UDCT v7.13 Post-registration II: Hydrus I Jeans Sign-Boundary and Hessian Reproducibility Audit

UDCT v7.13 Post-registration II: Hydrus I Jeans Sign-Boundary and Hessian Reproducibility Audit This follow-up technical report presents an independent reproducibility audit of the numerical records published in UDCT v7.13 Post-registration I, focusing on Jeans sign-boundary diagnostics and Hessian-related calculations for observationally informed Hydrus I dwarf-galaxy models. The archived analysis covers 24 candidate sign-transition brackets, 48 endpoint evaluations, and 288 saved six-arm numerical profiles. Under the registered strict classification criteria, 18 endpoint evaluations are robust-positive, 30 remain unresolved, and none provides a robust-negative common-domain witness. Consequently, none of the 24 candidate brackets is confirmed as a strict sign transition. The audit distinguishes repeated endpoint evaluations from unique parameter coordinates and identifies an important difference between native-grid minima and minima evaluated over a shared radial comparison domain. These findings limit the interpretation of apparent negative values and reinforce the need for explicit radial-domain reporting. Independent checks of archived numerical arrays, source-code provenance, and selected reproducibility controls are documented. These checks do not constitute a complete rerun of every original physical calculation, a self-consistent three-dimensional modified-gravity Hessian solution, or a direct fit to individual Hydrus I stellar line-of-sight velocity observations. The report concludes with a preview of proposed UDCT v7.14 preregistration tests involving individual-star observational likelihoods, three-dimensional field and Hessian calculations, convergence criteria, and independently specified falsification thresholds. Related research UDCT v7.13 Post-registration I:https://doi.org/10.5281/zenodo.23539127 UDCT v7.13 Preregistration:https://doi.org/10.5281/zenodo.23342971 Reproducibility repository https://github.com/wspaik5/UDCT_v7.13_Postregistration_II_Reproducibility_Audit Reserved DOI for this report https://doi.org/10.5281/zenodo.23559995 Keywords: Hydrus I; dwarf galaxies; Jeans equation; Hessian diagnostics; modified gravity; GQUMOND; sign-boundary analysis; numerical reproducibility; preregistration; independent audit.