Kinematic Lensing via the Topological Shear Index: Mapping Macroscopic Spacetime Deformations Beyond the Zone of Avoidance

Abstract

Mapping cold stellar streams, dwarf galaxy remnants, and obscured mass concentrations in the Galactic halo is fundamentally constrained by interstellar dust extinction in regions such as the Zone of Avoidance (ZoA) and molecular cloud complexes. We present an updated, non-parametric astrometric diagnostic framework centered on the Topological Shear Index (TSI)—a lightweight computational pipeline designed for blind, exploratory mapping of localized velocity shear in transverse proper motion fields. In this Version 2 pipeline, foreground suppression is driven by strict parallax filtering (ϖ < 0.5 mas) without applying artificial proper motion cutoffs, ensuring that high-velocity stream members (such as GD-1 stars with μ_tot ≈ 6–12 mas/yr) are preserved. The framework incorporates an orthographic tangent-plane tensor engine to eliminate metric pole compression (cos δ distortions), an Interquartile Range (IQR) outlier rejection gate, catalog-level Monte Carlo error propagation (K = 100), Benjamini-Hochberg False Discovery Rate (FDR) control (α = 0.05), and differential Galactic rotation subtraction. We evaluate the pipeline using Gaia DR3 proper motion data across two full-scale 20° × 20° benchmarks: the cold stellar stream GD-1 (α = 148°, δ = +36°) and an isotropic null control field (α = 60°, δ = +15°). Over GD-1, the pipeline isolated persistent peculiar shear nodes (leading candidate at α = 154.0°, δ = +36.5° with Z = 3.68σ, Q_FDR = 0.014, TSI_peculiar = 1.086) aligned along the known stream spine. In the isotropic null benchmark, FDR control suppressed > 99.8% of background fluctuations, demonstrating high statistical selectivity. This framework provides an efficient, reproducible diagnostic tool for hypothesis generation in wide-field astrometric searches for Galactic substructure. Keywords: Astrometry; Topological Shear Index (TSI); Proper Motions; Stellar Streams; Gaia DR3; False Discovery Rate (FDR); Galactic Substructure.