Return Theory (RT) — Cosmological Observable Reconstruction, Frozen Dataset (CC, SN, BAO) - v40

This dataset contains the frozen observable-level implementation of Return Theory (RT) in its v40 state. Return Theory is formulated as a framework of observable reconstruction rather than a global redshift remapping. A common backbone is defined by a field q(z) extracted from Cosmic Chronometers (CC), a preferred axis extracted from Supernovae (SN), and a time-reconstruction law. Distinct observables are generated through dataset-specific operators acting on the same backbone. The dataset includes three observational branches: Cosmic Chronometers (CC): A derivative-based observable is constructed, where the reconstructed expansion rate is given by the baseline expansion rate multiplied by a time-reconstruction factor derived from the effective field q_eff. Supernovae (SN): An integral-kernel observable is used. The comoving distance is reconstructed through an integral over redshift, where the integrand is modified by a factor depending on the effective field q_eff along each line of sight. Baryon Acoustic Oscillations (BAO): A geometric observable is constructed at the catalog level. A BAO-specific parameter (lambda_BAO = 0.52) is introduced, which is treated as a local parameter specific to BAO and not as a global scaling parameter. The effective field is defined as: q_eff(z, n) = q(z) × (1 + A_SN × (n · a)) where: q(z) is extracted from CC, a is the preferred axis from SN, n is the line-of-sight direction. The admissibility condition is: 0 ≤ q_eff < 1 The frozen v40 state satisfies the following consistency conditions: The SN observable improves relative to the baseline (negative delta chi-square). The CC observable is reproduced at machine precision. The BAO observable remains admissible with a non-zero anisotropic signal. This dataset contains: frozen code for all branches (CC, SN, BAO), input datasets, derived data tables, execution logs, figures, summary JSON files, and an Overleaf-ready LaTeX project. Baseline definition clarification: The baseline branch used in this dataset corresponds to a no–dark-energy cosmology (Lambda = 0). It is not a pure matter-only (Einstein–de Sitter) model. The baseline expansion function includes both a matter term proportional to (1+z)^3 and an additional geometric term proportional to (1+z)^2. Therefore, the baseline should be interpreted as a no-dark-energy reference branch rather than a matter-only universe. Data Sources: The datasets used in this release originate from publicly available cosmological surveys and compilations. Supernovae (SN):Derived from the Pantheon+ compilation (including Pantheon+SH0ES).The dataset has been processed into the file:data/sn_catalog_final.csv Cosmic Chronometers (CC):Compiled from published CC measurements (e.g., Moresco et al. and related works).The dataset has been processed into:results/rt_baseline_family_scan_v1/best_baseline_projection_table.csv Baryon Acoustic Oscillations (BAO):LRG clustering catalogs corresponding to large-scale structure surveys (e.g., eBOSS/DESI LRG samples):- LRG_NGC_clustering.dat.fits- LRG_SGC_clustering.dat.fits These datasets are used in processed form within this package. Users are encouraged to consult the original survey publications for raw data access and detailed data descriptions. The dataset corresponds to the reproducible state used in the accompanying theoretical reference: Return Theory: A Fundamental Theory of Observable Reconstruction https://doi.org/10.5281/zenodo.19277020 This release represents an observable-level closure of the RT framework under the frozen criterion. No claim of global likelihood completeness is made at this stage.