Branch Opening and Regime Architecture in a Covariant Scalar-Tensor Framework

This record contains the Appendix J reproducibility package for the manuscript Branch Opening and Regime Architecture in a Covariant Scalar-Tensor Framework.

The package provides the CSV table, Python reproduction script, README file, requirements file, and verification note used to reproduce the reduced two-dimensional branch-odd sign audit on THINGS H I moment maps in Appendix J. The audit uses matched MOM0 and MOM1 products for 33 THINGS galaxies. The MOM1 map supplies the line-of-sight velocity field, while the MOM0 map supplies the H I morphology proxy used to construct the reduced branch-odd carrier.

The calculation removes a reduced axisymmetric circular velocity field, constructs a morphology-based branch-odd direction from the smoothed H I intensity structure, projects the carrier along the line of sight, and compares its sign with the residual velocity field. The selected branch side is treated as a binary convention for each isolated disk, while the reported quantities measure the sign-score excess, continuous alignment, and block-scale spatial coherence.

The main summary table reports, for each processed galaxy, the valid-pixel count, selected branch side, sign score S_chi, continuous alignment statistic A_chi, 16 x 16 block score, block SEM, residual-velocity diagnostics, and automatically inferred geometry quantities. The verification note records the sample-level results: 33 processed galaxies, zero processing failures, mean(S_chi - 1/2) = 0.018986, median(S_chi - 1/2) = 0.009256, mean(A_chi) = 0.042010, selected-branch S_chi > 1/2 in 33/33 systems, and selected-branch A_chi > 0 in 27/33 systems.

The output is framed as a reduced public-data residual-sign stress audit rather than as a final branch-detection claim or a precision dynamical model. Its role is to expose an orientation-sensitive two-dimensional residual channel that is compressed away in one-dimensional azimuthally averaged rotation-curve readouts.