Return Theory (RT): Supernova Anisotropic Axis Model — Observational Fit and Reproducible Data Release

This dataset provides a complete observational implementation of the anisotropic supernova (SN) model derived from Return Theory (RT), formulated within an observational geometry framework. The model introduces a directional dependence in the luminosity distance through a single preferred axis on the sky. The construction is mapping-driven and does not rely on empirical corrections or phenomenological parameterizations external to the RT framework. The release includes: - A full PRD-style manuscript ("RT_observational_model_SN_final.pdf") presenting the formalism, likelihood construction, and statistical results.- Frozen supernova dataset (catalog and covariance matrices) used in the fit.- Complete implementation code for the anisotropic axis model.- Output results from multiple runs, including best-fit parameters, chi-square scans, and comparison tables.- Figures corresponding to the manuscript (axis map, residuals, parameter contours, and likelihood landscape).- An implementation report documenting the numerical pipeline, model construction, and likelihood evaluation. Model construction:The RT observational model is based on a mapping from observational coordinates into an effective anisotropic expansion rate. The Hubble function H_RT(z, θ) is derived from RT geometry, and the luminosity distance is computed via line-of-sight integration. The anisotropy is parameterized through an axis direction and amplitude, both determined directly from the data. Statistical methodology:The likelihood is constructed using the full covariance matrix of the supernova sample. Parameter estimation is performed via chi-square minimization. Model comparison outputs include χ² values and residual distributions. No external priors or empirical calibration layers are introduced. Reproducibility:All components required to reproduce the results are included:- Data (catalog and covariance)- Code (single-entry executable script)- Results (full run outputs)- Figures (exact manuscript versions) The structure is organized to allow direct re-execution of the pipeline and verification of all reported quantities. Relation to Return Theory:The model is derived from the observational geometry of Return Theory (RT), where observational quantities are interpreted through mapping-dependent structures rather than assumed background dynamics. Reference:Return Theory (RT) — Fundamental theory of observational accessDOI: https://doi.org/10.5281/zenodo.19277020 This release corresponds to the supernova (SN) observational layer and is designed as a reproducible component for subsequent multi-probe analyses (e.g., BAO and CC).