SIF v1.0 (Legacy): Cosmological Information Simulation — Characterization & Calibration of the First Numerical Implementation

This work presents SIF v1.0 (Legacy), the first complete numerical implementation of the Structural Information Framework (SIF) for cosmological simulation. SIF is a unified theoretical framework designed to study the role of information structure in physical systems, with potential applications ranging from cosmology to quantum physics and condensed matter. This specific release focuses on cosmological information simulation, evaluating whether dark energy-like behavior (w ≈ -1.0) can emerge naturally from the structural dynamics of information fields on spherical manifolds. Key Findings & Numerical Characterization Through rigorous grid resolution sweeps, perturbation recovery tests, and $dt$-convergence analysis, we characterize the numerical behavior of the framework and report the following critical insights: Algorithm-Induced Attractor: The stable attractor behavior observed in the simulation (w ≈ -1.0) is identified as a mathematical consequence of the algorithm's specific structure—namely, the combination of unitary norm conservation and Spherical Harmonic Transform (SHT) discretization leakage acting as a Power Iteration operator—rather than an emergent continuous physical property. Grid Resolution Dependence: The precise coordinate of the attractor equation of state w is directly dependent on grid resolution, varying systematically from $-1.0025$ to $-0.9980$ under different grid densities. Integration Artifact: $dt$-convergence tests demonstrate that the observed attractor behavior is largely a numerical integration artifact of the explicit Euler scheme, rather than an independent physical prediction. Conclusion on Observational Alignment While the current framework can be calibrated to match modern observational constraints—such as the Planck 2018 constraint of -1.03 ± 0.03 and the Pantheon+ constraint of -1.011 ± 0.031—this alignment constitutes post-hoc consistency via parameter tuning rather than an un-tuned, independent prediction of the underlying physical theory. The source code, legacy package, and documentation are provided herein to serve as a benchmark for future non-artifact, implicit, or higher-order geometric integrators within SIF.