Simulated Topological Detection of the 1.054 Berard Constant in Synthetic Rubin LSST Data Streams (v15)

Simulated Topological Detection of the 1.054 Berard Constant in Synthetic Rubin LSST Data Streams (v15) This dataset contains a synthetic verification of a topological data analysis (TDA) pipeline designed to detect loop-like (H1) homology features in large-scale cosmic point clouds. Using the author-proposed Tau-Yuan-Dupke Pipline -- comprising Yuan 2n-3m Gaussian difference filtering, Dupke facotr-2 radial oversampling, and GUDHI AlphaComplex perisistent homology -- we demonstrate recovery of a planted torodial shell at radius 1.054 (approximately 7h-1 Mpc) from a stochastic background of 15,000 uniform random points. This is a controlled simulation, not a blind detection. The 1.054 shell is injected into the synthetic point cloud before analysis. The purpose is to establish a topological benchmark: proving the pipeline can isolate a persistent H1 feature at a specified scale against noise, in preparation for application to real survey data. The deposit includes the Python source code, the three-panel output figure (Tav Ring geometry, radial resonance histogram, GUDHI persistence diagram), a compiled LaTeX abstract with full references, and a falisfiable prediction stating that an identical H1 signature will appear in raw 2026 Euclid Heritage Deep Field or Rubin LSST Gold Sample data without manual signal injection. Explicit confirmation and falsification criteria are provided. All named constructs (Berard Constant, Tav Ring, Tau-Yuan_Dupke Pipeline) are original terminology introduced by the author or their respective author(s).