Cosmic Potential Field I: A Preliminary Theoretical Framework for Scale-Dependent WJ Gravity and Cosmic Tension Dynamics

This Zenodo record provides an open-access version of the WJ dynamical framework materials and associated reproducibility packages. The WJ framework is a phenomenological gravitational and cosmological model in which a global accumulation-rate parameter, g_w, is used to describe a time-dependent weak-field acceleration scale. The materials deposited here are intended to document the calculations, numerical tests, and supporting scripts used in the accompanying manuscripts and supplementary analyses. Main scientific components 1. Local galaxy-rotation benchmark using SPARC The framework is applied to 118 galaxies from the SPARC database using published baryonic masses and observed flat velocities. After a single global normalization of the acceleration scale, the model produces forward asymptotic velocity predictions without introducing galaxy-by-galaxy halo parameters, individual acceleration-scale adjustments, distance corrections, inclination corrections, or stellar mass-to-light-ratio tuning as fitting parameters. The median absolute fractional residual for the 118-galaxy benchmark is 9.74 per cent. 2. Intermediate-redshift benchmark-control analysis using KROSS/Sharma data The framework is also evaluated using a balanced nine-object KROSS/Sharma sample at redshifts approximately 0.84 to 0.96. For each object, the time-dependent WJ prescription and a static local-a_0 control use the same catalogue baryonic quantity, radius, transition relation, and velocity uncertainty. The comparison contains WJ-favouring cases, static-a_0-favouring controls, and a degenerate control. It is therefore presented as a mixed intermediate-redshift benchmark-control diagnostic rather than as a complete resolved rotation-curve validation. 3. Diagnostic analysis of UGC 07125 UGC 07125 is treated as a high-residual diagnostic case. The original SPARC catalogue inputs give a predicted asymptotic velocity of 107.74 km s^-1 compared with the reported flat velocity of 64.57 km s^-1, corresponding to a residual of 66.86 per cent. Using the central Cosmicflows-3 Tully-Fisher distance adopted in the SN 2020qmp study lowers the prediction to 95.64 km s^-1 and the residual to approximately 48.1 per cent, but does not eliminate the discrepancy. The case is therefore presented as a useful target for future extended H I kinematic mapping and improved distance, inclination, and geometry constraints, rather than as a resolved validation case. 4. Conditional high-redshift test using REBELS-25 The framework is applied to the published baryon-dominated mass model of REBELS-25 at z = 7.31. Because the cosmic age is only approximately 0.70 Gyr at this redshift, the time-dependent acceleration scale is strongly suppressed and the predicted rotation curve is close to the baryonic Newtonian limit. Under the adopted conditional mass model, the predicted velocity at r approximately 2 kpc is 350.7 km s^-1, consistent with the reported maximum rotation speed of 374 (+86/-91) km s^-1. Because the adopted mass normalization contains kinematic information, this agreement is treated as a conditional consistency check rather than as an independent parameter-free confirmation. The principal falsifiable prediction is a declining outer rotation curve at currently unresolved radii, testable with future high-resolution ALMA or JWST-assisted kinematic observations. 5. Additional cosmological and phenomenological materials This record also includes broader theoretical and numerical materials related to the WJ framework, including exploratory calculations concerning the Hubble expansion, Type Ia supernova consistency tests, CMB-scale phenomenology, time-of-flight considerations, and other proposed observational diagnostics. These broader components are provided as a theoretical overview and reproducibility archive. They should be interpreted as part of an ongoing phenomenological programme rather than as a complete relativistic theory. Included data and code packages This Zenodo deposit contains supplementary reproducibility packages, including: 1. WJ_Hubble_Validation_Package.zip This package contains code, input data, and output tables for the Hubble-expansion and Pantheon+ Type Ia supernova calculations described in the broader WJ framework materials. 2. WJ_MNRAS_supplementary_code_data_2026-08-04.zip This package contains galaxy-dynamics supplementary materials for the SPARC flat-velocity benchmark, the UGC 07125 diagnostic calculation, the conditional REBELS-25 rotation-curve calculation, and the KROSS/Sharma intermediate-redshift benchmark-control analysis. The KROSS/Sharma materials include the plotting script, source-quality and visual-review input tables, the manuscript-facing source table, and PDF, PNG, and SVG versions of the benchmark-control figure. Both packages include README files describing the data sources, scripts, usage instructions, evidence roles, limitations, and output products needed to reproduce the deposited calculations. Data sources The deposited calculations make use of publicly available or published data products, including the SPARC database, public KROSS/Sharma catalogue products, published ALMA measurements and modelling for REBELS-25, Pantheon+ Type Ia supernova data, Planck 2018 cosmological results, Fermi-LAT materials, SH0ES-related published values, and relevant JWST/CEERS/ERS literature. Original datasets remain subject to the citation and usage policies of their respective authors and collaborations. Scope and limitations The WJ framework materials deposited here are presented as a phenomenological and exploratory modelling programme. The galaxy-dynamics component is designed as a forward kinematic test with a single global normalization and no galaxy-by-galaxy adjustable parameters. The SPARC analysis is a local consistency benchmark, the KROSS/Sharma analysis is a mixed intermediate-redshift benchmark-control diagnostic, UGC 07125 is an unresolved local diagnostic case, and REBELS-25 is a conditional high-redshift consistency test and outer-curve forecast. The broader cosmological materials are intended to document theoretical development and reproducibility, and they do not constitute a complete relativistic theory. Competing interest and patent disclosure The author declares a potential competing financial interest. W. Zhang has filed a patent application, Application No. 2026102178711, related to computational and theoretical methodologies associated with the WJ framework. The patent application did not influence the reporting of the astronomical data analysis or the reproducibility materials deposited here. License and use This record is provided for academic research, verification, and reproducibility. Commercial use of the author's original theoretical and computational materials is not permitted without prior permission. Third-party datasets included or referenced in the packages remain governed by their original licenses and data-use policies.