Empirical Validation and Certification of Prime Curvature Geometry

This paper presents an empirical certification of the Prime Curvature Geometry Conjecture for Goldbach (PCGC-Goldbach), as formulated in Riemers2026-PCGH. All tested instances with 4 ≤ 2n ≤ 23# ≈ 2.5852×10^8 are certified to satisfy the geometric curvature bounds predicted by PCGC-Goldbach. The certification spans a discrete family of fixed-scale Goldbach windows and covers more than 16 billion non-trivial test scenarios, with no violations observed across the entire tested range. Beyond aggregate verification, the paper provides detailed extremal and pointwise analysis of the certified bounds together with a fully reproducible computational pipeline. All certified claims are grounded in explicit enumeration rather than probabilistic heuristics, and the associated data products and verification artifacts are archived to permit independent audit and falsification.