As policy within the Orion's Arm Universe Project we do not see sophonts of a lower toposophic level engaging in deliberate acts of conflict with sophonts of a higher toposophic level and emerging victorious. Despite this it is logical to assume that occasionally, under nearly miraculous circumstances, it may happen that a lower toposophic being, or group, will be able to capture, harm or even kill an entity of a higher toposophic level.
We do not dismiss the possibility of such victories, but realistically given the disparity in power between higher and lower toposophic beings the odds of successes are vanishingly small. If such a thing does happen, it almost certainly involves a combination of extraordinary factors. Such factors might include, but are not limited to, an alliance of myriad lower toposophic factions, a mistake or series of mistakes by the higher toposophic entity in question, an event in the surrounding environment insufficiently understood or predicted by the higher toposophic entity, or near-parity of the toposophic levels between the combatants. The fewer such factors in play, the less likely it is for the lower toposophic being to succeed, and the odds are almost nil even under the best of cases.
Conflict is a major part of drama. Stories about characters struggling against or finding their places in a universe ruled by the Archai are likely to be among the most common stories that will be written in the OA universe. Characters that struggle in vain against fate or its transapient equivalent, characters who fail to realize that they are acting as tools of unseen forces, and characters that are given gifts of power and achieve great things for themselves or for their benefactors can all be excellent resources for examining the human (or post-human or near-human) condition. Tragedy, catharsis, and even comedy were used by the Greeks and others in their stories about the relations between gods and men, and the concept of hubris was a frequent element; all of this is open to a contributor within the Orion's Arm scenario.
Although intertoposophic conflict will occur, it should be noted that the Orion's Arm Universe Project is not specifically looking for content of this nature. We are not interested in munchkinism or following clichéd sci-fi tropes. We are not interested in, or capable of, addressing each and every edge case that one might conceive. Our purpose and intent is to comprehend life in the setting, and to deal with what is ordinary for modosophonts up through the year 10,600 a.t. That alone is quite a challenge for now, but if the proposed material is of exceptional quality, fits within the intent of the project, and serves to examine life in the setting we are willing to be convinced. Any such material must fully take into account the abilities of the higher toposophic in question; this includes not only their technology but also their vastly superior intellect and diverse range of philosophies, not to mention thousands of years of cultural development by the transapients' equivalent of a culture. Here is a partial list of examples for consideration:
Higher toposophic entities will deal with those of a lower toposophic as their individual philosophies dictate. This may be to either the benefit or the harm of the lower entity, and the distinction between the two may or may not be apparent to those of a lower toposophic. It is more common than not for a higher toposophic entity to achieve its goals through indirect means, although efficiency and a process of reasoning unknowable to the lower toposophic entities involved may influence these actions.
It is often in the best interest of high toposophics beings to have lower toposophics beings believe, fervently, in the notion that they can't win a fight with them. Higher toposophic individuals and groups may act accordingly as they interact with the societies they are in, seeking to reinforce such beliefs.
Some modosophont individuals, groups, or civilizations take a very dim view of those members of their culture who abuse or unnecessarily kill lower toposophic life forms, sometimes to the point of intervening to prevent such killing or abuse or even to reverse its effects as best as they are able. There is no reason to think that transapient individuals, groups, or civilizations will be any less compassionate.
Modosophont civilizations generally will not tolerate the continued existence of any lower toposophic life form that has killed, harmed, or even just seriously inconvenienced one of their members, assuming they have the means to kill it. There is no reason to think that transapient civilizations will be any more forgiving.
It is important to note that civilization is a major factor in all interactions. By definition, transapient beings in the setting are members of or the products of a civilization that is thousands of years old. It might be argued by analogy that they might be harmed or inconvenienced by ordinary sophonts in the same way that humans might be vulnerable to some predators, pests, parasites, and diseases. While that might be true in abstract, the best comparison would be not with Paleolithic or Agricultural Age humans, or even with present-day humans, but with the humans of the OA setting. Armed with tens of thousands of years of accumulated knowledge and self-improvement, they can safely ignore hazards such as sharks or smallpox that would have laid low even the brightest human of the past. Likewise the very first individuals to achieve a higher toposophic level might have been vulnerable to lesser beings just as primitive humans once were to other life forms, but that is ancient history in the OA setting.
By definition it is impossible to out-think or out-perform, on its terms, an individual or group at least one toposophic level above oneself, all other things being equal. If the protagonist wins due to an obvious intellectual failing of the higher toposophic, the logic is faulty. While they are not all-knowing, the separation of intellectual capabilities from one level to another is extreme. If, as an author or reader, you could think of the action as a point of failure, you can be sure the higher toposophic antagonist can as well - and will act accordingly. They will not leave the keys to the cell in easy reach of their prisoners for example - unless they intended for them to escape.
By definition it is impossible to in any way comprehend or reverse engineer technology of more than one toposophic level above oneself. These technologies do not exist at the lower toposophic levels because they require the cognitive abilities of the higher toposophic level in question to create or understand them.
It is generally impossible to correctly operate technology - especially weapons - designed for sophonts of at least one toposophic level above oneself. This is really an extension of the point above. You might be able to operate an S4 paperweight, but not an S4 weylforge.
At a toposophic differential of two or more levels the higher toposophic can effortlessly model the mind and intellect of the lower toposophic. This means that the lower toposophic individual or group is unlikely to do anything that might surprise or confound the higher toposophic(s) involved in the conflict.
The greater intellectual capacities of post-singularity sophonts will allow them to avoid, or manipulate, most situations in which such conflicts could occur. A human being can, with foresight, avoid a hornet's nest and then come back later better prepared to deal with it. Higher toposophic entities will be able to avoid unpleasant situations involving lower toposophic beings until they are ready to deal with them even more easily.
If brought to conflict, by mistake, misfortune, or an extraordinary sequence of events, higher toposophic beings will have at their disposal resources - both intellectual and material - that the lower toposophic beings will not. Even without being "armed to the teeth", this set of advantages will generally allow the higher toposophic entity a decisive victory in such conflict. Such victory need not involve the destruction of the opponent. Effortless escape, memory-editing of the attacker, and other non-lethal victories are also possibilities, and may be more attractive ones to the higher toposophic defender.
An individual, population or society of lower toposophics may, or may not, be able to overcome an individual of higher toposophic level if the latter is weakened, unprepared, or somehow lacks the knowledge or means to defend itself from the former. One example of this might be a dedicated non-combatant hyperturing lacking the capability to defend against a lower toposophic armada. This scenario is a dangerous one for the lower toposophic assailants as such a dedicated hyperturing is likely in the service of a society of its peers, or of an even higher toposophic. There are of course other logical scenarios.
Lower toposophic beings, or alliance of same, that win in a conflict an individual or group of a higher toposophic can almost never be sure that they have won. Did the higher-S sophont provoke a fight in order to further some inscrutable plan? Did they actually defeat the being, or merely defeat an eidolon, a false avatar? The lower toposophics involved should question their role in the victory. Were they pawns of another higher toposophic? Does their entire race exist at the whim of yet a third high toposophic being, who carefully prepared them to strike at a competitor's vulnerability? If that is the case, the victors were no more victorious than a scalpel is victorious over a tumour - and possibly just as disposable.
In many instances of potential or actual intertoposophic conflict both sides will be fully sophont beings and will be fully aware of some or all of the factors described here. This awareness will influence their actions and potential actions accordingly.