From Topological Models to Telescope Data: Empirical Tests of Hybrid Linear–Cyclic Dynamics in High-Energy Astrophysical Systems | FAIR data

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: cross‑mission reconstruction stability across independent observatories, near‑cyclic reconstructed dynamics in pulsar timing residuals, reconstructed dynamical transitions in active galactic nuclei. Beyond these core tests, supplementary descriptor‑space analyses examine: recurrent reconstruction populations, descriptor‑space outliers, reconstruction overlap and degeneracy, 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: the empirical datasets used in the study, descriptor exports and reconstruction tables, computational pipelines for large‑scale nonlinear reconstruction, 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.