Magic doesn't really come in pieces. Does he have, like, one of what he's calling a 'piece', so she can see it and point out more?

Sure.  Here's one of his earliest prototypes, which will probably be easier to understand: an 'adder' which takes in three inputs and produces two outputs, as can be repeated and tiled together to make a system that does binary addition.  In this case, he had to do a huge amount of hammering and tweaking forces with other forces in order to make the things-isomorphic-to-bits interact in the right way for each adder, and then he had to specialize some of that work for every adder in his system being chained together to make an additionizer.

It'll probably be clearer what this system is trying to do if he sketches out on the whiteboard how it adds 1110 + 1101 = 11011 (14 + 13 = 27).

First a 1, a 0, and a fixed 0 enter this adder, which outputs a 1 to the final sum's 0th column, and outputs a 0 to the carry bit entering the next adder...

Okay, yeah, she thought he was trying to input candidates for laws to test, and wanted things to narrow down the range of tests to run. She...might be able to help with this - there are magic items that need to be able to do limited internal computation - but she's less sure where to start. 

It is very pretty, though. She will acknowledge this very grudgingly because it'd be much nicer if people who want to kill you lost the ability to make beautiful things or something.

It feels like they should. It feels in Carissa like the impulse to make beautiful things, to invent, to discover, to test the laws of magic and twist them to your own purposes, to send little pieces running and swinging until blindly they do math, to step a little closer to godhood, cannot coexist with the impulse to annihilate people, any more than the sun can coexist with the dark. It feels like all that is wonderful about Keltham, all his fascinations and habits and playfulness and curiosity and quirks in what he notices and cares about, cannot coexist with the goal he's set himself.

Of course, isn't that what Keltham was telling her all along, that they can't coexist, that none of what makes him him can exist in a mind that is plotting to annihilate her and everyone else, and that he's decided to do it anyway for some reason.

There's no point in saying anything, so she doesn't say anything. She works on trying to make the magic do what he wants. 

Elsewhere and Later

"Your Infernal Majestrix."

"Most High.  I've called you here to inform you that our former colony, the city-state of Korvosa, has overthrown their previous ruler, Queen Ileosa Arabasti, and seeks a closer relationship with Cheliax henceforth.  They're not willing to submit themselves directly to our rule, nor adopt any policies aimed at the damnation of their populace.  But they have appealed to us for a Chelish appointee at their court who can, in the words of the revolutionary council, keep an eye on their next Queen and let everyone know if the new Queen is doing anything batshit insane."

"I'd say that sounded encouraging.  If not for the part where you apparently think this merits an urgent report to myself, and you haven't told me yet what batshit insanity the previous Queen was practicing."

"Nothing apocalyptic, just killing everyone in the city in a mad bid for immortality.  Doesn't matter, one of your proteges shut it down before it could disrupt our shipping with Varisia.  Fortunate it played out that way, really.  Queen Illeosa was a Chelish expatriate.  If it hadn't been one of our own to stop her, it could have been quite bad for relations with Korvosa, or what was left of it."

"One of my proteges?  They are all within Cheliax so far as I know."

"Oh, you didn't send Pilar there, then, and conceal the fact from me?  I'd wondered."

"No, actually."

"Mm.  Good to know.  I would have considered that a Crown matter more than a Church affair."

"On other topics.  I don't directly receive reports about heresies against Asmodeus, and I understand why you're not forwarding those on to me.  But given the political relevance to Chelish diplomacy of what Carissa Sevar is doing in various countries with her 'Sevarites', I have not actually avoided hearing about Sevar unconcernedly summoning a devil to purchase souls, casually executing a paladin who opposed her, or offhandedly daringly rescuing a captured inquisitor of Asmodeus.  Is there possibly something you're not telling me about Carissa Sevar's current standing vis-a-vis Lawful Evil and Hell?"

"It's a matter on which I haven't deemed it wise for you to know everything I know.  If you're thinking of raising your hopes about your ex-lover, I'd consider that premature."

"Mm.  It is somewhat of a Crown matter as to whether or not she's liable to try taking the Crown.  Do I need to make sure my throne room is properly clean beforehand, so I'm not embarrassed if Carissa Sevar strolls in expecting it to be ready for use?  That sort of thing, Aspexia.  That sort of thing.  The stability of the Chelish state does require me to keep track of that sort of thing."

"Given my current knowledge, Abrogail, I will be very, very pleasantly surprised if I find myself willing to back Carissa Sevar in an attempted assumption of your throne, does she deem it important enough to be worth taking from you."

"Does Sevar know that would be your reply?"

"That, I don't know."

Elsewherer and Laterer

"I admit, I wasn't expecting to meet you here."

"Can't exactly say I know the feeling.  At least, not recently."

"I can cast Plane Shift, these days, so I'm your ride to the City of Brass."

"I have scrolls for that."