Also for some reason he's abruptly...sad, and restless, and doesn't want to be sitting alone save for a mage-construct servant refilling his tea and his own endlessly looping thoughts replaying the past. He wants to be making forward progress on something that isn't just inside his own head.
- and also isn't scrying Velgarth, which is the main obvious next step on his mental to-do list, but he's still flinching about it, in a way that feels at least somewhat bad to push back against. This is not normally a problem he has! But he feels like he only just got to a a state where he can be fairly confident he isn't going to randomly cry if a confusingly good thing happens, or panic if he tries to do magic and is blocked, and he doesn't feel like it's very stable yet.
And...is it time-sensitive? His options for doing anything about it are limited, and if he actually drags his mind down that line of thought - which is also flinchy but less so - he acknowledges that he does just know enough about the Empire he built to narrow down his guesses. There would have been an immediate panicked report when he Gated out. They would have tried to reach him with the comms spell and order him to return to Jacona - which failed, obviously - and tried to scry him and target him with a Gate-search, which also failed.
(It's possible they did scry him in the Haighlei Empire and just didn't have the range for a Gate, which is a potential point of divergence - they would know he was buying diamonds, which would let them predict more confidently where he was going - but even scrying is range-limited, especially the overpowered variants that could have gotten through his shield-talisman.)
At the point when immediately retrieving him had clearly failed, the investigation would slow down and spread out. The Office of Inquiry is going to be thoroughly questioning everyone from the research site. They'll be trying to rederive the full technique for interworld Gates - which he doubts anyone but him can figure out in less than a decade-long research project, he didn't teach Aritha the Gate-search routing and without the headband she might not be clever enough to recall it even if he had; he's barely clever enough, it would have taken him months without the headband for the most difficult parts, and he has vastly more practice at chunking mathematical-spatial concepts to fit more complexity into his magic. They'll be trying for interworld scrying as well, which they might be able to get by dragging everything out of Aritha's head - she's seen him actually cast the spell - and throwing it at the most brilliant researchers in the Empire, but he overall thinks this is unlikely; if he has to put numbers on it, maybe one in twenty odds? In the remaining 95% of cases, re-deriving it from scratch might still go faster than Gates, but - six months to a year.
(Aritha is probably having a terrible time. Altarrin genuinely feels bad about that. He wanted her to be in a better situation for having worked with him.)
...They're not going to try to contact Tar-Baphon, because Bastran isn't an idiot, and because even if Bastran manages to lose the throne in the aftermath of this - which Kastil will be fighting tooth and nail against, Kastil doesn't like either of the pretenders in the current rebellions - the candidates likely to take his place are - more conservative than that. More likely to stick to what's known to work, which is NOT trying to mess around with other worlds that have scary gods.
(He's also going to feel terrible if Bastran dies as a result of this. He already feels kind of terrible for leaving Bastran behind, despite the fact that there is no conceivable scenario where he could have kidnapped the Emperor, and if he had the Empire would be facing a genuine disaster now.)
The most serious risk is...that Aritha did follow enough, in the process of watching him scry Iomedae, for the Empire's best researchers to figure out scrying in days or weeks rather than months. And that Bastran orders a major effort to collect intelligence on the other world, and they aren't careful enough, and some poor fool scries Tar-Baphon and ends up compulsioned and Tar Baphon takes the Empire from there.
One in twenty that they'll even have the option in the next week. One in...three odds, maybe, that Bastran is careless enough, and they get unlucky enough (and Altarrin thinks this isn't a case where the gods of Velgarth are going to steer for the worst luck, even if They could see what they were doing it seems very bad from their perspective for the Empire to end up suborned by an incredibly disruptive powerful spellcaster from another world). But he's not sure of that, so call it one in two.
One in forty, then, that if he does nothing and Iomedae does nothing, the Empire ends up belonging to Tar-Baphon in the next week.