ISF Paper IV: Testing Independent Structure Formation Across ψ-Branches with 258,000 BOSS Galaxies

We test the independent structure formation (ISF) hypothesis — that dark matter consists of ordinary matter on gravitationally coupled but electromagnetically isolated ψ-branches, each developing its own cosmic web — using 258,153 BOSS DR12 LOWZ galaxies. The ISF prediction is spatial autocorrelation of dark matter fraction residuals at cosmic web scales (10–50 Mpc) after controlling for galaxy properties. A random forest regression explains 91.3% of f_DM variance; the residuals show highly significant spatial autocorrelation (z-scores up to 28σ) that survives redshift slicing and is not proportional to the galaxy two-point correlation function. However, three diagnostic tests identify the signal as a residual redshift systematic: (1) the signal is 3–4× stronger along the line of sight than transverse, ruling out isotropic 3D structure; (2) SDSS plate-level residuals show significant excess variance (ANOVA p ~ 10⁻¹⁰⁹); and (3) redshift carries 215σ spatial autocorrelation among input features versus 7.7σ for the f_DM residual itself. We conclude with a clean null result for ISF, constraining the marked correlation function to w < 10⁻⁴ at 10–50 Mpc. This is Paper IV in the RDT dark matter prediction series. Version 2 Add public git repo with all analysis tools under active development with MIT License.