The recurring workflow

Across the theory and all ten application systems, the same six-stage workflow provides the organizing spine of the book.

Declaration fixes the objects, arrows, equations, and universal properties that give success a type. Differentiation turns a failed composite into a local sensitivity or interaction signature. Quotienting removes variation that is null for the declared decision. Localization assigns the surviving obstruction to a cover of modules, agents, contexts, skills, relations, or argument fragments. Repair searches only within a registered language of admissible changes. Admission then tests the candidate against evidence independent of the signal that proposed it. Rejection and abstention are therefore successful outcomes of a well-specified workflow, not merely failures to optimize.

This separation is the practical heart of lincs. A residual can diagnose a broken promise without identifying its cause. A localized cause need not support a feasible repair. A repair that reduces the training obstruction need not preserve meaning. Each transition requires its own assumptions and its own certificate.