Relational System Operation
What this is
A RelationsSystemOperation is a RelationalOperation that satisfies U_G condition 6: it is itself a named object in the universe.
Condition 6 requires that generative operations — the endofunctions that map R within itself — are not external to the system. They are entities in R. The system contains its own operations.
This is not a design choice. It is what condition 6 produces: a universe in which the operations that generate structure are themselves elements of that structure. A system whose operations are unnamed or external to the universe does not satisfy condition 6 and is not a full RelationsSystem.
What being an entity requires
A RelationsSystemOperation MUST have an identity — it is in R, not merely applicable to R. It MUST be referenceable from other entities in R. It MUST be invocable: there must be a way to apply it to its carrier within the system.
An operation that exists only as a mathematical fact about R but cannot be named, cited, or invoked within R is not yet a RelationsSystemOperation. It is a RelationalOperation that has not yet satisfied condition 6.
Scope
Every RelationsSystemOperation acts on a specific carrier within R. The carrier may be a fiber H_t, the whole of R, a class of objects, or a sub-algebra. The carrier is part of the operation’s identity — two operations with the same effect on different carriers are different RelationsSystemOperations.