Brand an object type with a phantom property whose type is keyof T, so that a wider key set is NOT assignable to a narrower one. This makes mapper-produced object return types invariant in their key set: a mapper for a superset type can no longer be substituted where a mapper for a subset is expected.

The brand sits in a covariant property position. A union of keys (e.g. 'bar' | 'extra') is NOT assignable to a narrower union (e.g. 'bar'), so the structural subtyping that would normally permit ExactReturn<{bar; extra}> → ExactReturn<{bar}> is blocked at the brand.

The brand is declared optional so that plain object literals (which don't carry the brand at runtime) can still be returned directly from mapper functions — freshness checks already catch excess properties for fresh literals. The brand only constrains composition: assigning the result of one mapper into a slot that expects a different mapper's output.

Distributes over unions so ExactReturn<NestedOutput | null> becomes ExactReturn<NestedOutput> | null, leaving primitives and null/ undefined untouched. Arrays of objects have their elements branded, so an array of a superset element type also can't be substituted.

Tuples are preserved element-by-element, so positional and length information is not widened away when mapper outputs contain tuple types.