Structural Irreducibility in Hadronic Spectroscopy: A Two-Invariant Classification

We propose that the correct basis for classifying hadronic configurations is not quark content but structural class membership, determined by two independent invariants: the topological winding number of the field configuration and the stoichiometric type of the colour-singlet decomposition. Configurations sharing both invariants with a simpler reference object are not new particle species; they are composites of that reference object — a conclusion that follows from the composition principle, which states that structural class is exhausted by these two invariants and admits no further refinement from kinematic data. We show that the tetraquark (qqq̄q̄) shares both invariants with the meson (qq̄) and is therefore a di-meson molecule, not an exotic hadron. The pentaquark (qqqqq̄) does not share the meson’s stoichiometric type and is therefore genuinely irreducible — a new structural class. The baryon’s topological winding number is integer-quantized and distinct from all other configurations; baryon number conservation follows from this quantization without additional postulate. All three conclusions are derived from invariants that any particle physicist already accepts. No new dynamical model is proposed