There needs to be some process which, given a context, specifies what value shards should be created (or removed/edited) to better work in that context. Not clear we can't think of this as constituting the system's immutable goal in some sense, especially as it gets more powerful. That said it would probably not be strongly coherent by your semi-formal definition.

I think you are onto something, with the implication that building a highly intelligent, learning entity with strong coherence in this sense is unlikely, and hence, getting it morally aligned in this fashion is also unlikely. Which isn't that bad, insofar as plans for aligning it that way honestly did not look particularly promising.

Which is why I have been advocating for instead learning from how we teach morals to existing complex intelligent agents - namely, through ethical, rewarding interactions in a controlled environment slowly allowing more freedom. 

We know how to do this, it does not require us to somehow define the core of ethics mathematically. We know it works. We know how setbacks look, and how to tackle them. We know how to do this with human interactions the average person can do/train, rather than with code. It seems easier and more doable and promising in so many ways. 

That doesn't mean it will be easy, or risk free, and it still comes with a hell of a lot of problems based on the fact that AIs, even machine learning ones, are quite simply not human, they are not inherently social, they do not inherently have altruistic urges, they do not inherently have empathic abilities. But I see a clearer path to dealing with that than to directly encoding an abstract ethics into an intelligent, flexible actor.

EDIT: I found out my answer is quite similar to this other one you probably read already.

I think not.

Imagine such a malleable agent's mind as made of parts. Each part of the mind does something. There's some arrangement of the things each part does, and how many parts do each kind of thing. We won't ask right now where this organization comes from, but take it for given.

Imagine that---be it by chance or design---some parts were cooperating, while some were not. "Cooperation" means making actions that bring about a consequence in a somewhat stable way, so something towards being coherent and consequentialist, although not perfectly so by any measure. The other parts would oftentimes work at cross purposes, treading on each other toes. "Working at cross purposes", again, in other words means not being consequentialist and coherent; from the point of view of the parts, there may not even be a notion of "cross purposes" if there is no purpose.

By the nature of coherence, the ensemble of coherent and aligned parts would get to their purpose much more efficiently than the other parts are not-getting to that purpose and being a hindrance, assuming the purpose was reachable enough. This means that coherent agents are not just reflectively consistent, but also stable: once there's some seed of coherence, it can win other the non-coherent parts.

Conclusion 1: Intelligent systems in the real world do not converge towards strong coherence

It seems to me that humans are more coherent and consequentialist than other animals. Humans are not perfectly coherent, but the direction is towards more coherence. Actually, I'd expect that any sufficiently sophisticated bounded agent would not introspectively look coherent to itself if it spent enough time to think about it. Would the trend break after us?

Would you take a pill that would make you an expected utility maximiser?

Would you take a pill that made you a bit less coherent? Would you take a pill that made you a bit more coherent? (Not rhetorical questions.)

(A somewhat theologically inspired answer:)

Outside the dichotomy of values (in the shard-theory sense) vs. immutable goals, we could also talk about valuing something that is in some sense fixed, but "too big" to fit inside your mind. Maybe a very abstract thing. So your understanding of it is always partial, though you can keep learning more and more about it (and you might shift around, feeling out different parts of the elephant). And your acted-on values would appear mutable, but there would actually be a, perhaps non-obvious, coherence to them.

It's possible this is already sort of a consequence of shard theory? In the way learned values would have coherences to accord with (perhaps very abstract or complex) invariant structure in the environment?