role-indexing

The Recursive Boundary: Whole–Unit Reindexing in the μ Topology v0.1

FRC μ assignments are indexed relations among an object, its role, and a declared system boundary; they are not permanent labels attached to objects. This paper defines a bounded system, an indexed role map, and a boundary-change record. It proves the consistency of whole–unit reindexing: the same object can be a bounded unit at one boundary and a component of a larger unit at another without contradiction because the predicates have different boundary indices. 'Fractal' is restricted to recurrence of the component–unit–relation pattern under boundary change, not geometric self-similarity or fractal dimension.