The biggest gap in understanding bone formation is "How do osteocytes cause precipitation of the inorganic salt calcium phosphate?"

(How hard can that be?)

The answer isn't that osteocytes secrete calcium phosphate, because if they did you would be able to see it in electron microscope sections (in which calcium phosphate shows up very clearly as dense black globs.)

Osteocytes do secrete (and synthesize) the collagen part of bone (1/3 by weight).

Theories:

#1 ("Osteoid Theory") Maybe some chemical binds to calcium ions and to phosphate ions, strongly enough to make them precipitate out of solution even at low concentrations.

(Alternative names could be the "Anti-EDTA Theory", or the reduced solubility theory.)

#2 "Inhibition-Everywhere-Else Theory" Maybe normal body fluids contain high enough concentrations of calcium ions and phosphate ions that they would precipitate out of solution, except their precipitation is inhibited everywhere else than at the locations of bones. So bone forms wherever precipitation isn't inhibited.

#3 Pumping of ions into membrane vesicles that bud off osteocytes. Spheres of membrane are often released from osteocytes; maybe these membranes have enzymes that pump calcium ions into their interior, and/or pump phosphates inward, so that the salt precipitates inside the vesicles; and then the vesicles burst, or something.

#4 Maybe phosphates that were covalently bound to proteins get cut free by phosphatase enzymes, thus creating localized concentrations of phosphate ions that are larger than the "solubility product" (in combination with the normal calcium ions in normal extracellular body fluids.

#5) "Ice-Nine Theory" based on Kurt Vonnegut's science fiction novel "Cats' Cradle". Is it possible that the crystalline packing and/or bonding between calcium and phosphate in bone is different (and much less soluble than) what precipitates when you mix a solution of dissolved calcium chloride with a solution of dissolved sodium phosphate, with an activation energy barrier between the regular crystalline structure and this different crystalline structure bone is made out of, and that some enzyme catalyzed conversion to the crystalline structure of which bone is made. (Look at the diagram on the last page of the Wikipedia article about ice.)

Please try to invent more alternative theories. (& decide if #5 is the same as #1)

Note, all but #5 were invented by other people, who advocated them. For some reason, people who invent a new theory tend to believe it is correct.

Experiments and other relevant data:

Notice that calcium carbonate (instead if phosphate) is used for skeletons of echinoderms, brachiopods, coral, mollusks, some sponges, bird eggs, among other examples. Only vertebrates use calcium phosphate (that I know of; please tell me of other examples). Even the otoliths in our inner ear are made of calcium carbonate. But I don't know the mechanism of formation (secretion) of calcium carbonate, either.

The dentine layer of teeth is almost the same as bone (but lacks osteoclasts). The enamel layer of teeth contains 95% calcium phosphate, and 5% non-collagen protein.

I don't know whether the mechanism of calcium phosphate precipitation is the same.

Strontium ions, zirconium ions, technetium ions, and some others get incorporated into bone. This fact is the basis of "bone scans" in medicine. These ions are said to be "bone seeking", but it must be some sort of trapping. Magnesium ions are NOT bone seeking, but behave similar to calcium in many ways. Fluoride ions get incorporated into bone and teeth, and probably make them stronger.

Except for the roof of our skull, the rest of the skeleton is first made out of an entirely different, jell-like material called cartilage. In other words, when you were an embryo your radius, your ulna, your femur, etc. were pieces of cartilage the same shapes as the bones that will then be formed at the same locations, by destruction and replacement.

Cartilages often becomes calcified, but I don't know what anion (phosphate, or something else?) is used to make a calcium salt (It may be sulfate) Thus, it is a good question whether calcification of cartilage has any part of the same mechanism as bone formation. I don't know the answer.

A sharp boundary is (often? always?) present at the leading edge of areas where cartilage is becoming calcified. It is often called "the tide line", because of its appearance.

A few bones (the roof of our skull, fish scales) are formed from dense sheets of collagen. I don't know whether the mechanism of calcium phosphate precipitation is the same.

It would be especially interesting to know if the same collagen fibers are retained, or whether they are destroyed and replaced by new collagen fibers in bone (as happens when cartilage is replaced by bone.

It is not difficult to dissect pieces of developing bone (= ossifying cartilage) out of the legs and wings of 6 to 12 day chicken embryos, and put them in tissue culture medium.

Possible experiments on pieces of ossifying cartilage in tissue culture :