[en] Investigations aimed at putting the topological theory of particles on a more quantitative basis are described. First, the incorporation of spin into the topological structure is discussed and shown to successfully reproduce the observed lowest mass hadron spectrum. The absence of parity-doubled states represents a significant improvement over previous efforts in similar directions. This theory is applied to the lowest order calculation of elementary hadron coupling constant ratios. SU(6)_W symmetry is maintained and extended via the notions of topological supersymmetry and universality. Finally, efforts to discover a perturbative basis for the topological expansion are described. This has led to the formulation of off-shell Feynman-like rules which provide a calculational scheme for the strong interaction components of the topological expansion once the zero-entropy connected parts are known. These rules are shown to imply a topological asymptotic freedom. Even though the nonlinear zero-entropy problem cannot itself be treated perturbatively, plausible general assumptions about zero-entropy amplitudes allow immediate qualitative inferences concerning physical hadrons. In particular, scenarios for mass splittings beyond the supersymmetric level are described