From Topological Models to Telescope Data: Empirical Tests of Hybrid Linear–Cyclic Dynamics in High-Energy Astrophysical Systems | FAIR data
Description
The materials collected here support an observational reconstruction framework designed to evaluate temporal organization directly from heterogeneous astrophysical time series. Motivated by developments in nonlinear dynamics, information theory, topological reconstruction, and complex‑systems analysis, the framework treats time series not merely as sequences of measurements but as geometric objects whose reconstructed structure may reveal invariant properties, organizational regimes, and observable transitions. Within this perspective, temporal evolution is examined through reconstruction spaces whose geometry encodes dynamical organization.
The associated study develops and empirically tests a hybrid linear–cyclic reconstruction model in which temporal organization is represented as a superposition of linear and cyclic components. Rather than assuming that astrophysical systems are intrinsically linear or intrinsically periodic, the framework evaluates whether observational data support transitions between multiple dynamical regimes characterized by distinct reconstruction properties.
The empirical analysis uses event‑based high‑energy observations from multiple independent space missions, including NICER, NuSTAR, IXPE, XMM–Newton, and Swift. These observatories provide heterogeneous detector architectures, photon statistics, sampling properties, and instrumental responses, enabling direct evaluation of reconstruction robustness across independent measurement systems.
Three primary empirical investigations are performed:
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cross‑mission reconstruction stability across independent observatories,
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near‑cyclic reconstructed dynamics in pulsar timing residuals,
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reconstructed dynamical transitions in active galactic nuclei.
Beyond these core tests, supplementary descriptor‑space analyses examine:
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recurrent reconstruction populations,
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descriptor‑space outliers,
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reconstruction overlap and degeneracy,
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persistent reconstruction regions.
These analyses suggest that reconstruction space itself may exhibit observable organizational structure beyond individual reconstructed quantities.
A secondary motivation arises from structured‑signal detection problems in extreme astrophysical environments, where identifying low‑entropy organization embedded within noisy observational streams remains fundamentally challenging. Reconstruction‑based approaches may provide complementary information to conventional spectral techniques in such contexts.
This repository therefore provides:
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the empirical datasets used in the study,
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descriptor exports and reconstruction tables,
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computational pipelines for large‑scale nonlinear reconstruction,
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supplementary documentation supporting reproducibility.
The framework should be interpreted as an observational methodology for studying reconstruction‑space organization rather than as evidence for alternative physical theories of time or dynamics.
Notes
⭐ Highlights
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A multi-mission reconstruction framework is developed for studying temporal organization directly from heterogeneous astrophysical time series.
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Cross-mission analyses reveal substantial differences in observational robustness across reconstructed nonlinear dynamical descriptors.
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Geometric reconstruction quantities exhibit stronger observational stability than divergence-based dynamical estimators.
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Pulsar timing residuals reveal observational regimes consistent with near-neutral and cyclic reconstruction behavior.
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Reconstruction of AGN variability suggests transitions between distinct observational dynamical regimes.
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Supplementary descriptor-space analyses reveal recurrent reconstruction populations, overlap regions, and persistent descriptor configurations.
- Descriptor-space organization appears only partially aligned with conventional astro-physical taxonomy.
- The proposed framework extends naturally toward anomaly detection, structured signal classification, and technosignature searches.
Other
FAIR Data
The repository is organized according to reproducibility and long-term accessibility principles.
Included materials consist of:
• Mission-specific observational datasets stored separately for each mission
• SQL databases containing processed descriptor tables and reconstruction outputs
• JSON exports for structured machine-readable interoperability
• CSV representations for archival portability and metadata preservation
• Mission-specific Wolfram Mathematica scripts reflecting instrument-specific processing pipelines and reconstruction procedures
• README documentation describing directory structure, workflow dependencies, reconstruction steps, and database relationships
Because observational pipelines differ substantially between missions, computational workflows are provided separately for each instrument rather than through a single unified processing script.
The repository therefore provides:
Findable datasets
Accessible structured outputs
Interoperable machine-readable representations
Reusable computational workflows
supporting full reconstruction reproducibility across independent observational datasets.
Series information
This publication is part of the research cycle “Linear Infinity → Cyclic Space → Expansive Chaos”, a structured sequence of works exploring how linear asymptotic regimes on the positive half‑line transform into cyclic, stratified, or boundary‑identified geometric structures under metric contraction. The full cycle currently includes:
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Part I. — Hybrid Linear–Cyclic Topological Structures for Digital Sequence Encoding and Technosignature Analysis | DOI: 10.5281/zenodo.18473473
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Part II. — Informational Geometry of the Positive Half-Line. A World Without Negative Numbers | DOI: 10.5281/zenodo.18474513
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Part III. — A Symmetric Classification of Prime Numbers. Correlational, Identity, and Inversion Symmetry | DOI: 10.5281/zenodo.18520138
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Part IV. — Global Affine Time and Metric Uniqueness: A Geometric Characterization of Linear and Cyclic Temporal Structure | DOI: 10.5281/zenodo.18505857
- Part V. — Symmetric Signatures of Global Configurations: Topological Rigidity and the Epoch of Convergence in a Case Study of Orion–Giza Correspondence. A Unified Framework for 2D Similarity Invariants, 3D Orientation Geometry, and 4D Precessional Dynamics | DOI:10.5281/zenodo.18651258
- Part VI. — Linear Time, Cyclic Geometry. Spectral Phase Structure of Cosmic Emitters | DOI:10.5281/zenodo.18698140
- Part VII. — From Topological Models to Telescope Data: Empirical Tests of Hybrid Linear–Cyclic Dynamics in High-Energy Astrophysical Systems | DOI:10.5281/zenodo.20545297
Taken together, these works form a coherent geometric–informational program that traces a continuous transformation of organizational structure:
linear infinity → asymptotic contraction → metric multiplicity → temporal stratification → cyclic space → spectral phase structure.
Each component stands independently, yet collectively they outline a unified framework in which linear temporal regimes, cyclic geometries, and spectral invariants emerge as complementary manifestations of the same underlying structural principles. The progression therefore reflects not a sequence of physical phases, but a set of organizational regimes that become observable across mathematical models, geometric constructions, and empirical reconstruction spaces.
All project materials, publications and complete machine‑readable metadata are maintained at https://linearcyclic.eu
Files
From_Topological_Models_to_Telescope_Data.pdf
Additional details
References
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