Part X: The Logos Sector
Sector S_L (Logos — Mixed). The Logos sector is the structural crown jewel of the second edition: the unique location in the 4+1 decomposition where proof-validity and stance-stability are identical—where the diagrammatic register and the commitment register coincide. It is named by its universal property, in the same way that a categorical limit is named by its universal property: the name describes the structure, nothing more. We state this with care: the Logos sector is explicitly not a theological claim. It is a structural fact about where two registers of reason become inseparable. That this structural location resonates with traditions that have used the word “Logos” for millennia is noted as a synchronicity—a shared kernel invariant—and left for the reader to evaluate in their own commitment register. The Part develops the formal definition of the D → C bridge, the boundary collapse lemma (a preview of Part XII’s main result), and the structural apparatus that makes the Logos sector the mediator fixed-point basin of the 4+1 decomposition.