The Galoisian Boundary: An Exploratory Critique of Higher-Dimensional Physics

This paper explores a novel epistemological perspective on the macroscopic dimensionality of physical spacetime, proposing that the Abel-Ruffini theorem may serve as a structural blueprint rather than a mere artifact of algebraic notation. We introduce the exploratory Tripartite Galoisian Solvability Framework, which maps the algebraic unsolvability of general polynomials of degree n ≥5 conceptually onto the physical, structural, and computational boundaries of the spacetime continuum. By analyzing conceptual parallels across Hurwitz’s theorem on normed division algebras, topological braid theory, and the holographic Bekenstein bound, we investigate the hypothesis that the physical vacuum encounters a profound stability threshold in dimensions D ≥5. We argue that the predictive challenges of the String Landscape in higher-dimensional frameworks could be interpreted as the physical expression of the non-solvability of the symmetric group Sn for n≥5. Rather than presenting a definitive empirical proof, this work offers a unifying mathematical critique, suggesting that our observed 4-dimensional universe emerges as a mathematically optimized bound where geometry, topology, and physical information processing remain algorithmically tractable.