Emergent Yukawa Forces in Sedenionic Quantum Gravity: A Dark-Matter-Free Reformulation Beyond MOND and WIMP Paradigms

We propose a foundational reformulation of quantum gravity and quantum field theory by replacing the continuous spacetime manifold with a causal lattice framework based on sedenionic algebra and displacement operators. This formulation enforces microcausality and saturation principles, allowing physical laws to emerge from non-commutative operator dynamics. Gravitational interactions are represented by commutators of symmetric and anti-symmetric sedenionic spinor fields, giving rise to both attractive Yukawa-type corrections and a repulsive component interpretable as dark energy. Notably, we demonstrate that flat galactic rotation curves can be accurately modeled without invoking dark matter halos or MOND modifications, using a stretched exponential mass distribution and an emergent Yukawa potential. The framework naturally generates the internal gauge symmetries of the Standard Model from the decomposition of sedenions and resolves quantum divergences without renormalization. This theory suggests that gravity, dark energy, and the stability of galactic structures arise from deeper algebraic geometry rather than ad hoc hypotheses, potentially marking a paradigm shift in fundamental physics.