Lensing Excess as a Geometric Projection: A No-Refit Prediction with \(A_{\rm rel}=19/15\)

Abstract

We test whether the galaxy-galaxy lensing excess (where light appears to cross more geometry than massive tracers) follows a universal geometric conversion rather than a fitted dark matter halo amplitude. Derived from tensor projection identities, the leading optical closure predicts a fixed, zero-parameter amplitude: Arel=19/15=1.2667 . Empirical Validation: We freeze this exact theoretical number and confront it—without refitting any optical amplitude—against independent observational data: KiDS isolated: Extracts Arel=1.2674±0.0315 (0.02σ offset). HSC S16A holdout: Arel=1.348±0.083 (0.97σ offset; rejects the scalar A=1 closure at >3.6σ). GAMA holdout: Statistically compatible ( χ2/N=1.190, PTE =0.271). SLACS strong lenses: Reduces residuals under both Chabrier and Salpeter IMF assumptions. SPARC/THINGS control: Forcing the optical factor into orbital dynamics worsens the fit, demonstrating strict channel separation (it is an optical projection, not a scalar force modification).