The Modal Triplet Theory Program B5: Relative Saturation, Conditional Extended Carriers, and String-Like Realizations

Version 2. This paper replaces absolute encoding saturation by a typed relative notion defined with respect to a category of realizations, equivalences, constraints, boundary data, and allowed factorizations. In a finite-dimensional local model it proves that first-order factorization is detected by connected components of the bipartite derivative-incidence graph; connected incidence gives infinitesimal indecomposability, and injectivity of the combined derivative additionally gives local isolation. Scope boundary. Saturation alone does not force extended carriers, critical dimension, anomalies, worldsheets, or duality. String-like realizations and the q79 branch remain conditional on their explicit completion gates.