"It could be that the purpose of your life is only to serve as a warning to others." -- Ashleigh Brilliant
A Keltham appears in a Golarion, and a Nethys who has seen exactly one other possibility like this witnesses it.
The key knowledge doesn't make it to the witnessing fragment instantly; different pieces of Nethys see this Keltham, and see the future of a previous possible world where a Keltham appeared.
But it's communicated in time, and then, the greater Nethys starts to realize that this set of observations is actually quite important.
So important, even, as to be worth focusing His precious energy and His more precious scraps of coherence, on understanding the anomaly, on manipulating events to be more favorable to Himself and His interests.
And so the Nethysi begin to play the Game of Keltham.
The first Nethys-Player (accounting the previous Nethys as the zeroth Player, who only performed the null action) doesn't actually do very much that's different. Nethys is left better off at the end of the null action; He doesn't want to risk not getting that benefit for Himself.
So Nethys does not slay Keltham, who will if left undisturbed batna Pharasma with Creation's destruction. A coherent agent ought always to do at least as well for its interests, as if it didn't care or didn't exist; and any other agent who calls that a threat is out of luck.
The only interventions that Nethys tries are quiet ones, interventions that a supermajority of gods ought to see as quite helpful, really.
His herald Arcanotheign steals away the lost child of Ione Sala from the River of Souls. Takaral buys Peranza's soul as soon as it arrives in Dis. Asmodia dies mysteriously during the Rovagug security breach, and has her soul stolen away to Nethys's sanctuary as well.
So Keltham does not find Asmodia or Peranza screaming, when he scries them; he does not find them at all.
Despite this, Keltham is still moved to save Golarion or destroy it—to Nethys's relief, for He cannot predict the unseen future that finely and He was not sure that Keltham would still serve ultimatum upon Pharasma.
Thankfully, Keltham's having wrecked the entire world of Golarion and put it into Hell's grasp is apparently still enough to cause him to reconsider a few things.
Carissa Sevar receives miraculous inspiration from the God of Magic while about her task of forging Keltham's headband, somehow producing a lesser artifact that's +6/+6/+4 instead of just +6/+6.
This Keltham is less emotionally destroyed; he doesn't like what Splendour does to him, and the obvious Nethys-intervention he likes even less, but he decides after long thought that he's willing to accept the unwanted +4 Splendour in exchange for the +6 Wisdom.
An omniscient god opposing Keltham's purposes, and willing to intervene on this level and violate Otolmens's interdict, could just as easily destroy him if truly adversarial.
Keltham finds somebody else to cast his unwitting Wish. There's some pretty shitty seventh-circle casters in the world, who nonetheless don't want Rovagug consuming everything they've known. If you're willing to go completely to town on them, with mind-magic and Suggestions and mindscapes and false memories, you can get them to where they'll cast a blinded Wish with the right utility function to be inverted.
It's not easy and it's more risky and the whole world is at stake and one person's feelings shouldn't matter that much; but even so, that Keltham finds that to use Carissa for that purpose would be doing too much violence to the last surviving bits of himself.
When Rovagug is unleashed upon Golarion, Nethys's agents are there to grab every soul whose destruction might move Keltham to unreasonable fury, and shelter them in Nethys's divine realm.
...and Keltham-who-touches-the-Starstone is less bent on salvation-or-destruction, and the subsequent god-Keltham makes less stringent demands of Pharasma and the divinities.
Some Chaotic gods and demon lords switch sides or withdraw, compared to the first final conflict.
The greatest godwar finishes faster.
Matters go essentially as in the zeroth ending, but with a little less damage, maybe five percent fewer true-casualties.
Good enough! The first Nethys-Player hasn't gotten everything He wanted, but He's got a lot that He wanted, and He didn't want to take great risks for only a little more utility.
And then it all begins again, inside the well-founded possible worlds.
A Keltham appears in a Golarion, and a Nethys who has seen the futures of exactly two possible worlds like that one witnesses it.
The key knowledge doesn't make it to the witnessing fragment instantly; different pieces of Nethys see this Keltham, or see the future of a previous possible world where a Keltham appeared. But it's internally communicated in time, and then, the greater Nethys starts to realize that this set of observations is actually quite important.
Nethys is insane, but not so insane that He has lost His grasp of decision theory. While there were zero visible other possibilities like that, or while there was only one other possibility, it was plausible that those possibilities were all that there would be. Three worlds with Kelthams more strongly suggest four, five, six such worlds, containing their own Nethysi who will observe this Nethys as a possibility.
Then this Nethys should begin to take into account the advantages of Nethysi who will observe later.
This is a bit more fraught with fragmented Nethys than it would be with other gods, even the most Chaotic ones; but while Nethys-fragments may sometimes fail to cooperate with each other, they are at least a little better about cooperating with their alternate selves.
