Deriving the G-Algebra Dark Matter Mass Scale via Discrete Loop Expansion

In the Standard Model, dark matter is an ad-hoc particle introduced to resolve gravitational anomalies, possessing mass but no electromagnetic interaction. In Computational Finitism, dark matter is not an exotic addition; it is a structural necessity of the non-associative substrate. Building upon the algebraic derivation of the electron as an Octonionic Möbius Defect, we demonstrate that dark matter consists of topological knots confined strictly to the 2 channels of the Topological Redundancy Buffer (TRB). Because these G-algebra knots are orthogonal to the 7 Fano channels, they exhibit zero electromagnetic coupling (perfect darkness). However, they still exert a "maintenance load" on the vacuum hardware, curving the TRB buffer and manifesting as gravity. Applying the discrete loop expansion, we derive the dark sector's geometric coupling fraction to be exactly 2/44. This yields a fundamental dark matter mass scale of mx≈ 3.183 MeV. Furthermore, we predict that when these knots collide in high-density galactic halos, they trigger a "Möbius Phase Flip," ejecting monochromatic photons at exactly 3.18 MeV. We provide dual computational proofs, statistical and mechanical, validating this mechanism, and propose a falsifiable search target for next-generation gamma-ray telescopes in the unexplored "MeV Gap."