The Future Program of Computational Finitism: Discrete Loop Expansion in Non-Associative Algebra and the Rationalization of 1/2π

The transition from continuous Quantum Electrodynamics (QED) to a discrete, finite causal graph requires a fundamental re-evaluation of the primitive operations governing the substrate. In The Scalar Wall, we documented a systematic negative result: scalar Modulo-9 cellular automata, regardless of dimensionality or update rule, fail to produce chirality or localized defects due to the commutativity of addition and the non-conservative nature of modulo arithmetic. Consequently, the primitive operation of the universe cannot be scalar; it must be algebraic. In this paper, we establish the Future Program of Computational Finitism by elevating the substrate to a non-associative Octonionic G-algebra. We demonstrate that the continuous loop integrals of Feynman diagrams are replaced by a Discrete Loop Expansion, a finite summation over the combinatorial geometry of the octonionic multiplication table. Crucially, we prove that the continuous geometric constant 1/(2), ubiquitous in QED, is naturally rationalized by the discrete algebra as the exact fraction 7/44. This 0.04%discrepancy is not an error, but the finitist truncation inherent in mapping a discrete rational lattice to a macroscopic continuous observation. Finally, we introduce the 8th algebraic dimension as the structural origin of Dark Matter, setting the stage for the derivation of the G-algebra dark matter mass scale.