A Localisation Tool for Riemann Zeta Zeros from a Matchstick Game on the Riemann Sphere

Overview This repository provides the official implementation, datasets, and mathematical framework for a novel discrete-geometric approach to analyzing the Riemann Zeta function and localizing its non-trivial zeros. Moving away from purely continuous complex analysis, this work reformulates the fundamental properties of prime number generation (the Matchstick Game) as a purely combinatorical and topological folding problem directly mapped onto the Riemann Sphere. Key Methodology Geometric Prime Unfolding: The classical multiplicative structure of prime numbers is transformed into a discrete spatial layout on a spherical target space. The critical line (sigma = 0.5) naturally emerges as the starr, invariant equator under north-south reflection symmetry (s - 1-s). Riesz-Weighted Inversion: To detect and isolate the non-trivial zeros without relying on traditional analytical continuations, the framework introduces a robust algorithmic tool called the V-Indicator. This indicator leverages historical Riesz-mean weights to act as an "equator detector," scanning the spherical geometry for absolute minima. Deterministic Bounding (Zero-Free Corridors): The algorithm generates explicit, computer-verified error certificates. It proves that as the number of discrete steps N increases, the deterministic security corridor enclosing the true minimum sharpens universally. Scientific Integrity & Scope Following rigorous scientific standards, the paper includes a detailed multi-zero analysis ("B17 Self-Protection") demonstrating that early-stage local symmetries (such as a recurring 2.56 scaling factor found at the first zero) dynamically shift into global variances as higher dimensions (t) are computed. The method does not claim a full analytical proof of the Riemann Hypothesis, but offers an honest, scalable, and highly stable algorithmic evolution over traditional numerical verification tools.