Geometric-State Formalism for Hadronic Structure and Transitions Structural Selection and Transition Geometry in Strong-Interaction Systems

Abstract This work introduces a geometric-effective formalism for describing hadronic structure and transitions beyond purely algebraic classification schemes. The central thesis is that hadronic states should not be understood solely as elements of symmetry-defined multiplets, but as structurally selected configurations within a continuous manifold of dynamically admissible states. Within this framework, each hadronic configuration is represented as a point on an effective state manifold equipped with a metric that encodes the cost of internal reconfiguration under relativistic dynamics. Observable states correspond to local extrema of a variational functional, while decay processes are interpreted as geodesic trajectories on this manifold. This approach provides a unified description of: ● mass hierarchies as geometric stability moduli, ● multiplet splitting as curvature-induced structure, ● decay channel preference as minimal-action transition paths. A minimal toy model demonstrates that the baryon decuplet mass spectrum can be reproduced with high accuracy using a reduced geometric construction. A complementary transition model shows that channel suppression naturally emerges from geometric path length in state space. The formalism does not replace Quantum Chromodynamics or effective field theory, but introduces an additional structural-geometric layer of description that addresses a persistent gap in hadronic physics: the absence of a unified principle explaining why certain admissible configurations emerge as experimentally clean, stable, and dynamically preferred