# Online Resource 1: Reproduction Package

**Article title:** Temporal Slot Selection in an FRW Disformal Background under External Hubble-Constant Constraints  
**Journal:** General Relativity and Gravitation  
**Author:** Atsushi Otsuka  
**Affiliation:** Independent Researcher, Osaka, Japan  
**Corresponding author:** Atsushi Otsuka, otsuka.omnis@gmail.com  
**ORCID:** 0009-0009-8241-1922

**Caption:** Online Resource 1 contains the reproduction package for the numerical background-sector calculations reported in the article. It includes processed observational input files, the Python reproduction script, shell runners for the no-external-H0, Planck-like, and SH0ES-like cases, optional H0-profile scan data, and machine-readable reference outputs for direct table checks.

This package reproduces the numerical background-sector calculations used in the manuscript "Temporal Slot Selection in an FRW Disformal Background under External Hubble-Constant Constraints".

The package contains the processed observational input files, the Python reproduction script, shell runners for the reported numerical cases, optional profile-scan data, and machine-readable reference outputs for direct table checks.

## Quick run

```bash
python -m py_compile sector_selection_calc.py
./run.sh                 # Planck-like external-H0 main run
./run_no_prior.sh        # no-external-H0 boundary diagnostic
./run_shoes.sh           # SH0ES-like robustness check
./run_all_reference.sh   # all three reference runs
```

## Main Planck-like matched-complexity result

The selected internal comparison is spatial-only 1p versus temporal-only 1p.

| branch | H0 | chi2_data | chi2_H0 | chi2_tot |
|---|---:|---:|---:|---:|
| spatial-only 1p | 62.1302 | 1435.5848 | 111.0851 | 1546.6699 |
| temporal-only 1p | 66.4064 | 1409.4353 | 3.9488 | 1413.3841 |

```text
Delta chi2_data(space1 - time1) = 26.1495
Delta chi2_H0(space1 - time1)   = 107.1362
Delta chi2_tot(space1 - time1)  = 133.2858
```

## Full-branch diagnostic status

The full two-slot branch is optimized as a higher-profile diagnostic branch. Because the full branch contains the temporal-only 2p branch as the `gamma = 0` subspace, the full branch is seeded from the temporal-only 2p optimum embedded at `gamma = 0` and then re-optimized over the full parameter vector.

```text
Planck-like full:
H0        = 66.3653
n         = 5.0000
gamma     = -0.0550
chi2_data = 1293.9636
chi2_H0   = 4.2822
chi2_tot  = 1298.2458
```

The full branch is not selected as the main model because it is not a matched-complexity competitor to the one-parameter branches and because it reaches the profile boundary `n = 5.0`.

## Data and reference outputs

Processed input data are stored under `rawdata/`.
Optional profile-scan data are stored under `optional_figure_data/`.
Reference outputs are stored under:

```text
results_planck_reference/
results_no_prior_reference/
results_shoes_reference/
```

Each reference-output directory contains per-model JSON files, a CSV summary, a Markdown summary, and a run manifest.

See `REFERENCE_VALUES.md` for exact table values and `RESULTS_OVERVIEW.md` for a compact output summary.
