How Often Do Humans Legitimately Win?

[Vitto]

That said - what makes you think that humans possess 'distinct intelligence' as transapients intend it?

Is quite difficult, as per setting's rules, compare their "intelligence" or "operative system", call them as you want, but I think that is quite simple to agree that both share traits that an animals maybe barely shows, like planning, creating objects or imporving themselfs.
My disagree was more on the human-bear side.
As usual I should think twice and explain myself more, sorry!  

And that's only for an S1. By the time you get to S3 (where you kind of topped out here) you have a brain that outmasses the entire Biosphere of the Earth and a mind that can model every human being on Earth (meaning it could effectively run our entire civilization) 'single handedly' with only a tiny fraction of its attention. Are you really going to argue that such a being is really just a human being with super powers?

I always think on those situation as conflict among opponents that have no more than one S level between them. And that already is quite overwhelming.

This is kind of like saying that a single human armed with a sling can defeat the United States in a war because technically the sling could kill a single soldier.

While a lot of SF is hugely enamored of reducing conflict down to a simplistic punching match of guns against armor or 'shields' (which conveniently decrease in strength as the plot requires it), actual warfare is much more involved. And is going to be vastly more involved when transapients are involved, especially S3.

Put another way - that 'hyper-awareness' means that the S3 is going to know what the humans are up to long before they can martial the resources to threat it's physical structure in any way. And there are any number of things it can (and will) do before they have launched so much as a single ship. Think Batman levels of crazy prepared multiplied by quadrillions. The would be attackers could suddenly have their nanoimmune systems malfunction and kill them all. Or turn off their eyes. Or Rewrite their minds such that they all become willing slaves of the transapient. Or all turn on each other and wipe themselves out. Or their weapons could all turn on them. Or their culture could undergo some number of changes that result in them no longer having any desire to attack the transapient.

Even if the humans manage to launch their weapons - the S3 can field vastly more energy than they can. It can shoot down their weapons - likely before they've done more than barely launch. Or detonate the local star and habs. Or detect the weapons via gravity wave interferometers and use conversion powered lasers to destroy them. Note also that hitting even a planet size object is extremely hard at near c due to Lorentz contraction and related issues. But most likely the S3 would stop the attack before it ever started. So it would still win. And the inherent inferiority of mere humans (sacks of dirty water with an overinflated sense of their own value) would be proven once again . 

More editorially, any such conflict would fall under our intertoposophic conflict guidelines - LINK

Again, my  bad way to express myself: there is no way a modos civilization could beat a Moon Brain, I never intended to insinuate that.
Still, on a single S level gap there could be an opportunity: the amount of antimatter needed to crak open a Moon Brain would be quite a lot, but probably any S1 can put its manipulator on the right amount to blow the home of any S2, if its target is not very widely dispersed among habitats, orbitals or the entire crust of a planet.

Link to the article/story in question,please?

Per our current Canon this is basically impossible and the article likely needs to be modified.

The God Web Itself!
"The Version War Period" paragraph. It doesn't describe the S level of the attackers but from the fact they were a whole clade I doubt  they were more than S2 and, anyway, we are talking about a wormhole for archai use during the Version War, so at least S4, if not directly S5.
Pretty nasty way to leave this valley of tears...

See above, both in general and re intertoposophic conflict. The odds of this ever happening are astronomically low.

Yup! I noted that a long ago. The only two example made that I know are a mad wandering S1 and an S2 during the Version War that got bold and was ambushed my weapons hidden in a moon (still survived).