THAT certainly SOUNDS like 'spellsilver' is one particular element on the Periodic Table.  A series of chemical reactions like that is one that filters atoms by which chemical reactions they participate in, which goes by the behavior of their electron shells and orbitals.

If this were a novel, Keltham would be figuring out how to get a known number of atoms of spellsilver, into some measuring-volume he can weigh, precisely relative to Civilization's known weights and measures that he would have cleverly recovered by various means, so that he could figure out the atomic weight, thence the atomic number, then deploy his encyclopedic knowledge of how best to mine every single element.

Since Keltham has not memorized how to mine every element, he's not actually prioritizing figuring out which element this is.

Questions immediately to mind:

Which part of this process is the most expensive one - finding new sand deposits, the cost of acid, the cost of labor?

Is the purity of the resulting metal important - is there such a thing as higher-purity spellsilver that's more expensive and useful for more powerful magic?

Are there any other kinds or variants known of spellsilver?

Do they know that bone is itself mostly made of a mixture of two other elements, and have they tried each of those two elements separately?

Can spellsilver be magnetized?

Anybody tried messing with this process by running currents of ordered lightning through it?

Does magic get used on any step?

What's everything that's already been tried that doesn't work?

The sand is about half the cost by itself. Most of the remaining costs are located in the steps having to be done exactly right or they'll ruin your spellsilver process, so  and ensuring all the ingredients are of appropriate purity and that the complex process is followed exactly right by someone with enough alchemical skill to notice if some desired result isn't happening and to tweak it along the way. 

The purity of the resulting metal is very important, it needs to be very highly pure, but it's a threshold - at some point it's pure enough to interact with magic the right way, and past that point there aren't known gains to higher purity though also they cannot very easily get much higher purity. 

They haven't isolated constituent-bits of bone. Spellsilver can be magnetized though no one has ever thought of that as particularly important that these people know of. ....no one has tried hitting their careful alchemical process with lightning, no, that sounds like probably it would make something go wrong or catch fire! Prestidigitation gets used to separate out the precipitate in acid but you don't have to use it for that, it's just faster. Magic gets used to manipulate things while they're in glass jars not exposed to the air. 

....everything that's been tried and doesn't work is something they can happily spend the rest of the afternoon recounting.

If the sand is half the cost, then fixing the rest of this reduces the cost of spellsilver by at most a factor of 2, which isn't very much by Civilizational standards.  Why is the sand expensive - shallow, easily exhausted deposits, no huge deposits ever found?

.... a factor of two would still be an enormously huge deal and make him the richest person in the world probably? Monazite is mostly mined from shallow waters; it is believed to form in the breakdown of rocks and, because it's so light, tend to be carried away to the sea, where it'll gather in places. You can find trace amounts of it in any given rock but that's not very useful.

Is there a known process, including a known magical process, for telling whether existing ores or strange new rocks would have spellsilver content?

Are there other known spellsilver-containing ores from which nobody has figured out how to extract spellsilver cheaply and reliably, such that the current cheapest process is based on monazite?  Or is monazite the only such ore known?

There are definitely other known spellsilver-containing ores - they have on hand a yellowish rock that contains spellsilver ores. Sometimes people try to extract the spellsilver from them. Sometimes they even succeed but it's much costlier than the existing process. Wizards who work with spellsilver a lot can tell that impure spellsilver is meant to be spellsilver, and some of them claim to have the sensitivity to tell from rocks that have only a moderate amount of spellsilver ore.

Which ore would make spellsilver cheapest, if extracting all the spellsilver out of that ore was miraculously very cheap?

Probably this rock here in their array of example rocks. It's chemically fairly like monazite sand, but a mineral? There's a decent amount of it and it's not primarily mined underwater, which makes it easier to have sl-ow paid employees do the mining. It's not favored because you basically have to turn it into monazite sand to even start, and that does take magic, and you need stronger acids for some reason.

Rough price reduction in spellsilver if the spellsilver content of that rock was extractible for free?

...It's hard to guess? People don't try to systematically mine it, and they'd have to start. Significantly more than a factor of two, though.