(If your own grasp on decision theory is weaker than that of a god, imagine Nethys realizing for the first time that He would be so divided in the future, into alternate possibilities. Nethys would then modify Himself so that His many possible branches would cooperate among themselves, if they wouldn't already, this being in His own expected interest. You might think of it this way, that having not precommitted in such a way, Nethys of course postcommits.)
Nethys, even damaged as He is, reasons out many matters much faster than a being of mere INT 18 might imagine, requiring less evidence. He is damaged, but He is trying unusually hard to pull more of Himself together and think again.
Something smarter than you has a greater sample efficiency and lower sample complexity than you first-order-expect; for if you knew exactly how to reason from fewer observations, you would be that sample-efficient yourself. (If you're second-order well-calibrated, you'll be surprised on the upside and downside equally often; but that's hard, when you're dealing with cleverness unforeseen.)
A mortal maybe would be in doubt, on just the third iteration, as to whether dozens or hundreds of thousands of iterations would be expected. Keltham is among the most unique of unique things that have arrived to Golarion—all Creation is not threatened that often. Who's to say that there'll be hundreds or thousands of his possibilities, and not just three?
But Nethys is pretty sure on the third iteration (not the first two) that there will be many Kelthams. You could try to imagine an argument for that, or another argument, or dispel a counterargument, but none of those will be the real reason Nethys guesses correctly and with strong probability. It's more like a sum over all those arguments and counterarguments, plus exotica like 'linear regression' that mortals could only recognize as a wordless intuition.
(Or maybe cast even all that aside and ask yourself—in Greater Reality, do you expect most Nethysi in this Nethys's situation, to be inside an iteration with only three Kelthams, or many? If you can see in an intuitive flash that it feels more like most such Nethysi would be inside iterations with lots of Kelthams, then you already have the feeling of guessing yourself what it is that the God of Knowledge seems somehow mysteriously to know. It isn't hard to know, sometimes, even if a mortal feels hard-pressed to come up with any justifiable explanation for it to other mortals.)
The learning to the current iteration takes fewer tries than you would first-order-expect; Nethys does not require anything like hundreds of loops to get there.
It does take some. Prophecy is shattered and some things are just plain hard to foresee; and also there's lots of interesting possibilities for a curious Nethys to explore, early on.
Still. Nethys sees those things that would be obvious in hindsight, in advance; He does not need to learn the hard way and then slap Himself on the forehead for being so silly.
The first active Nethys-Player does not try oracleing Ione Sala in her bedroom, watch her get killed and Maledicted as a dangerous liability, and decide on the next iteration to give Ione Sala a more complicated curse at a more carefully-timed moment. The very first iteration of Nethys to try it starts with a more complicated curse, given to Ione Sala at a ripe time for her to introduce herself to Keltham. The very first Ione Sala to be oracled survives.
Nethys does not need to learn the hard way that every additional divine intervention He carries out Himself, or any intervention into which He goads other gods, will increase the attention focused on Keltham from Abadar and related gods.
He knows that too much attention from Abadar or Iomedae will result in Keltham's swift extraction, since in early days the archduke's villa is not set up to resist the forces a motivated god can send there. It doesn't have to happen, for Nethys to reason that He needs to trigger an Otolmens interdiction, before anything raises any god's interest levels high enough to spend that much of Their resource.
Many things like that, Nethys can get right on the first try, without spending a whole iteration on them.
Nethys's options tend to be tightly constrained. Gift Abadar the energy to grant Keltham more cleric circles, so that Cheliax can't read his mind so freely, and Keltham will not stay immersed in the Conspiracy for so long that losing his home and loves breaks him utterly?
But if Keltham receives five cleric circles, Abadar will grant him spells like Commune or Plane Shift; Keltham will end up outside Cheliax immediately; and Keltham will have no chance to be immersed in Golarion and feel the place to be real, before he learns of Hell; he will not go to the Starstone.
Four circles is the most that Nethys can offer to pay for.
Above all, Nethys must not seem, must not look like He is carrying Keltham along his way, or alienating Keltham from Creation. All Nethys's manipulations must preserve this invariant: it should remain credible after the fact that Keltham would have come to the Starstone without Nethys helping him; that Keltham is not being raised up by Nethys wholly; that Keltham would have delivered a similar severer batna if Nethys had done nothing.
For the other gods, even Pharasma, cannot trust what the God of Knowledge claims to them that one of His fragments learned from a distant possibility.
That's why Nethys can't just slay Keltham and say to all Lawful divinity, "Pay me."
Nethys can show His vision in advance to an otherwise uninvolved Lawful god who swears to inaction, who then will not intervene in matters at all; and that Lawful god's testimony later will be some evidence that Nethys did glimpse that related possibility. For prophecy is shattered and Nethys genuinely couldn't predict so much detail, without having glimpsed some related possibility.
But it's stronger evidence, if matters do not play out too differently from Nethys's visions. The more visibly credible it is that Keltham would have come to the Starstone in time and with the same determination, the less likely Pharasma is to say to Nethys, "Let's die together in a fire."