The Mass Concept in the Layer Theory of Spacetime: Part IV: Full Matter–Higgs–Gauge Mode Space, Hadron Spectroscopy, and Geometric Closure of Light and Strange Composite States

The Mass Concept in the Layer Theory of Spacetime – Part IV develops a unified geometric treatment of light mesons and strange baryons within the same layered five-dimensional framework previously used for fermion masses, neutrinos, and heavy hadrons. The central result is that visible hadron masses and spin splittings can be organized by a single matter–Higgs–gauge mode space in the operational layer coordinate z, without introducing new particles, new gauge interactions, or sector-specific confining potentials. In this framework, matter profiles, the localized Higgs background, and delocalized gauge support are treated as genuine profiles in z, while two-body and three-body composite systems are described by induced source and oscillation profiles in the same mode space. Observable hadron masses then arise from controlled even and odd low-energy reductions of this full structure. A central structural result is that the light pseudoscalar channels are identified as boundary-dominated states rather than ordinary bulk hadronic modes, while strange baryons require a universal strange-sensitive geometric completion in the even sector rather than ad hoc flavor-dependent correction terms. The final visible test set — including rho-pi, K*-K, Delta-N, Sigma*-Sigma, Xi*-Xi, and the visible masses of Sigma, Sigma*, Xi, Xi*, and Omega — is reproduced within MeV-scale residuals using current particle data. The construction remains compatible with the heavy-sector closure developed in Part III and yields a latent odd-sector target in the sss channel, providing a nontrivial benchmark for future nonperturbative tests. Part IV therefore closes the visible hadronic sector of the Mass Concept as a predictive and falsifiable extension of the same geometric mechanism developed in Parts I–III. The work is intended as a controlled effective five-dimensional profile theory of composite mass generation and hadron structure, with explicit separation between anchors, derived quantities, and genuine predictions.