Just like how you can reduce everything to a Turing Machine basis, or a physics basis.

I talk to plenty of mathematicians and we all agree that there is a basic notion of projection, and there are different ways you can project onto a subspace of the problem to preserve some relevant structure you want. Common memes include linear independence, maybe preserving group symmetries, state machines, etc. As just one basic operation in the toolkit of trying to formalize what "knowledge" is.

That is distinctly not "Bayes Theorem".

I was giving a positive account of the tools that mathematicians have come up with in order to deal with mere "true/false" dichotomies, but a negative account of coherency.

If you think the notion of knowledge is merely Bayesianism, fine. Even lesswrong (one of the most prominent spaces that loves to larp Bayesianism), rightfully, tries to incorporate larger notions of knowledge into their frameworks, but sure. Let's not forget that interventionalism is a different framework built to address the shortcomings of Bayesianism - but many people mix them up and just think "Ah, something must be probabalistic and update weights! Must be Bayesian!" without rigorously thinking through their framework, bordering on unfalsifiability with how quickly the boundaries change on their mental models. And that's not even accounting for how mathematical structure itself arises, which is completely outside of the domain of Bayesianism, except in a vacuous post-hoc sense.

And this is exactly what I meant by the previous comment. Mathematicians can give many local accounts for things, but I do not think there has been a coherent account of all of these patchwork theories and analogies yet.

It does seem the strongest thing we have to address the distributed knowledge problem is LLM's - but it's not Bayesianism you reduce to, it's linear algebra. And even then, that's more of just generalizing intelligence, not necessarily coming up with the structure that OP (or knowledge workers) want. Maybe you want to create 1 centralized AGI such that it will "never lie", whatever that means?

Again, if you think the notion of knowledege is purely Bayesian, then go ahead, go implement what the OP requested through "mere Bayesianism", whatever that means. I'd be hard-pressed to find a person actually living that kind of life, authentically "Bayesian", and not reasoning through a ton of heuristical context shifts like I've described.

Again, of course, you can reduce everything to a Bayesian context vacuously, just like how I can reduce things to Turing machines or a physical basis - that doesn't explain the higher level phenomena in an actionable way for humans to talk about - as I assume you want to talk about this.