Fundamental Reform of the Circular Metric: From Euclidean π to Torsion K Geo via the PR-TAU 5.2.3 Protocol

This paper proposes a fundamental revision of the circular constant π within the framework of a rigid and discrete spacetime. We demonstrate that the use of the Euclidean value π eucl ≈ 3.14159 constitutes an ideal approximation that does not represent the actual vacuum metric. By introducing the local geometry coefficient KGeo ≈ 3.1434, (calibrated value: 3, 143405) derived from the intrinsic vacuum rigidity (ϵ), we resolve the topological discontinuities at the heart of the seven Millennium Prize Problems. Baryonic mass is identified as the energy residue required for topological closure under this torsion metric.