A Testable Hypothesis for Dynamical Dark Energy as a Spatially Propagating Field: Observational Tests and Constraint

This version includes preliminary observational constraint analyses using Planck, WISE × SuperCOSMOS, SDSS, Pantheon+, and Cosmicflows-4 datasets. Added analyses include ISW tomography, dipole and quadrupole anisotropy tests, harmonic-space CMB–galaxy cross-correlation measurements, multipole localization studies, redshift-sliced analyses, and robustness checks involving Galactic masking, mask apodization, galaxy-position randomization, and jackknife resampling. The updated analyses did not reveal robust statistically significant evidence for a cosmological-scale preferred axis, anisotropic late-time expansion signature, or propagating dark-energy front, thereby placing initial observational constraints on the simplest detectable forms of the proposed framework. However, the analyses identified a localized low-redshift CMB–galaxy cross-correlation anomaly in the southern sky. The feature is independently reproduced using both WISE × SuperCOSMOS and SDSS galaxy samples and appears consistently across the SMICA, NILC, SEVEM, and Commander Planck component-separation maps. The anomaly survives multiple robustness tests, including masking variations, position randomization controls, and jackknife resampling. Its physical origin remains unknown, and the results should be regarded as exploratory pending independent confirmation and formal look-elsewhere corrections. DOI: https://doi.org/10.5281/zenodo.20546821