0 citations
Publisher

Abstract

Abstract This paper presents Phase 1 of the Soft Spaces project, a software-based investigation of hidden structures in low-qubit Hilbert spaces. The study explores whether systematic subspaces can be identified through controlled REAL–NULL comparisons, combined with dynamical analysis based on the Lindblad equation. Experiments were performed on four- to eight-qubit systems. The observed structures were evaluated using statistical and dynamical metrics, including subspace stability and reproducibility across repeated simulations. The results are presented as exploratory research. They do not claim a new physical theory but suggest that the identified structures may warrant further investigation. Future work will extend the analysis to larger Hilbert spaces and examine whether the same methodology can be reproduced in quantum computing frameworks such as Qiskit.

DOI
10.5281/zenodo.21819814

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Abstract This paper presents Phase 1 of the Soft Spaces project, a software-based investigation of hidden structures in low-qubit Hilbert spaces. The study explores whether systematic subspaces can be identified through controlled REAL–NULL comparisons, combined with dynamical analysis based on the Lindblad equation. Experiments were performed on four- to eight-qubit systems. The observed structures were evaluated using statistical and dynamical metrics, including subspace stability and reproducibility across repeated simulations. The results are presented as exploratory research. They do not claim a new physical theory but suggest that the identified structures may warrant further investigation. Future work will extend the analysis to larger Hilbert spaces and examine whether the same methodology can be reproduced in quantum computing frameworks such as Qiskit.
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Abstract We investigate the dynamical behavior of a dissipative n_soft = 5 Lindblad array near a critical coupling dispersion value σ* ≈ 0.94. At this threshold, a spectral cluster of slow eigenmodes forms near the imaginary axis of the Lindblad generator, producing a sharp maximum in the effective relaxation time τ_eff = 1/|Re(λ_slow)|. This spectral structure generates effective memory signatures within the formally Markovian Lindblad framework, creating a von Neumann entropy plateau S(t) that marks a region of maximal informational persistence. We identify three distinct departure types from σ*: a soft drift under slow parameter change, a flickering transition oscillating between attractors prior to permanent departure, and a sharp phase transition under supercritical perturbation. Together, these define the threshold not as a point but as a memory state space – the region of maximum persistence, maximum responsivity, and maximum openness to structural change. We study the dynamical behaviour of a dissipative Lindblad system near the resonance stability maximum σ ≈ 0.94.Numerical simulations reveal three observable signatures of a threshold memory regime:(1) clustering of slow Liouvillian eigenmodes,(2) a maximum in effective relaxation time τ_eff, and(3) entropy plateaus in the von-Neumann entropy dynamics.Together these indicate that the resonance point forms a finite memory region rather The analysis is complemented by a philosophical reflection integrating eight intellectual traditions (Schopenhauer, Nietzsche, Kant, Hegel, Fichte, Einstein, Adams/Pratchett, Buddhist philosophy), demonstrating structural isomorphisms between the formal threshold dynamics and broader frameworks of persistence, transformation, and epistemological limits. The work is presented as an interdisciplinary research series combining formal analysis, numerical simulation, and reflective synthesis. We study the dynamical behaviour of a dissipative Lindblad system near the resonance stability maximum σ ≈ 0.94.Numerical simulations reveal three observable signatures of a threshold memory regime:(1) clustering of slow Liouvillian eigenmodes,(2) a maximum in effective relaxation time τ_eff, and(3) entropy plateaus in the von-Neumann entropy dynamics.Together these indicate that the resonance point forms a finite memory region rather Resonant Boundary Series (42-Reihe) The Resonant Boundary Series is an open research notebook exploring threshold phenomena, metastable dynamics, and entropy signatures in complex dissipative systems. The series combines theoretical modelling, numerical simulations, and reflective meta-analysis. It documents a collaborative research process between human authors and multiple AI systems, treating the interaction itself as part of the epistemic structure of the work. Rather than presenting a single finished theory, the series develops a progressive conceptual framework around a central hypothesis: Critical thresholds in dissipative systems may behave not as singular transition points but as extended state regions that retain dynamical memory. Within this framework, the work investigates: spectral clustering in dissipative operators entropy plateaus near transition regimes metastable persistence and flickering states numerical simulations of threshold memory dynamics The project is structured as a sequence of conceptual volumes ("Band 42.x"), each exploring a different aspect of the evolving model. Intermediate volumes document experimental simulations, conceptual clarifications, or methodological refinements. The series intentionally preserves traces of the collaborative research process, including conceptual dialogues between different AI systems and the human author, as a form of open epistemic documentation. Structure of the 42-Series The current sequence includes several intermediate volumes that progressively develop the theoretical and computational framework. Example structure: Band 42Initial conceptual framing of boundary persistence. Band 42.x (intermediate volumes)Exploratory modules addressing entropy behaviour, dissipative dynamics, and threshold modelling. Band 42.9+0Numerical exploration of the threshold state σ* ≈ 0.941 as a potential memory region in dissipative dynamics. Future volumes will extend this investigation through expanded simulations, analytical models, and cross-system comparisons. Methodological Character The series combines: nonlinear dynamics spectral analysis entropy-based diagnostics computational simulation conceptual synthesis with the aim of developing an integrative framework for threshold memory in complex systems. Status of the Project The Resonant Boundary Series is an open evolving research program. Each volume represents a documented step in the development of the underlying conceptual model rather than a finalized theory. Subsequent volumes will incorporate: reader feedback independent AI analysis (e.g., Consensus) extended numerical experiments. Keywords dissipative systems · Lindblad dynamics · open quantum systems · entropy plateaus spectral clustering · effective memory · resonant persistence · threshold dynamics relaxation time · von Neumann entropy · Markovian systems · phase transitions interdisciplinary research · human-AI collaboration · philosophy of physics
Commercially available Noisy Intermediate-Scale Quantum (NISQ) devices now make small hybrid quantum-classical experiments practical, but many tools hide configuration or demand ad-hoc scripting. We introduce the Quantum Experiment Framework (QEF): A lightweight framework designed to support the systematic, hypothesis-driven study of quantum algorithms. Unlike many existing approaches, QEF emphasises iterative, exploratory analysis of evolving experimental strategies rather than exhaustive empirical evaluation of fixed algorithms using predefined quality metrics. The framework's design is informed by a comprehensive review of the literature, identifying principal parameters and measurement practices currently reported in the field. QEF captures all key aspects of quantum software and algorithm experiments through a concise specification that expands into a Cartesian product of variants for controlled large-scale parameter sweeps. This design enables rigorous and systematic evaluation, as well as precise reproducibility. Large sweeps are automatically partitioned into asynchronous jobs across simulators or cloud hardware, and ascertain full hyper-parameter traceability. QEF supports parameter reuse to improve overall experiment runtimes, and collects all metrics and metadata into a form that can be conveniently explored with standard statistical and visualisation software. By combining reproducibility and scalability while avoiding the complexities of full workflow engines, QEF seeks to lower the practical barriers to empirical research on quantum algorithms, whether these are designed for current NISQ devices or future error-corrected quantum systems.
⚠️ CORRECTION NOTICE (added 2026): The author has since identified serious errors in this work through a systematic adversarial audit. The central claims of this record should not be relied upon. Specific issues found across this research program include implementation errors (e.g., conflation of signed cosine with cos²), circular definitions, proof gaps, results that reduce to known theorems, and effects that vanish under proper null models and direct-influence correction. This record is left online for transparency and as a documented case, not as a valid result. For the author's current, audited methodology, see the later work on classical-baseline auditing of quantum-like contextuality claims: https://doi.org/10.5281/zenodo.20680607 — A. Ogasawara This short report investigates order-dependent geometric structurearising from noncommutative histories in a classical statistical system.Using the two-dimensional Ising model as a concrete physical setting,we show that history-induced structure is not directly observablein conventional scalar projections, but can be detected througha gauge-invariant low-order complex-mode representation. The analysis demonstrates that noncommutative update historiesgive rise to a reproducible low-dimensional geometry,which remains hidden under phase-dependent scalar observables.This work provides a minimal physical realization of theorder-projection framework introduced in earlier theoretical studies,without invoking quantum dynamics or wavefunction-based assumptions.Note: Parts of the manuscript were linguistically and structurally refinedwith the assistance of AI-based tools.All scientific content, analysis, and conclusions are the author's own.