We need a BIOASSAY that can identify and purify whatever substance is somehow able to attract and immobilize calcium and/phosphate ions enough so that they will precipitate out of solution even where their concentrations would be (much?) too low to cause precipitation in ordinary body fluids.
Purifying some chemical that has this precipitation-stimulating ability would be a major step toward discovering/confirming that the mechanism of ossification really does work by means of "Osteoid." = "Ion Precipitation Factor" or "Reverse Chelation" (suggest another name?)
[E.D.TA, E.G.T.A both chelate divalent cations, in the sense of making them much more soluble.]
Their existence raises the question whether the exist, or could exist in principle, substances that have the opposite effect: making cations less soluble (in some other sense than as an anion whose calcium salt is much less soluble than calcium phosphate.
We should consider the important question whether it might be thermodynamically impossible for reverse chelation to occur. Some input of energy might be required, as is necessarily true for trans-membrane ion pumps.
(For example, try to imagine a membrane having a one-way permeability, calcium ions diffusing inward, but unable to diffuse outward. Such a combination of properties can't occur without some kind of energy input.)
Consider that photograph of the demineralized chicken leg bone that was so flexible it could easily be bent in a knot:
What would happen if this knotted, decalcified bone were then soaked in a water solution of calcium phosphate? Almost certainly the decalcified bone would reabsorb both calcium and phosphate ions.