The Kursk "Special Operation" is designed to draw troops from the Donbas and create a dilemma for Ruzzia: either they loose Kursk or they divert troops from the east. In any of those cases the consequences can be of strategic level.
So, is it possible that Ukraine would withdraw? Yes, who knows when. Are they going to leave on their own as gesture of good will Nah.
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UA doesn't have enough troops to take Kursk, and their supply lines are already stretched as is. Regardless, this confirms my statement, this mission it to put political pressure on Putin to pull troops from the east. It'd be interesting to later read who's idea was it to think that Russia could be pressured with reputational damage, to put it mildly that's not really a thing Russians are really known for. So far looks like UA just opened a new front for themselves where RU can use their conscript force, while continuing to loose in Donbas. The game is what happens first, either Putin succumbs to pressure within, or UA looses their military potential. We shall find out soon enough.
Remember at the start how Russia went deep within Ukraine, all the way up to Kiev in fact, 'uncontested'. They went in that deep without anywhere near the force structure to actually fight and hold. Ukraine/NATO was actually prepped and capable of fighting since they planned to 'do' the break-away provinces and had been setting up for it for years. The reason they did nothing was that it was a trap. Russia was, as I predicted at the time, to smart to fall for it.
I suspect that the Kursk thing is also a trap. Over and over since the SMO Ukraine has mostly been fighting a 'social media' war since they are increasingly unable to accomplish anything of substance on the battlefield. For several reasons they will jump at anything where they can achieve enough of a PR victory to impress the retard classes they will go all in even knowing that total failure and huge losses are the inevitable outcome. Krinky was a good example. The losses can get and do get effectively papered over with Western mainstream media PR.
I think that Russia sees this 'UA/NATO-can-be-baited' phenomenon fairly clearly and sets Ukraine up with fake 'wins' just to bait them in. Since an increasing fraction of the UA conscripts are just waiting for their chance to surrender to the Russians, the Kursk operation would necessarily require participation of the more solid and motivated troops and they are becoming increasingly rare. Would Russia accept the plunder of the Kursk region just for the opportunity to entrap the remaining solid troops? I don't know. It would be a very shrewd and effective move if they made that decision. For my part I'll wait and see, but will be evaluating to support of detract from this hypothesis.
Again, as I have hypothesized here countless times, the loss of territory and Slavic population stock from the Ukraine region is not a bug for the Zelenski and the people running him; it's a feature. Very possibly the deal for what Russia would get out of their efforts and playing their part was planned and agreed upon ahead of time, and they probably got a pretty good deal.
Theories apart, you cannot win to a big Soviet army with a smaller Soviet army playing the Soviet style of war. You need to use what makes you different from your enemy, namely more speed, better intelligence and make the war as asymmetric as possible. That is the Kursk offensive. Regardeless of Ukraine holding the whole territory or not, they are certainly holding the PoW and certainly creating a reputational problem for Putin and the Ruzzian army.
If you think of it, Ruzzia wants territory XYZ in Ukraine, their troops are there, their allocation of air power is there and the trench system is massively overconstructed in the east and the South. Now, why would it be better to have a chunk of Donbas or a chunk or Kursk and Belgorod?
It is practically the same, if you ask me probably Kursk is less destroyed. So, why not? Just capture as much Kursk as you can and later you can choose to trade it... or not.