Transported source markings and an independently prescribed native host marking are different inputs. If the native host refinement \(q_W\) is independently supplied, a prescribed embedding \(f\) must satisfy
With a free embedding and equal dimensions, quadratic classification requires equal Arf invariants. This is the rank-eight case: both quotient spaces have dimension 6.
For \(d\ge4\), the dyadic host has at least one spare symplectic plane. The complement's Arf type can absorb the difference, so either source Arf type admits an embedding into the supplied native quadratic host.
Reading the diagram
Dimension controls symplectic room. Arf controls a quadratic isometry class. A pointwise equation controls an already chosen embedding.
Scope
Capacity does not manufacture a canonical native finite marking or identify it with the transported marking. That comparison remains outside the general realization proof.