Is the earth's iron core corroding away?

[HydrogenBond]

The critical state of water causes minerials to become very soluble in water. This solubility increases in the presence of small ions. This observations implies that hydraulic pressure combined with mantle heat should allow water to be continuous from the surface of the earth to the mantle as critical water dissolves its way to the mantle.

 

Seismic data indicates that the mantle is a dense fluid and the core is solid. This implies that the laws of chemistry should at least parttially apply within the fluid mantle and solid core even if they are plasma chemical states. This being said, with water continuous from the surface into the mantle, shouldn't the concentration gradient and chemical potential between the upper mantle water/small ions and an iron core cause the water/ions to flow to the core and corrode/dissolve it? If so, shouldn't the ocean levels be dropping, especially since the core is 1000 time more massive than the oceans.

 

One may argue that mantle density would inhibit bulk transport of water to the core, slowing an possible corrosion. The way around this is that with oxygen everywhere in the mantle, only hydrogen needs to diffuse from the mantle to the core. Near the core hydrogen can hook up with local oxygen for corrosion. If this corrosion analysis is reasonable and since the oceans levels are not dropping does this imply that an iron core does not exist?