Algebraic Stabilization of Topological Foam at the Big Bounce Singularity via Hypertensor Fields

The ultimate catastrophe arising from the interface of general relativity and quantum gravity is the gravitational singularity. Traditional cosmological models fail to control the fragmentation of topological foam when curvature diverges during the Big Bounce (¨a > 0).To resolve this limitation, this paper develops Hypertensor Field Theory anchored in Rough Operator Algebra (ROA). We redefine the singularity not as a physical collapse to a zero dimensional point, but as an ’algebraic non-identity limit’ state within the ROA space. By elevating the quantum Bohm potential pressure term to a multidimensional anisotropic tensor divergence (∇_µ^tensor V_Q^µν ), we mathematically prove that fragmenting topological foam grids are stabilized through hypertensor networks. Consequently, the universe avoids zero dimensional collapse and executes a smooth, multidimensional repulsive expansion.