Simulated Topological Detection of the 1.054 Berard Constant in Synthetic Rubin LSST Data Streams (v19.1)

Update: v19.1 — Density-First, TDA-Confirmed Pipeline (supersedes v15) This deposit updates the original v15 simulation (DOI: 10.5281/zenodo.18880631) with a fundamentally revised detection pipeline and comprehensive validation results. What changed and why. Blind testing of the v15 pipeline revealed that its preprocessing steps (Yuan 2n–3m filtering, planar slice, and core excision) manufactured H1 persistence features from pure noise, producing a 100% false positive rate across 21 trials. A step-by-step diagnostic confirmed that the combination of planar slicing and core excision carved an annular geometry from any input, topologically guaranteeing the H1 feature the pipeline claimed to detect. The original Death/Birth > 1.5 threshold was not selective: random noise exceeded it by a factor of 100. The v19.1 architecture replaces the original approach entirely. Detection now proceeds in three stages: (1) a radial density scan comparing observed bin counts against the analytical expectation for a uniform cube, flagging overdensities exceeding 5σ; (2) shell-projected TDA, which extracts points in the flagged radial band, projects them onto the unit sphere, and checks angular topology against a null distribution; and (3) an annular self-calibration scan that repeats the analysis at multiple radii within the same dataset, requiring the candidate radius to stand out from non-candidate radii. Final detection requires the density scan plus at least one confirmation channel. Validation results (v19.1): Blind suite: 19/19 correct (7 TP, 12 TN, 0 FP, 0 FN). Sensitivity 100%, specificity 100%. Harmonic sweep: 10/10 Tav harmonic modes detected when injected (k=1 through k=10). Null harmonic check: 0/10 false detections with no injection. The falsifiable prediction from v15 remains unchanged: when applied to raw 2026 Euclid Heritage Deep Field or Rubin LSST Gold Sample data, the pipeline should detect a radial overdensity near the 1.054 normalized scale (approximately 7 h⁻¹ Mpc) without manual signal injection. If only noise-level counts appear at this scale, the Tav Topology model is falsified. The v19.1 pipeline is the instrument now registered to perform that test. All terminology (Berard Constant, Tav Ring, Tau-Yuan-Dupke Pipeline) is original to the original author(s) and does not appear in peer-reviewed literature.