Energy stored in *what* in a magnetic air gap?

[TimFox]

Say we have an iron cored inductor with a steady DC current flowing through it and the core has a small air gap. Furthermore, the inductor is not saturated. The inductor holds a certain amount of energy. AFAIK, for the most part that energy is in the magnetic flux in the airgap, not the actual iron core.

Question - how does this energy exist in nothing? It's not like an iron core that has it's magnetic domains rotated, or a capacitor that has it's dielectric stressed somehow? Energy seems to be stored in nothing at all. What has changed in that air gap?

Note that magnetic flux density (B-field) exists in vacuo, for example in the interior of an air-core solenoid coil.  If we add a permeable material (e.g., ferromagnetic iron or paramagnetic magnesium) to the system, the magnetic moment of the material aligns to that field to produce a large polarization, which adds to the field.  A diamagnetic material (e.g., bismuth or graphite) on the other hand will polarize in the opposite direction and reduce the field.