The Poincaré Conjecture was a central question in topology, concerning the characterization of three-dimensional spheres. It proposed that every simply connected, closed 3-manifold is homeomorphic to a 3-sphere.
Formulated by Henri Poincaré in 1904, the conjecture remained open for a century and drove major developments in geometric topology. Its resolution would confirm a fundamental property of three-dimensional spaces.
In 2003, Grigori Perelman provided a proof based on Richard Hamilton's Ricci flow program, which was later verified and accepted by the mathematical community. Perelman declined the Millennium Prize.
The Poincaré Conjecture was resolved by Perelman through Ricci flow. The structural framework developed here examines the same topological question from a different organizing principle — one that does not rely on geometric deformation but on the intrinsic behavior of loops and their structural closure properties in 3-manifolds.
The approach is purely topological. Details will be made available upon publication.