Automated Topological Shear Detection (S 3 ) in Gaia DR3: A Novel Computational Pipeline for Isolating Ultra-Cool Substellar and eTNO Candidates

The identification of ultra-cool substellar objects and extreme Trans-Neptunian Objects (eTNOs)in dense astrometric surveys is inherently constrained by their severe optical faintness and thelimitations of traditional photometric color-matching techniques. In this Research Note, we present anovel, automated computational pipeline that bypasses standard photometric priors by identifyingmacroscopic geometric anomalies in the celestial background. Utilizing deep astrometric data fromGaia DR3, the algorithm derives a continuous tensor field to isolate localized spatial shear against theregional Kinematic Standard of Rest (KSR). To quantify this, we introduce the Topological ShearIndex (TSI)—a mathematical ratio of macroscopic curl to divergence—designed to extract coherentkinematic vortices from stochastic N-body noise.The pipeline is equipped with a dual-tier extragalactic vetting protocol (utilizing NVSS radiocross-matching and Pan-STARRS1 optical SED analysis) and a grid-based orbital dynamics module.Deployment across multiple astrometric environments successfully eliminated high-redshift quasarcontamination and isolated a prime, stationary ultra-cool candidate (Gaia DR3 46170657914192640).The target exhibits a distinct methane absorption signature (W1 − W2 = 0.84) coupled with anextreme kinematic deficit (μ 1.31 mas/yr), generating a > 500× divergence between its theoreticalphotometric and kinematic distances. This robust reductio ad absurdum distance paradox validatesthe pipeline’s capability to detect discrete anomalies, classifying the target as either a deeply boundeTNO in the Oort cloud (> 10, 000AU) or a hyper-distant Y-dwarf halo interloper. The completePython source code and vetted datasets are provided to ensure full methodological reproducibility.Keywords: Gaia DR3, Topological Shear, eTNO, Brown Dwarfs, Astrometry, Computational Astrophysics,Python