UDCT v7.14 Exploratory Findings: The p=1.5 Boundary in QUMOND

UDCT v7.14 Exploratory Findings: The p=1.5 Boundary in QUMOND Research status: Exploratory investigation and archival record. This work is not a formal preregistration. This research archive documents the UDCT v7.14 exploratory investigation of QUMOND-related Hessian behavior, stationary Jeans-equation consistency, and phase-space admissibility in dwarf-galaxy models, with particular attention to Hydrus I. The investigation preserves 50 exploratory steps, together with preliminary audit records, supporting research documentation, and Python/CSV/JSON materials intended to facilitate independent reproducibility checks. The study examines mathematical and physical consistency boundaries, including the investigated p=1.5 boundary, under specified model assumptions. These exploratory findings are not presented as confirmed universal thresholds or as evidence of observational superiority over MOND, QUMOND, GQUMOND, or dark-matter models. Calculations using observationally motivated Hydrus I inputs are distinct from direct statistical fitting to individual stellar line-of-sight velocity measurements. No completed observational validation is claimed. Archived materials Preliminary exploratory audit records (1–6) Hessian exploratory Steps 01–25 Hessian exploratory Steps 26–50 Consolidated research PDF and supporting documentation Python, CSV, and JSON reproducibility materials Future research Formal UDCT v7.14 preregistration will be conducted separately, with explicitly defined new hypotheses, prospective tests, numerical procedures, and acceptance or falsification criteria. Previously explored findings will not be represented as newly preregistered predictions. GitHub repository: https://github.com/wspaik5/UDCT_v7.14_Exploratory_p1.5_Boundary Keywords: QUMOND, GQUMOND, Hessian, Jeans Equation, Phase-Space Consistency, Hydrus I, Dwarf Galaxies, Exploratory Research, Reproducibility, Modified Gravity.