She will arrange a catapult demonstration for her Supremacy.

The trick is that you tell the Spark designing the catapult's flinging motion to make it so that the cargo's trajectory goes up quickly but down slowly.

Then the Spark does that.

Huh!

Physics is almost certainly different here, unless very important parts of this system are being omitted from the description! She'll just check...

"Are there... parachutes? Or anything? Why does the cargo come down slowly?"

Because the catapult knows what is good for it if it doesn't want to be disassembled.  All invention is a contest of wills to see who is more stubborn, the laws of physics or you.

Hmph. This will bear further investigation.

....

....

....

Opalyn shakes her head and breaks out of her confused reverie.

"All right! Off you go then! Everyone report back here tomorrow morning so we can sync up on our plans!"

Bidden, they go!

What's Opalyn doing the rest of the day?

Good question!

Theoretically she should go back to bed, but between the adrenaline rush of discovering that her interdimensional patron has been sparknapped and the aftereffects of the sour carrot drink, she does not feel incredibly sleepy!

She needs to give her staff time to execute their orders without her bugging them to report on other things.

Is it light out yet? Maybe now is a good time to wander around the castle or even the city and gather her own firsthand data about this place.

It's summertime and they're not that close to the equator; even during the unfortunately early morning, the sky is dim blue light on the darker side and warming and brightening on the other.

Great, then she'll... not change her clothes, because she doesn't have any new clothes yet... note to self, should ask Dame Fleur about that. She'll wash her face and freshen up just a bit, and then head out to explore the castle.

Are the maps of a size that she can roll them up and take them with her?

She'll also bring paper and pen.

She can roll up the maps, sure, and carry those.  It'd be a pretty large map if Opalyn couldn't even lift it once rolled!

Relatively few people are about, at these hours; there's nobody in this cozy common room nearby, for example, though some sort of automated breakfastmaking(?) machinery is already burbling quietly to itself.

"Cozy," sure, that's a way to describe this vast atrium!

Opalyn infers that Doctor Disaster is actually quite wealthy, especially if this is just one minor common room and not, say, the main receiving room for the whole castle. And the windows look fairly clean, despite how numerous and inaccessible they are. That suggests that the cleaning crew is pretty well staffed and efficient - or, potentially, that there are mechanical window-cleaning bunnybots or something.

Can she tell if any of the machines on the tables do anything intelligible, or if they're just inscrutable tangles of gears?

This machine probably has something to do with making coffee!

And Opalyn thought the espresso machines at her old workplace were enigmatic! She'll avoid bumping any of the mysterious levers sticking out of the coffee machine as she walks by; she doesn't want steam burns!

What's down the next corridor as she leaves the atrium? And more importantly, does it seem like the paper map matches the castle territory?

Normal hallways and stairs in a modest interior decorating style, pretty much more or less where the map says they should be!

Also this person, looking not unfriendly.

"Oh hello, good morning, excuse me!"

That's three greetings. Opalyn should finish up with the greeting segment and move on to the main body of her utterance now.

"I'm new here. Can you tell me how safe it is to wander around the city alone in the early morning? Or any other time of day, really?"

Little Damar?  It's about one of the safest places in existence!  Plenty of people are still alive in Little Damar who'd have long since been dead if they lived anywhere else.

"So glad to hear it! Can you tell me how to get to the food market?"

It's not so much that Opalyn wants to buy food... or has any money to pay for it. It's just that when she travels on Earth, she always likes to check out the local grocery store. Exploring a grocery store tells her a lot about where she is: how wealthy or poor they are, what kinds of things grow locally, what weird snacks they have. And usually there's no dickering at grocery stores; you're left alone to browse and pick things you want and then pay at the end.

Huh.  There's enough turns along the shortest path from here to there that it seems hard to remember a set of directions like that.

However, it also seems solvable to compose a more memorable set of directions that will still arrive at that destination.

So, it's not the shortest path, but you'd get there if you went that way, then went up, up, down, down, left, right, left, right, B, A, and then start.

Opalyn starts to write down the instructions and then realizes she doesn't actually have to. Also what would 'start' even mean in this context? Is she being interdimensionally trolled or is this particular sequence of steps somehow fundamental to physics in a way that transcends dimensions?

"This may seem like a strange question, but... is that often a path to get from one place to another? Or is it really just the instructions to get from the palace to the food market and that's it?"

Sorta?  It's a decades-old memorable password based on a famous story about one of the recent Heterodynes getting lost in an alternate universe, and castle-builders will often arrange for that pathway to go somewhere interesting from an interesting starting point.  But in this case, it seemed sorta the right direction, so ve visualized the actual pathway, and in fact that'd take Opalyn to a Little Damar entrance where the smaller of two grocers ought to have a shop visible from there.  It was the fourth memorable set of directions ve tried before one worked.

"Is the... Heterodyne? Is that a family name? Anyway, is that Heterodyne still living? What's their name?"

Kazuality Heterodyne, and prooobably not although you never really know with Sparks.  She was last seen being swallowed by some sort of gigantic snake made out of mirrors along with her harem of enslaved logicians.

The Heterodyne dynasty is among the most famous, long-lasting, and terrifying Spark families on the planet.  They rule from Mechanicsburg.  It is wise to live your life in a fashion that never causes them to think about you in any way.

How far away is Mechanicsburg from here and what kinds of things should Opalyn not do if she doesn't want to get their attention?

Because, unspoken, Opalyn is now somewhat dying to get their attention and find out if there are any records about Kazuality's trip to some version of what was presumably Earth! But maybe this tale is so well known she can read about it in any library and not get involved with the scariest people on the planet.

(Also... harem of enslaved logicians? Opalyn doesn't ask.)