Three?  Four?  Ten?  Twenty?  Two point one?

.....probably more like ten than four or twenty?

That'll do it for Recursive Headband Production if anything does, since half the cost of headbands is labor anyways.

Do they know the actual purity they need on the metal, like, 99%, 95%, how much of the process expense is getting the metal pure enough vs. turning it into a metal at all, do they know if the impurities are other metals...

More like 95%. Most of the expense is getting it pure enough, only real novice alchemists screw up badly enough to fail at turning it into a metal at all. They have some jars with some spellsilver-impurities if he wants to examine them.

The one guy is kind of emotional about this, not that a non-Chelish person would be able to tell.

Let's have a look at those jars.  Do their contents look like metal?

It looks like there's both some metal and some other stuff in there.

That possibly means electrolytic refining shouldn't be his first line of attack.

How much of the expense is acids of required purity?  Including downstream effects from minimum-purity acids making the process finickier?  If very-high-purity acids of all the required types were free, how would that change the non-ore cost of spellsilver?

They haven't really tried a wide variety of acids, failing at that stage ruins your materials and it's something of stabbing wildly in the dark to find anything that works better than the recommended procedure, so it's hard to know if it'd be less finicky with better acids. Acids are quite expensive, maybe a quarter of overall costs.

(In the same fashion that the literate, science-fiction-and-fantasy-reading children of another place might know how to make gunpowder (out of 75% saltpeter which is that white stuff found in manure piles that seems to have a cooling effect, 15% sulfur which is that yellow stuff evaporated from hot springs that smell like rotten eggs, and 10% charcoal, along with rules about mixing the powder to a dough and then grinding and sieving it), most dath ilani kids who read isekai fic have some idea how to produce industrial quantities of high-purity sulfuric acid, and purify the nitric and hydrochloric acids that are easy to make downstream of those.)

Well, he was basically figuring he'd have to reconstruct mass-quantity high-purity acid production at some point, so maybe that could be among the first things tried.

There's also a pretty obvious idea for something to try instead of bone, if that part of the process is at all finicky.  They've had the conversation about the crazy patentgratuity arrangement on this, where the Project gets 80% of excess profits above 20% increase, and if they want to capture money for scaling production like sane people they need to talk to Chelish Governance or the Project about that, correct?  Keltham is aware this is kind of an insane arrangement, they're working out a more difficult saner one in the background, but the Project needs to capture tons of value so it can reinvest in like 200 different other things that will need doing.

That was explained, yes. These researchers don't exactly understand the details of the arrangement but they'll report all their profits and pay what's required.

All right, so if the final step of the process seems worth messing with at all - if they're losing spellsilver from it, or it's finicky, or transforming the bone to a usable-purity final ingredient is expensive - try burning seashells to ash and using the ash.  That'll get you a purer version of one underlying component of bone that Keltham would guess is the important one of the two.  Better yet would be 'limestone' but Keltham doesn't remember off the top of the head how to describe which kind of rock that is, short of testing out different kinds of rock to see which ones behave chemically like 'limestone' should.

People have occasionally talked like spellsilver gets depleted in the process of making magic items.  How does depleted spellsilver differ from the non-depleted sort?

The usual way of making magic items doesn't deplete the spellsilver. The magic item will have as much spellsilver as was put into it and later you can pull it out and use it to make something else. 
 
If you make a mistake in magic item making, you can ruin the spellsilver. It looks the same, only wizards can tell anything is different, but it won't hold magic anymore. You can also do that deliberately, though it's hard to imagine why anyone would.

Carissa, you looked like you were pulling magic out of spellsilver from a distance, which Keltham would sorta expect to deplete that magic?  Did Keltham just totally mismodel what was going on, or is that not the usual way of making a magic item?

That is indeed not the usual way of making a magic item! Usually you want to work the spellsilver into the item, which gives you the option of reusing it later. The way Carissa did it destroyed several thousand gold pieces of spellsilver. There are use cases for that method, usually for making an item you can't work the spellsilver into directly, but it's rare to be willing to waste that much money.