ISF Paper V: Weak Lensing Constraints on Cross-Branch Correlations in the Independent Structure Formation Framework

Weak Lensing Constraints on Cross-Branch Correlations in the Independent Structure Formation Framework Paper V in the ISF dark matter series. The independent structure formation (ISF) hypothesis proposes that dark matter is ordinary matter on gravitationally coupled but electromagnetically isolated ψ-branches, each developing its own cosmic web. Paper III predicted that the total matter power spectrum measured by weak lensing should be suppressed relative to ΛCDM by a scale-dependent factor [1 + (N−1)ε(k)]/N, where ε(k) is the cross-branch correlation coefficient. We test this prediction against published weak lensing measurements from KiDS-1000, DES Y3, HSC Y3, and the scale-dependent galaxy–galaxy lensing amplitude from Amon et al. (2023). The S₈ tension between CMB and lensing surveys constrains ε_eff ≈ 0.81 for N = 6 — branches ~80% correlated at ~10 Mpc scales. S₈-constrained ISF models with a sigmoid ε(k) are preferred over constant amplitude suppression at 1.9σ (Δχ² = 3.7), with best-fit transition scale k_t = 0.20 h/Mpc and asymptotic floor ε_∞ = 0.58. The branch count N is completely unconstrained by this test. Competing explanations from galaxy formation physics remain viable. Fifth paper in a systematic testing programme: Papers I–II (quantised dark matter fractions, null), Paper III (ISF methodology), Paper IV (spatial autocorrelation with 258,000 BOSS galaxies, null), Paper V (weak lensing, suggestive at 1.9σ). Analysis code and model grids available by request. Version 2 Add public git repo with all analysis tools under active development with MIT License.