The χ-Field as Dark Matter: Comprehensive Validation Across 10 Independent Tests with No Per-Galaxy Fit Parameters

Dark Matter Phenomenology from Spatial Variations of the χ Field in the Lattice Field Medium This paper investigates whether phenomena commonly attributed to particle dark matter arise instead from spatial inhomogeneities in the χ field of the Lattice Field Medium (LFM), governed by the canonical wave equation: d^2E/dt^2 = c^2 ∇^2E − χ(x,t)^2 E Within LFM, gradients and large-scale redistribution of the χ field modify effective inertial response in the low-acceleration regime. From this dynamics, the paper derives a closed-form velocity enhancement law and shows that, in the deep low-acceleration limit, the baryonic Tully–Fisher relation (v^4 ∝ M_bar a0) follows as a necessary consequence rather than a fitted empirical rule. The characteristic acceleration scale a0 is fixed by cosmology as a0 = cH0/(2π), with no per-galaxy or per-dataset tuning. The framework is tested against thirteen independent observational probes spanning galactic, cluster, and cosmological scales, including SPARC galaxy rotation curves, the baryonic Tully–Fisher relation, the radial acceleration relation, strong gravitational lensing, galaxy cluster mass profiles, the Bullet Cluster, wide binaries, dwarf spheroidals, ultra-diffuse galaxies, and early massive galaxies observed by JWST. Where applicable, comparisons with standard MOND formulations are presented under consistent assumptions. The analysis uses only published observational data and fixed theoretical inputs. Observational successes, partial agreements, and tensions are all reported explicitly. The results suggest that a collisionless, non-radiating χ-field substrate can reproduce many signatures attributed to dark matter without invoking new particle species, while remaining falsifiable in specific low-acceleration and small-system regimes. All analysis scripts, source data, and reproduction instructions are provided in the accompanying Zenodo package.