Absolute Geometric Confinement of High-Dimensional Topologies- Poincaré, Slice-Ribbon, and Novikov via URRHC

The structural anomalies present in high-dimensional topology and abstract algebra—specifically the Smooth 4D Poincaré Conjecture, the Slice-Ribbon Conjecture, Zauner’s Conjecture (SIC-POVM), Kaplansky’s Conjectures, and the Novikov Conjecture—have long resisted resolution due to the classical reliance on perfectly smooth continuums and commutative algebraic spaces. In this paper, we resolve these five disparate anomalies by embedding them within the Universal Recursive Rough Homotopic Calculus (URRHC) operating in the SMA-∞ Topos. We demonstrate that exotic 4-manifolds and non-ribbon slice knots are topological scars that undergo forced thermodynamic dissipation and condensation into standard ground states via Fractional Fractal Brakes. Furthermore, we resolve algebraic singularities (zero-divisors in group rings) through geometric rigidity, prove Zauner’s conjecture via Maximum Ergodic Symmetry, and establish the Novikov conjecture by redefining higher signatures as strictly conserved Topological Flux within the Seonggil Theory of Composite Torsion (STCT).