Void-Weighted Line-of-Sight Integrals as Probes of the Primordial Magnetic Field, the Integrated SachsWolfe Eect, and Rotation Curve Asymmetry

Abstract

We present the complete mathematical framework of the Ariza Length family a set of line-of-sight integral operators dened over the cosmic void network, eachdesigned to quantify a distinct physical aspect of the interaction between photonsor test particles and the large-scale structure of the universe.The family currently comprises six members: the geometric LA, the density-weighted LA,ρ, the kinematic Λkin, the volume-weighted LVA , the eigenvalue-weightedLλA, the unied LV λA , and the BAO-integrated LBAOA,ρ . Each member is formallydened, physically motivated, and connected to at least one falsiable observationalprediction.The density-weighted length LA,ρ is proposed as a phenomenological proxy forthe accumulated gravitational metric perturbation along the line of sight in the per-turbed FLRW universe the Geodesic LOS Tension TLOS motivating a testablecorrelation between void traversal and the CMB Integrated SachsWolfe signal.The kinematic non-atness statistic Λkin is computed for the complete SPARCsample of 175 disk galaxies using published rotation curves Lelli2016, yielding a re-producible dataset with Λkin ∈ [0.000, 0.254] (median = 0.039). Note: Λkin measuresdeviation from a at rotation law, not approachingreceding asymmetry; the latterrequires separately published two-sided curves.All numerical results in this manuscript use real, published observational datawith exact bibliographic references. No simulated or approximated data are reportedas observational results.