The Poincaré Conjecture as a Separating Principle: A Support Vector Machine Framework for Classifying Void Topology in Embedded Simply Connected 3-Manifold Objects

This work explores the implications of the Poincaré Conjecture for systems of embedded simply connected objects. By shifting attention from object topology to the topology of void space, the work introduces a Support Vector Machine framework for classifying spatial configurations using homological invariants of complementary space. The manuscript includes theoretical foundations, algorithmic pseudocode, and references bridging topology, geometry, and machine learning.