From Relational Metamodes to Effective Matter Sectors in EPPQ

This preprint is the third article in the EPPQ research program. It addresses a specific open problem left by the previous papers: the controlled passage from relational metamodes to effective matter sectors and continuous field configurations. The manuscript introduces an enriched relational state space, replaces infinite-penalty constraints with intrinsic admissibility conditions, and defines a well-posed intrinsic Hessian on the admissible manifold. On that basis, it proves a sector decomposition result for regular metamodes, derives a universal quadratic form of connection-Laplacian type for bosonic sectors, formulates conditional continuum-limit results in terms of energy-form convergence, and establishes a sector-preserving decoherence theorem. For the fermionic sector, the manuscript resolves the earlier obstruction by incorporating combinatorial spin admissibility directly into the discrete state space. Under explicit geometric hypotheses, this yields a conditional route from admissible discrete lifted transport data to spin structures on the emergent continuum, together with a natural candidate for an effective Dirac operator. The paper is careful to distinguish three levels of claims: results proved internally in the discrete formalism, conditional results that rely on established convergence and spin-geometry literature, and questions that remain open. In this sense, the work does not claim a full derivation of the Standard Model or Einstein dynamics, but provides a rigorous intermediate step in the EPPQ program toward effective matter, field sectors, and emergent relativistic structure.