The Geometric Origin of Black Holes: Macroscopic Fracture Limits and Topological Punctures

This paper resolves the singularity paradox of legacy physics by applying the
Geometric Foundation of Knowledge to a 4-dimensional relational architecture.
Legacy physics predicts infinite density at the core of a black hole, representing a
mathematical breakdown. By defining the observable universe as a strictly con-
strained 3-dimensional defect manifold (P4i=1 xi = 0), we demonstrate that black
holes are not infinitely dense objects, but macroscopic structural fractures. Utiliz-
ing the framework’s seven-stage derivation template, the black hole is classified as
a Critical Fracture Limit. When local curvature exceeds the absolute architectural
bound (κmax), the 3D manifold physically tears, severing local tangent vectors and
fully exposing the region to the 4D orthogonal substrate.