The Geometric Origin of "Dark Matter": Unclosed Relational Pathways in the 24-Regular Graph

This paper resolves the dark matter anomaly by strictly applying the Geo-
metric Framework of Knowledge to a purely relational 4-dimensional architecture.
While the observable universe operates as a 3-dimensional defect manifold defined
by closed relational loops, exactly 12 orthogonal relational vectors within the 24-
regular graph cannot geometrically close. Utilizing the framework’s seven-stage
derivation template, we mathematically prove that these 12 unclosed orthogonal
vectors impose a continuous, macroscopic compatibility strain on the 3D manifold.
This framework derives the exact gravitational signatures attributed to ”dark mat-
ter” strictly through relational network tension, definitively refuting the need for a
physical substrate, hidden sectors, or undiscovered dark particles.